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Tan Math notes
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| <li><a href="#丹丹的數學筆記">丹丹的數學筆記</a> | |
| <ul> | |
| <li><a href="#地圖比例尺">地圖/比例尺</a></li> | |
| <li><a href="#xx率利息">xx率/利息</a></li> | |
| <li><a href="#數據題">數據題</a></li> | |
| <li><a href="#三角函數">三角函數</a></li> | |
| <li><a href="#相似嘅圖形／立體">相似嘅圖形／立體</a></li> | |
| <li><a href="#平面公式">平面公式</a></li> | |
| <li><a href="#立體公式">立體公式</a></li> | |
| <li><a href="#對稱">對稱</a></li> | |
| <li><a href="#因式分解">因式分解</a></li> | |
| <li><a href="#調換主項">調換主項</a></li> | |
| <li><a href="#解方程">解方程</a></li> | |
| <li><a href="#機率">機率</a></li> | |
| <li><a href="#座標">座標</a></li> | |
| <li><a href="#mc-calc-機大法">MC calc 機大法</a></li> | |
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| <h1 id="丹丹的數學筆記">丹丹的數學筆記</h1> | |
| <h2 id="地圖比例尺">地圖/比例尺</h2> | |
| <h3 id="解釋">解釋</h3> | |
| <p>比例尺例子：1:10000 （比例）<br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>1</mn><mtext>m</mtext><mo>=</mo><mn>1</mn><mn>0</mn><mn>0</mn><mtext>cm</mtext><mo>=</mo><mn>1</mn><mn>0</mn><mn>0</mn><mn>0</mn><mtext>mm</mtext></mrow><annotation encoding="application/x-tex">1\text m=100 \text {cm}=1000 \text{mm}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.64444em;"></span><span class="strut bottom" style="height: 0.64444em; vertical-align: 0em;"></span><span class="base"><span class="mord mathrm">1</span><span class="mord text"><span class="mord mathrm">m</span></span><span class="mrel">=</span><span class="mord mathrm">1</span><span class="mord mathrm">0</span><span class="mord mathrm">0</span><span class="mord text"><span class="mord mathrm">cm</span></span><span class="mrel">=</span><span class="mord mathrm">1</span><span class="mord mathrm">0</span><span class="mord mathrm">0</span><span class="mord mathrm">0</span><span class="mord text"><span class="mord mathrm">mm</span></span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>(</mo><mi>m</mi><mo>)</mo><mo>×</mo><mn>1</mn><mn>0</mn><mn>0</mn><mo>=</mo><mo>(</mo><mi>c</mi><mi>m</mi><mo>)</mo></mrow><annotation encoding="application/x-tex">(m)\times 100 = (cm)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.75em;"></span><span class="strut bottom" style="height: 1em; vertical-align: -0.25em;"></span><span class="base"><span class="mopen">(</span><span class="mord mathit">m</span><span class="mclose">)</span><span class="mbin">×</span><span class="mord mathrm">1</span><span class="mord mathrm">0</span><span class="mord mathrm">0</span><span class="mrel">=</span><span class="mopen">(</span><span class="mord mathit">c</span><span class="mord mathit">m</span><span class="mclose">)</span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>(</mo><mi>c</mi><mi>m</mi><mo>)</mo><mo>÷</mo><mn>1</mn><mn>0</mn><mn>0</mn><mo>=</mo><mo>(</mo><mi>m</mi><mo>)</mo></mrow><annotation encoding="application/x-tex">(cm)\div 100 = (m)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.75em;"></span><span class="strut bottom" style="height: 1em; vertical-align: -0.25em;"></span><span class="base"><span class="mopen">(</span><span class="mord mathit">c</span><span class="mord mathit">m</span><span class="mclose">)</span><span class="mbin">÷</span><span class="mord mathrm">1</span><span class="mord mathrm">0</span><span class="mord mathrm">0</span><span class="mrel">=</span><span class="mopen">(</span><span class="mord mathit">m</span><span class="mclose">)</span></span></span></span></span><br> | |
| 實際<span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>→</mo></mrow><annotation encoding="application/x-tex">\rightarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.36687em;"></span><span class="strut bottom" style="height: 0.36687em; vertical-align: 0em;"></span><span class="base"><span class="mrel">→</span></span></span></span></span>地圖：地面距離<span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>→</mo></mrow><annotation encoding="application/x-tex">\rightarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.36687em;"></span><span class="strut bottom" style="height: 0.36687em; vertical-align: 0em;"></span><span class="base"><span class="mrel">→</span></span></span></span></span>變答案單位(x100? m->cm)<span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>→</mo></mrow><annotation encoding="application/x-tex">\rightarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.36687em;"></span><span class="strut bottom" style="height: 0.36687em; vertical-align: 0em;"></span><span class="base"><span class="mrel">→</span></span></span></span></span> <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>÷</mo></mrow><annotation encoding="application/x-tex">\div</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.58333em;"></span><span class="strut bottom" style="height: 0.66666em; vertical-align: -0.08333em;"></span><span class="base"><span class="mord">÷</span></span></span></span></span>比例<br> | |
| 地圖<span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>→</mo></mrow><annotation encoding="application/x-tex">\rightarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.36687em;"></span><span class="strut bottom" style="height: 0.36687em; vertical-align: 0em;"></span><span class="base"><span class="mrel">→</span></span></span></span></span>實際：實際距離<span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>→</mo></mrow><annotation encoding="application/x-tex">\rightarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.36687em;"></span><span class="strut bottom" style="height: 0.36687em; vertical-align: 0em;"></span><span class="base"><span class="mrel">→</span></span></span></span></span>變答案單位(<span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>÷</mo></mrow><annotation encoding="application/x-tex">\div</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.58333em;"></span><span class="strut bottom" style="height: 0.66666em; vertical-align: -0.08333em;"></span><span class="base"><span class="mord">÷</span></span></span></span></span> 100? cm->m)<span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>→</mo></mrow><annotation encoding="application/x-tex">\rightarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.36687em;"></span><span class="strut bottom" style="height: 0.36687em; vertical-align: 0em;"></span><span class="base"><span class="mrel">→</span></span></span></span></span> <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>×</mo></mrow><annotation encoding="application/x-tex">\times</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.58333em;"></span><span class="strut bottom" style="height: 0.66666em; vertical-align: -0.08333em;"></span><span class="base"><span class="mord">×</span></span></span></span></span>比例</p> | |
| <h3 id="習題">習題</h3> | |
| <ol> | |
| <li>比例 1:1000 地面300m 地圖距離cm？</li> | |
| <li>比例 1:10000 地圖3cm 地面距離m？</li> | |
| </ol> | |
| <h3 id="試前練習">試前練習</h3> | |
| <ol> | |
| <li>比例 1:10000 地面 400m 地圖距離cm？</li> | |
| <li>比例 1:1000 地圖 5cm 地面距離m？</li> | |
| </ol> | |
| <h2 id="xx率利息">xx率/利息</h2> | |
| <h3 id="解釋-1">解釋</h3> | |
| <p><strong>只適用於冇話每月/每季計 (初中應該無呢啲)</strong><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>n 年後／現在價值</mtext><mo>=</mo><mtext>舊值 (n 年前)</mtext><mo>×</mo><mo>(</mo><mn>1</mn><mo>±</mo><mtext>年率</mtext><msup><mo>)</mo><mi>n</mi></msup></mrow><annotation encoding="application/x-tex">\text{n 年後／現在價值}=\text{舊值 (n 年前)} \times (1 \pm \text{年率})^n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.75em;"></span><span class="strut bottom" style="height: 1em; vertical-align: -0.25em;"></span><span class="base"><span class="mord text"><span class="mord mathrm">n </span><span class="mord mathrm cjk_fallback">年後／現在價值</span></span><span class="mrel">=</span><span class="mord text"><span class="mord mathrm cjk_fallback">舊值</span><span class="mord mathrm"> (n </span><span class="mord mathrm cjk_fallback">年前</span><span class="mord mathrm">)</span></span><span class="mbin">×</span><span class="mopen">(</span><span class="mord mathrm">1</span><span class="mbin">±</span><span class="mord text"><span class="mord mathrm cjk_fallback">年率</span></span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.664392em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathit mtight">n</span></span></span></span></span></span></span></span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.58333em;"></span><span class="strut bottom" style="height: 0.66666em; vertical-align: -0.08333em;"></span><span class="base"><span class="mord">+</span></span></span></span></span> 定 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.58333em;"></span><span class="strut bottom" style="height: 0.66666em; vertical-align: -0.08333em;"></span><span class="base"><span class="mord">−</span></span></span></span></span> 要睇係咩率 中文5** 應該睇得明架 😘<br> | |
| 適當使用方程</p> | |
| <h3 id="習題-1">習題</h3> | |
| <ol> | |
| <li>存款5000 年利率1% 10年之後有幾多</li> | |
| <li>而家值1000 折舊率每年10% 三年前值幾多錢？</li> | |
| </ol> | |
| <h3 id="試前練習-1">試前練習</h3> | |
| <ol> | |
| <li>存款 2000 年利率2% 5年之後有幾多</li> | |
| <li>而家值1500 折舊率每年5% 五年前值幾多錢？</li> | |
| </ol> | |
| <h2 id="數據題">數據題</h2> | |
| <h3 id="解釋-2">解釋</h3> | |
| <p>假設 total 有 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.43056em;"></span><span class="strut bottom" style="height: 0.43056em; vertical-align: 0em;"></span><span class="base"><span class="mord mathit">n</span></span></span></span></span> 咁多個數據／數字</p> | |
| <h4 id="一堆數字">一堆數字</h4> | |
| <p>平均值：所有數加埋 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>÷</mo><mi>n</mi></mrow><annotation encoding="application/x-tex">\div n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.58333em;"></span><span class="strut bottom" style="height: 0.66666em; vertical-align: -0.08333em;"></span><span class="base"><span class="mord">÷</span><span class="mord mathit">n</span></span></span></span></span><br> | |
| 中位數：將所有數由小至大排好，然後如果 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.43056em;"></span><span class="strut bottom" style="height: 0.43056em; vertical-align: 0em;"></span><span class="base"><span class="mord mathit">n</span></span></span></span></span> 係雙數，就攞 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>(</mo><mtext>第 n 個數</mtext><mo>+</mo><mtext>第 n+1 個數</mtext><mo>)</mo><mo>÷</mo><mn>2</mn></mrow><annotation encoding="application/x-tex">(\text{第 n 個數}+\text{第 n+1 個數})\div 2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.75em;"></span><span class="strut bottom" style="height: 1em; vertical-align: -0.25em;"></span><span class="base"><span class="mopen">(</span><span class="mord text"><span class="mord mathrm cjk_fallback">第</span><span class="mord mathrm"> n </span><span class="mord mathrm cjk_fallback">個數</span></span><span class="mbin">+</span><span class="mord text"><span class="mord mathrm cjk_fallback">第</span><span class="mord mathrm"> n+1 </span><span class="mord mathrm cjk_fallback">個數</span></span><span class="mclose">)</span><span class="mbin">÷</span><span class="mord mathrm">2</span></span></span></span></span>，如果 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.43056em;"></span><span class="strut bottom" style="height: 0.43056em; vertical-align: 0em;"></span><span class="base"><span class="mord mathit">n</span></span></span></span></span> 係單數，就攞 第<span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>(</mo><mfrac><mi>n</mi><mn>2</mn></mfrac><mo>+</mo><mn>0</mn><mi mathvariant="normal">.</mi><mn>5</mn><mo>)</mo></mrow><annotation encoding="application/x-tex">(\frac n 2 + 0.5)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.75em;"></span><span class="strut bottom" style="height: 1.095em; vertical-align: -0.345em;"></span><span class="base"><span class="mopen">(</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.695392em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathit mtight">n</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.345em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mbin">+</span><span class="mord mathrm">0</span><span class="mord mathrm">.</span><span class="mord mathrm">5</span><span class="mclose">)</span></span></span></span></span> 個數<br> | |
| 模式：睇下邊個數最多個</p> | |
| <h4 id="棒形圖／折線圖／數字（項目）加頻數嘅表">棒形圖／折線圖／數字（項目）加頻數嘅表</h4> | |
| <p><strong>無論係咩圖都好，首先整番個 數字加頻數嘅表 先，要中位數嘅話要mark埋累積頻數，好似甘</strong></p> | |
| <table> | |
| <thead> | |
| <tr> | |
| <th align="right">數字</th> | |
| <th align="right">1</th> | |
| <th align="right">2</th> | |
| <th align="right">3</th> | |
| <th align="right">4</th> | |
| <th align="right">5</th> | |
| <th align="right">6</th> | |
| </tr> | |
| </thead> | |
| <tbody> | |
| <tr> | |
| <td align="right">頻數</td> | |
| <td align="right">5</td> | |
| <td align="right">9</td> | |
| <td align="right">13</td> | |
| <td align="right">19</td> | |
| <td align="right">11</td> | |
| <td align="right">3</td> | |
| </tr> | |
| <tr> | |
| <td align="right">累積頻數</td> | |
| <td align="right">5</td> | |
| <td align="right">5+9=14</td> | |
| <td align="right">14+13=27</td> | |
| <td align="right">27+19=46</td> | |
| <td align="right">46+11=57</td> | |
| <td align="right">57+3=60</td> | |
| </tr> | |
| </tbody> | |
| </table><p>累積頻數=上一個累積頻數+呢度嘅頻數<br> | |
| 平均值：所有 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>(</mo><mtext>數字</mtext><mo>×</mo><mtext>頻數</mtext><mo>)</mo></mrow><annotation encoding="application/x-tex">(\text{數字}\times \text{頻數})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.75em;"></span><span class="strut bottom" style="height: 1em; vertical-align: -0.25em;"></span><span class="base"><span class="mopen">(</span><span class="mord text"><span class="mord mathrm cjk_fallback">數字</span></span><span class="mbin">×</span><span class="mord text"><span class="mord mathrm cjk_fallback">頻數</span></span><span class="mclose">)</span></span></span></span></span> 加埋 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>÷</mo></mrow><annotation encoding="application/x-tex">\div</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.58333em;"></span><span class="strut bottom" style="height: 0.66666em; vertical-align: -0.08333em;"></span><span class="base"><span class="mord">÷</span></span></span></span></span> <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>頻數</mtext></mrow><annotation encoding="application/x-tex">\text{頻數}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.68333em;"></span><span class="strut bottom" style="height: 0.68333em; vertical-align: 0em;"></span><span class="base"><span class="mord text"><span class="mord mathrm cjk_fallback">頻數</span></span></span></span></span></span> 加埋<br> | |
| 中位數：然後如果 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.43056em;"></span><span class="strut bottom" style="height: 0.43056em; vertical-align: 0em;"></span><span class="base"><span class="mord mathit">n</span></span></span></span></span> 係雙數，就攞 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>(</mo><mtext>第</mtext><mfrac><mi>n</mi><mn>2</mn></mfrac><mtext>個數</mtext><mo>+</mo><mtext>第</mtext><mfrac><mi>n</mi><mn>2</mn></mfrac><mo>+</mo><mn>1</mn><mtext>個數</mtext><mo>)</mo><mo>÷</mo><mn>2</mn></mrow><annotation encoding="application/x-tex">(\text{第} \frac n 2 \text{個數}+\text{第} | |
| \frac n 2 +1 \text{個數})\div 2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.75em;"></span><span class="strut bottom" style="height: 1.095em; vertical-align: -0.345em;"></span><span class="base"><span class="mopen">(</span><span class="mord text"><span class="mord mathrm cjk_fallback">第</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.695392em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathit mtight">n</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.345em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord text"><span class="mord mathrm cjk_fallback">個數</span></span><span class="mbin">+</span><span class="mord text"><span class="mord mathrm cjk_fallback">第</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.695392em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathit mtight">n</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.345em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mbin">+</span><span class="mord mathrm">1</span><span class="mord text"><span class="mord mathrm cjk_fallback">個數</span></span><span class="mclose">)</span><span class="mbin">÷</span><span class="mord mathrm">2</span></span></span></span></span>，如果 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.43056em;"></span><span class="strut bottom" style="height: 0.43056em; vertical-align: 0em;"></span><span class="base"><span class="mord mathit">n</span></span></span></span></span> 係單數，就攞 第<span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>(</mo><mfrac><mi>n</mi><mn>2</mn></mfrac><mo>+</mo><mn>0</mn><mi mathvariant="normal">.</mi><mn>5</mn><mo>)</mo></mrow><annotation encoding="application/x-tex">(\frac n 2 + 0.5)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.75em;"></span><span class="strut bottom" style="height: 1.095em; vertical-align: -0.345em;"></span><span class="base"><span class="mopen">(</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.695392em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathit mtight">n</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.345em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mbin">+</span><span class="mord mathrm">0</span><span class="mord mathrm">.</span><span class="mord mathrm">5</span><span class="mclose">)</span></span></span></span></span> 個數。例如呢度第14個數就係2 果度（因為 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>5</mn><mo><</mo><mi>n</mi><mo>≤</mo><mn>1</mn><mn>4</mn></mrow><annotation encoding="application/x-tex">5\lt n\le 14</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.64444em;"></span><span class="strut bottom" style="height: 0.78041em; vertical-align: -0.13597em;"></span><span class="base"><span class="mord mathrm">5</span><span class="mrel"><</span><span class="mord mathit">n</span><span class="mrel">≤</span><span class="mord mathrm">1</span><span class="mord mathrm">4</span></span></span></span></span>），第15個數就係3果度（因為 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>1</mn><mn>4</mn><mo><</mo><mi>n</mi><mo>≤</mo><mn>2</mn><mn>7</mn></mrow><annotation encoding="application/x-tex">14\lt n\le 27</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.64444em;"></span><span class="strut bottom" style="height: 0.78041em; vertical-align: -0.13597em;"></span><span class="base"><span class="mord mathrm">1</span><span class="mord mathrm">4</span><span class="mrel"><</span><span class="mord mathit">n</span><span class="mrel">≤</span><span class="mord mathrm">2</span><span class="mord mathrm">7</span></span></span></span></span>）<br> | |
| 模式：頻數最多果個數</p> | |
| <h4 id="比咗累積頻數圖你">比咗累積頻數圖你</h4> | |
| <p>中位數：係打直嗰條軸到，係<span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mfrac><mi>n</mi><mn>2</mn></mfrac></mrow><annotation encoding="application/x-tex">\frac n 2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.695392em;"></span><span class="strut bottom" style="height: 1.04039em; vertical-align: -0.345em;"></span><span class="base"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.695392em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathit mtight">n</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.345em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>個位劃條橫線，然後係橫線同折線嘅交叉點劃一條向下嘅直線，條直線穿過嘅位就係答案</p> | |
| <h3 id="習題-2">習題</h3> | |
| <p>都係搵 平均值 中位數 模式</p> | |
| <ol> | |
| <li>5 2 0 1 3 1 4 0 1 1 9 1 0 2 6</li> | |
| <li>用上面個表做</li> | |
| <li><img src="https://i.investopedia.com/image/png/1524104173996/histogram_example.png" alt="Image result for histogram"><br> | |
| 數值係攞（上限+下限）／2</li> | |
| </ol> | |
| <h3 id="試前練習-2">試前練習</h3> | |
| <ol> | |
| <li>0 4 2 9 5 2 0 1 3 1 4 0 4 1 0</li> | |
| <li></li> | |
| </ol> | |
| <table> | |
| <thead> | |
| <tr> | |
| <th align="right">數字</th> | |
| <th align="right">1</th> | |
| <th align="right">3</th> | |
| <th align="right">5</th> | |
| <th align="right">7</th> | |
| <th align="right">9</th> | |
| <th align="right">11</th> | |
| </tr> | |
| </thead> | |
| <tbody> | |
| <tr> | |
| <td align="right">頻數</td> | |
| <td align="right">3</td> | |
| <td align="right">5</td> | |
| <td align="right">17</td> | |
| <td align="right">13</td> | |
| <td align="right">12</td> | |
| <td align="right">5</td> | |
| </tr> | |
| </tbody> | |
| </table><ol start="4"> | |
| <li><img src="https://www.originlab.com/doc/en/UserGuide/images/Histogram_Graph/Histogram_Graph4.png" alt="Image result for histogram"><br> | |
| 數值係攞（上限+下限）／2</li> | |
| </ol> | |
| <h2 id="三角函數">三角函數</h2> | |
| <p><img src="https://i.ytimg.com/vi/m5E3MzcBW2M/maxresdefault.jpg" alt="Image result for 三角函數"><br> | |
| （某人之前聲稱做咗好多次然後都係錯concept比我笑嗰啲）<br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>sin</mi><mo></mo><mi>θ</mi><mo>=</mo></mrow><annotation encoding="application/x-tex">\sin \theta =</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.69444em;"></span><span class="strut bottom" style="height: 0.69444em; vertical-align: 0em;"></span><span class="base"><span class="mop">sin</span><span class="mord mathit" style="margin-right: 0.02778em;">θ</span><span class="mrel">=</span></span></span></span></span> 離個角遠個條邊／斜邊<br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>cos</mi><mo></mo><mi>θ</mi><mo>=</mo></mrow><annotation encoding="application/x-tex">\cos \theta =</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.69444em;"></span><span class="strut bottom" style="height: 0.69444em; vertical-align: 0em;"></span><span class="base"><span class="mop">cos</span><span class="mord mathit" style="margin-right: 0.02778em;">θ</span><span class="mrel">=</span></span></span></span></span> 離個角近個條邊／斜邊<br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>tan</mi><mo></mo><mi>θ</mi><mo>=</mo></mrow><annotation encoding="application/x-tex">\tan \theta =</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.69444em;"></span><span class="strut bottom" style="height: 0.69444em; vertical-align: 0em;"></span><span class="base"><span class="mop">tan</span><span class="mord mathit" style="margin-right: 0.02778em;">θ</span><span class="mrel">=</span></span></span></span></span> 離個角遠個條邊／離個角近個條邊</p> | |
| <h2 id="相似嘅圖形／立體">相似嘅圖形／立體</h2> | |
| <h3 id="解釋-3">解釋</h3> | |
| <h4 id="各種比例嘅關係">各種比例嘅關係</h4> | |
| <p>要對應嘅邊／面積／體積先用得架</p> | |
| <div class="mermaid"><svg xmlns="http://www.w3.org/2000/svg" id="mermaid-svg-aZ3mYevIYAS2vlqm" height="100%" viewBox="0 0 467.65625 228" style="max-width:467.65625px;"><g><g class="output"><g class="clusters"></g><g class="edgePaths"><g class="edgePath" style="opacity: 1;"><path class="path" d="M181.69921875,55.93250517598344L55.328125,104L88.62922643442623,142" marker-end="url(#arrowhead168)" style="fill:none"></path><defs><marker id="arrowhead168" viewBox="0 0 10 10" refX="9" refY="5" markerUnits="strokeWidth" markerWidth="8" markerHeight="6" orient="auto"><path d="M 0 0 L 10 5 L 0 10 z" class="arrowheadPath" style="stroke-width: 1; stroke-dasharray: 1, 0;"></path></marker></defs></g><g class="edgePath" style="opacity: 1;"><path class="path" d="M128.94108606557376,142L162.2421875,104L195.54328893442624,66" marker-end="url(#arrowhead169)" style="fill:none"></path><defs><marker id="arrowhead169" viewBox="0 0 10 10" refX="9" refY="5" markerUnits="strokeWidth" markerWidth="8" markerHeight="6" orient="auto"><path d="M 0 0 L 10 5 L 0 10 z" class="arrowheadPath" style="stroke-width: 1; stroke-dasharray: 1, 0;"></path></marker></defs></g><g class="edgePath" style="opacity: 1;"><path class="path" d="M235.85514856557376,66L269.15625,104L302.45735143442624,142" marker-end="url(#arrowhead170)" style="fill:none"></path><defs><marker id="arrowhead170" viewBox="0 0 10 10" refX="9" refY="5" markerUnits="strokeWidth" markerWidth="8" markerHeight="6" orient="auto"><path d="M 0 0 L 10 5 L 0 10 z" class="arrowheadPath" style="stroke-width: 1; stroke-dasharray: 1, 0;"></path></marker></defs></g><g class="edgePath" style="opacity: 1;"><path class="path" d="M342.76921106557376,142L376.0703125,104L249.69921875,55.93250517598344" marker-end="url(#arrowhead171)" style="fill:none"></path><defs><marker id="arrowhead171" viewBox="0 0 10 10" refX="9" refY="5" markerUnits="strokeWidth" markerWidth="8" markerHeight="6" orient="auto"><path d="M 0 0 L 10 5 L 0 10 z" class="arrowheadPath" style="stroke-width: 1; stroke-dasharray: 1, 0;"></path></marker></defs></g></g><g class="edgeLabels"><g class="edgeLabel" transform="translate(55.328125,104)" style="opacity: 1;"><g transform="translate(-35.328125,-13)" class="label"><foreignObject width="70.65625" height="26"><div xmlns="http://www.w3.org/1999/xhtml" style="display: inline-block; white-space: nowrap;"><span class="edgeLabel">二次方 ^2</span></div></foreignObject></g></g><g class="edgeLabel" transform="translate(162.2421875,104)" style="opacity: 1;"><g transform="translate(-51.5859375,-13)" class="label"><foreignObject width="103.171875" height="26"><div xmlns="http://www.w3.org/1999/xhtml" style="display: inline-block; white-space: nowrap;"><span class="edgeLabel">開二次方 ^1/2</span></div></foreignObject></g></g><g class="edgeLabel" transform="translate(269.15625,104)" style="opacity: 1;"><g transform="translate(-35.328125,-13)" class="label"><foreignObject width="70.65625" height="26"><div xmlns="http://www.w3.org/1999/xhtml" style="display: inline-block; white-space: nowrap;"><span class="edgeLabel">三次方 ^3</span></div></foreignObject></g></g><g class="edgeLabel" transform="translate(376.0703125,104)" style="opacity: 1;"><g transform="translate(-51.5859375,-13)" class="label"><foreignObject width="103.171875" height="26"><div xmlns="http://www.w3.org/1999/xhtml" style="display: inline-block; white-space: nowrap;"><span class="edgeLabel">開三次方 ^1/3</span></div></foreignObject></g></g></g><g class="nodes"><g class="node" id="A" transform="translate(215.69921875,43)" style="opacity: 1;"><rect rx="5" ry="5" x="-34" y="-23" width="68" height="46"></rect><g class="label" transform="translate(0,0)"><g transform="translate(-24,-13)"><foreignObject width="48" height="26"><div xmlns="http://www.w3.org/1999/xhtml" style="display: inline-block; white-space: nowrap;">邊長比</div></foreignObject></g></g></g><g class="node" id="B" transform="translate(108.78515625,165)" style="opacity: 1;"><rect rx="5" ry="5" x="-34" y="-23" width="68" height="46"></rect><g class="label" transform="translate(0,0)"><g transform="translate(-24,-13)"><foreignObject width="48" height="26"><div xmlns="http://www.w3.org/1999/xhtml" style="display: inline-block; white-space: nowrap;">面積比</div></foreignObject></g></g></g><g class="node" id="C" transform="translate(322.61328125,165)" style="opacity: 1;"><rect rx="5" ry="5" x="-34" y="-23" width="68" height="46"></rect><g class="label" transform="translate(0,0)"><g transform="translate(-24,-13)"><foreignObject width="48" height="26"><div xmlns="http://www.w3.org/1999/xhtml" style="display: inline-block; white-space: nowrap;">體積比</div></foreignObject></g></g></g></g></g></g></svg></div> | |
| <h4 id="k方法-用係啲唔係直接相似嘅圖形到">k方法 用係啲唔係直接相似嘅圖形到</h4> | |
| <p>如果 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>a</mi><mo>:</mo><mi>b</mi><mo>=</mo><mn>3</mn><mo>:</mo><mn>5</mn></mrow><annotation encoding="application/x-tex">a:b=3:5</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.69444em;"></span><span class="strut bottom" style="height: 0.69444em; vertical-align: 0em;"></span><span class="base"><span class="mord mathit">a</span><span class="mrel">:</span><span class="mord mathit">b</span><span class="mrel">=</span><span class="mord mathrm">3</span><span class="mrel">:</span><span class="mord mathrm">5</span></span></span></span></span>，咁就可以設一個數，k/x/y 都好，然後 設<span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>a</mi><mo>=</mo><mn>3</mn><mi>k</mi></mrow><annotation encoding="application/x-tex">a=3k</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.69444em;"></span><span class="strut bottom" style="height: 0.69444em; vertical-align: 0em;"></span><span class="base"><span class="mord mathit">a</span><span class="mrel">=</span><span class="mord mathrm">3</span><span class="mord mathit" style="margin-right: 0.03148em;">k</span></span></span></span></span>, <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>b</mi><mo>=</mo><mn>5</mn><mi>k</mi></mrow><annotation encoding="application/x-tex">b=5k</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.69444em;"></span><span class="strut bottom" style="height: 0.69444em; vertical-align: 0em;"></span><span class="base"><span class="mord mathit">b</span><span class="mrel">=</span><span class="mord mathrm">5</span><span class="mord mathit" style="margin-right: 0.03148em;">k</span></span></span></span></span> 嚟做運算。所以 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>b</mi><mo>−</mo><mi>a</mi><mo>=</mo><mn>5</mn><mi>k</mi><mo>−</mo><mn>3</mn><mi>k</mi><mo>=</mo><mn>2</mn><mi>k</mi></mrow><annotation encoding="application/x-tex">b-a=5k-3k=2k</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.69444em;"></span><span class="strut bottom" style="height: 0.77777em; vertical-align: -0.08333em;"></span><span class="base"><span class="mord mathit">b</span><span class="mbin">−</span><span class="mord mathit">a</span><span class="mrel">=</span><span class="mord mathrm">5</span><span class="mord mathit" style="margin-right: 0.03148em;">k</span><span class="mbin">−</span><span class="mord mathrm">3</span><span class="mord mathit" style="margin-right: 0.03148em;">k</span><span class="mrel">=</span><span class="mord mathrm">2</span><span class="mord mathit" style="margin-right: 0.03148em;">k</span></span></span></span></span></p> | |
| <h3 id="習題-3">習題</h3> | |
| <ol> | |
| <li>有兩個相似嘅圓錐體，大嘅底部面積係 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>6</mn><mn>4</mn><msup><mtext>cm</mtext><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">64\text{cm}^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.814108em;"></span><span class="strut bottom" style="height: 0.814108em; vertical-align: 0em;"></span><span class="base"><span class="mord mathrm">6</span><span class="mord mathrm">4</span><span class="mord"><span class="mord text"><span class="mord mathrm">cm</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span></span></span></span></span>，細嘅底部面積係<span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>1</mn><mn>6</mn><msup><mtext>cm</mtext><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">16\text{cm}^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.814108em;"></span><span class="strut bottom" style="height: 0.814108em; vertical-align: 0em;"></span><span class="base"><span class="mord mathrm">1</span><span class="mord mathrm">6</span><span class="mord"><span class="mord text"><span class="mord mathrm">cm</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span></span></span></span></span>，求體積比。</li> | |
| <li>（好難架，畫圖會清晰好多）而家有個金字塔，分咗兩層，上下兩層嘅高度比係 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>2</mn><mo>:</mo><mn>3</mn></mrow><annotation encoding="application/x-tex">2:3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.64444em;"></span><span class="strut bottom" style="height: 0.64444em; vertical-align: 0em;"></span><span class="base"><span class="mord mathrm">2</span><span class="mrel">:</span><span class="mord mathrm">3</span></span></span></span></span>，已知下層嘅體積係 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>4</mn><mn>6</mn><mn>8</mn><msup><mtext>m</mtext><mn>3</mn></msup></mrow><annotation encoding="application/x-tex">468\text m ^3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.814108em;"></span><span class="strut bottom" style="height: 0.814108em; vertical-align: 0em;"></span><span class="base"><span class="mord mathrm">4</span><span class="mord mathrm">6</span><span class="mord mathrm">8</span><span class="mord"><span class="mord text"><span class="mord mathrm">m</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">3</span></span></span></span></span></span></span></span></span></span></span></span>，求上層體積。</li> | |
| </ol> | |
| <h3 id="試前練習-3">試前練習</h3> | |
| <ol> | |
| <li>有兩個相似嘅圓錐體，大嘅體積係 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>2</mn><mn>7</mn><msup><mtext>cm</mtext><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">27\text{cm}^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.814108em;"></span><span class="strut bottom" style="height: 0.814108em; vertical-align: 0em;"></span><span class="base"><span class="mord mathrm">2</span><span class="mord mathrm">7</span><span class="mord"><span class="mord text"><span class="mord mathrm">cm</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span></span></span></span></span>，細嘅體積係<span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>8</mn><msup><mtext>cm</mtext><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">8\text{cm}^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.814108em;"></span><span class="strut bottom" style="height: 0.814108em; vertical-align: 0em;"></span><span class="base"><span class="mord mathrm">8</span><span class="mord"><span class="mord text"><span class="mord mathrm">cm</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span></span></span></span></span>，求面積比。</li> | |
| <li>（好難架，畫圖會清晰好多）而家有個金字塔，分咗兩層，上下兩層嘅高度比係 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>2</mn><mo>:</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">2:1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.64444em;"></span><span class="strut bottom" style="height: 0.64444em; vertical-align: 0em;"></span><span class="base"><span class="mord mathrm">2</span><span class="mrel">:</span><span class="mord mathrm">1</span></span></span></span></span>，已知下層嘅體積係 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>1</mn><mn>2</mn><mn>5</mn><msup><mtext>m</mtext><mn>3</mn></msup></mrow><annotation encoding="application/x-tex">125\text m ^3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.814108em;"></span><span class="strut bottom" style="height: 0.814108em; vertical-align: 0em;"></span><span class="base"><span class="mord mathrm">1</span><span class="mord mathrm">2</span><span class="mord mathrm">5</span><span class="mord"><span class="mord text"><span class="mord mathrm">m</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">3</span></span></span></span></span></span></span></span></span></span></span></span>，求上層體積。</li> | |
| </ol> | |
| <h2 id="平面公式">平面公式</h2> | |
| <h3 id="解釋-4">解釋</h3> | |
| <ol> | |
| <li>正方形<br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>面積</mtext></mrow><annotation encoding="application/x-tex">\text{面積}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.68333em;"></span><span class="strut bottom" style="height: 0.68333em; vertical-align: 0em;"></span><span class="base"><span class="mord text"><span class="mord mathrm cjk_fallback">面積</span></span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>=</mo><msup><mtext>邊長</mtext><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">=\text{邊長}^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.887338em;"></span><span class="strut bottom" style="height: 0.887338em; vertical-align: 0em;"></span><span class="base"><span class="mrel">=</span><span class="mord"><span class="mord text"><span class="mord mathrm cjk_fallback">邊長</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.887338em;"><span class="" style="top: -3.13623em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>=</mo><msup><mi>l</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">=l^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.814108em;"></span><span class="strut bottom" style="height: 0.814108em; vertical-align: 0em;"></span><span class="base"><span class="mrel">=</span><span class="mord"><span class="mord mathit" style="margin-right: 0.01968em;">l</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>周界</mtext></mrow><annotation encoding="application/x-tex">\text{周界}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.68333em;"></span><span class="strut bottom" style="height: 0.68333em; vertical-align: 0em;"></span><span class="base"><span class="mord text"><span class="mord mathrm cjk_fallback">周界</span></span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>=</mo><mtext>邊長</mtext><mo>×</mo><mn>4</mn></mrow><annotation encoding="application/x-tex">=\text{邊長}\times 4</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.68333em;"></span><span class="strut bottom" style="height: 0.76666em; vertical-align: -0.08333em;"></span><span class="base"><span class="mrel">=</span><span class="mord text"><span class="mord mathrm cjk_fallback">邊長</span></span><span class="mbin">×</span><span class="mord mathrm">4</span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>=</mo><mn>4</mn><mi>l</mi></mrow><annotation encoding="application/x-tex">=4l</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.69444em;"></span><span class="strut bottom" style="height: 0.69444em; vertical-align: 0em;"></span><span class="base"><span class="mrel">=</span><span class="mord mathrm">4</span><span class="mord mathit" style="margin-right: 0.01968em;">l</span></span></span></span></span></li> | |
| <li>長方形<br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>面積</mtext></mrow><annotation encoding="application/x-tex">\text{面積}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.68333em;"></span><span class="strut bottom" style="height: 0.68333em; vertical-align: 0em;"></span><span class="base"><span class="mord text"><span class="mord mathrm cjk_fallback">面積</span></span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>=</mo><mtext>長</mtext><mo>×</mo><mtext>高</mtext></mrow><annotation encoding="application/x-tex">=\text{長}\times\text{高}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.68333em;"></span><span class="strut bottom" style="height: 0.76666em; vertical-align: -0.08333em;"></span><span class="base"><span class="mrel">=</span><span class="mord text"><span class="mord mathrm cjk_fallback">長</span></span><span class="mbin">×</span><span class="mord text"><span class="mord mathrm cjk_fallback">高</span></span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>=</mo><mi>w</mi><mi>h</mi></mrow><annotation encoding="application/x-tex">=wh</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.69444em;"></span><span class="strut bottom" style="height: 0.69444em; vertical-align: 0em;"></span><span class="base"><span class="mrel">=</span><span class="mord mathit" style="margin-right: 0.02691em;">w</span><span class="mord mathit">h</span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>周界</mtext></mrow><annotation encoding="application/x-tex">\text{周界}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.68333em;"></span><span class="strut bottom" style="height: 0.68333em; vertical-align: 0em;"></span><span class="base"><span class="mord text"><span class="mord mathrm cjk_fallback">周界</span></span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>=</mo><mtext>長</mtext><mo>×</mo><mn>2</mn><mo>+</mo><mtext>高</mtext><mo>×</mo><mn>2</mn></mrow><annotation encoding="application/x-tex">=\text{長}\times 2+\text{高}\times 2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.68333em;"></span><span class="strut bottom" style="height: 0.76666em; vertical-align: -0.08333em;"></span><span class="base"><span class="mrel">=</span><span class="mord text"><span class="mord mathrm cjk_fallback">長</span></span><span class="mbin">×</span><span class="mord mathrm">2</span><span class="mbin">+</span><span class="mord text"><span class="mord mathrm cjk_fallback">高</span></span><span class="mbin">×</span><span class="mord mathrm">2</span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>=</mo><mn>2</mn><mi>w</mi><mo>+</mo><mn>2</mn><mi>h</mi></mrow><annotation encoding="application/x-tex">=2w+2h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.69444em;"></span><span class="strut bottom" style="height: 0.77777em; vertical-align: -0.08333em;"></span><span class="base"><span class="mrel">=</span><span class="mord mathrm">2</span><span class="mord mathit" style="margin-right: 0.02691em;">w</span><span class="mbin">+</span><span class="mord mathrm">2</span><span class="mord mathit">h</span></span></span></span></span></li> | |
| <li>平行四邊形<br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>面積</mtext></mrow><annotation encoding="application/x-tex">\text{面積}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.68333em;"></span><span class="strut bottom" style="height: 0.68333em; vertical-align: 0em;"></span><span class="base"><span class="mord text"><span class="mord mathrm cjk_fallback">面積</span></span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>=</mo><mtext>底</mtext><mo>×</mo><mtext>高</mtext></mrow><annotation encoding="application/x-tex">=\text{底}\times\text{高}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.68333em;"></span><span class="strut bottom" style="height: 0.76666em; vertical-align: -0.08333em;"></span><span class="base"><span class="mrel">=</span><span class="mord text"><span class="mord mathrm cjk_fallback">底</span></span><span class="mbin">×</span><span class="mord text"><span class="mord mathrm cjk_fallback">高</span></span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>=</mo><mi>b</mi><mi>h</mi></mrow><annotation encoding="application/x-tex">=bh</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.69444em;"></span><span class="strut bottom" style="height: 0.69444em; vertical-align: 0em;"></span><span class="base"><span class="mrel">=</span><span class="mord mathit">b</span><span class="mord mathit">h</span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>周界</mtext></mrow><annotation encoding="application/x-tex">\text{周界}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.68333em;"></span><span class="strut bottom" style="height: 0.68333em; vertical-align: 0em;"></span><span class="base"><span class="mord text"><span class="mord mathrm cjk_fallback">周界</span></span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>=</mo><mtext>底</mtext><mo>×</mo><mn>2</mn><mo>+</mo><mtext>斜邊</mtext><mo>×</mo><mn>2</mn></mrow><annotation encoding="application/x-tex">=\text{底}\times 2+\text{斜邊}\times 2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.68333em;"></span><span class="strut bottom" style="height: 0.76666em; vertical-align: -0.08333em;"></span><span class="base"><span class="mrel">=</span><span class="mord text"><span class="mord mathrm cjk_fallback">底</span></span><span class="mbin">×</span><span class="mord mathrm">2</span><span class="mbin">+</span><span class="mord text"><span class="mord mathrm cjk_fallback">斜邊</span></span><span class="mbin">×</span><span class="mord mathrm">2</span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>=</mo><mn>2</mn><mi>b</mi><mo>+</mo><mn>2</mn><mi>l</mi></mrow><annotation encoding="application/x-tex">=2b+2l</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.69444em;"></span><span class="strut bottom" style="height: 0.77777em; vertical-align: -0.08333em;"></span><span class="base"><span class="mrel">=</span><span class="mord mathrm">2</span><span class="mord mathit">b</span><span class="mbin">+</span><span class="mord mathrm">2</span><span class="mord mathit" style="margin-right: 0.01968em;">l</span></span></span></span></span></li> | |
| <li>梯形<br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>面積</mtext></mrow><annotation encoding="application/x-tex">\text{面積}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.68333em;"></span><span class="strut bottom" style="height: 0.68333em; vertical-align: 0em;"></span><span class="base"><span class="mord text"><span class="mord mathrm cjk_fallback">面積</span></span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>=</mo><mfrac><mrow><mrow><mo fence="true">(</mo><mtext>上底</mtext><mo>+</mo><mtext>下底</mtext><mo fence="true">)</mo></mrow><mo>×</mo><mtext>高</mtext></mrow><mn>2</mn></mfrac></mrow><annotation encoding="application/x-tex">=\frac{\left(\text{上底}+\text{下底}\right)\times\text{高}} 2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 1.01em;"></span><span class="strut bottom" style="height: 1.355em; vertical-align: -0.345em;"></span><span class="base"><span class="mrel">=</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 1.01em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.485em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="minner mtight"><span class="mopen mtight delimcenter" style="top: 0em;"><span class="mtight">(</span></span><span class="mord text mtight"><span class="mord mathrm cjk_fallback mtight">上底</span></span><span class="mbin mtight">+</span><span class="mord text mtight"><span class="mord mathrm cjk_fallback mtight">下底</span></span><span class="mclose mtight delimcenter" style="top: 0em;"><span class="mtight">)</span></span></span><span class="mbin mtight">×</span><span class="mord text mtight"><span class="mord mathrm cjk_fallback mtight">高</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.345em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>=</mo><mfrac><mrow><mrow><mo fence="true">(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo fence="true">)</mo></mrow><mi>h</mi></mrow><mn>2</mn></mfrac></mrow><annotation encoding="application/x-tex">=\frac{\left(a+b\right)h} 2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 1.01em;"></span><span class="strut bottom" style="height: 1.355em; vertical-align: -0.345em;"></span><span class="base"><span class="mrel">=</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 1.01em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.485em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="minner mtight"><span class="mopen mtight delimcenter" style="top: 0em;"><span class="mtight">(</span></span><span class="mord mathit mtight">a</span><span class="mbin mtight">+</span><span class="mord mathit mtight">b</span><span class="mclose mtight delimcenter" style="top: 0em;"><span class="mtight">)</span></span></span><span class="mord mathit mtight">h</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.345em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>周界</mtext></mrow><annotation encoding="application/x-tex">\text{周界}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.68333em;"></span><span class="strut bottom" style="height: 0.68333em; vertical-align: 0em;"></span><span class="base"><span class="mord text"><span class="mord mathrm cjk_fallback">周界</span></span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>=</mo><mtext>上底</mtext><mo>+</mo><mtext>下底</mtext><mo>+</mo><mtext>左斜邊</mtext><mo>+</mo><mtext>右斜邊</mtext></mrow><annotation encoding="application/x-tex">=\text{上底}+\text{下底}+\text{左斜邊}+\text{右斜邊}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.68333em;"></span><span class="strut bottom" style="height: 0.76666em; vertical-align: -0.08333em;"></span><span class="base"><span class="mrel">=</span><span class="mord text"><span class="mord mathrm cjk_fallback">上底</span></span><span class="mbin">+</span><span class="mord text"><span class="mord mathrm cjk_fallback">下底</span></span><span class="mbin">+</span><span class="mord text"><span class="mord mathrm cjk_fallback">左斜邊</span></span><span class="mbin">+</span><span class="mord text"><span class="mord mathrm cjk_fallback">右斜邊</span></span></span></span></span></span><br> | |
| <img src="https://i.ytimg.com/vi/2Hll8gain4Q/maxresdefault.jpg" alt="Image result for 梯形 é¢ç©"></li> | |
| <li>圓形<br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>面積</mtext></mrow><annotation encoding="application/x-tex">\text{面積}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.68333em;"></span><span class="strut bottom" style="height: 0.68333em; vertical-align: 0em;"></span><span class="base"><span class="mord text"><span class="mord mathrm cjk_fallback">面積</span></span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>=</mo><mi>π</mi><mo>×</mo><mtext>半徑</mtext></mrow><annotation encoding="application/x-tex">=\pi \times \text{半徑}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.68333em;"></span><span class="strut bottom" style="height: 0.76666em; vertical-align: -0.08333em;"></span><span class="base"><span class="mrel">=</span><span class="mord mathit" style="margin-right: 0.03588em;">π</span><span class="mbin">×</span><span class="mord text"><span class="mord mathrm cjk_fallback">半徑</span></span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>=</mo><mi>π</mi><msup><mi>r</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">=\pi r^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.814108em;"></span><span class="strut bottom" style="height: 0.814108em; vertical-align: 0em;"></span><span class="base"><span class="mrel">=</span><span class="mord mathit" style="margin-right: 0.03588em;">π</span><span class="mord"><span class="mord mathit" style="margin-right: 0.02778em;">r</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>周界</mtext></mrow><annotation encoding="application/x-tex">\text{周界}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.68333em;"></span><span class="strut bottom" style="height: 0.68333em; vertical-align: 0em;"></span><span class="base"><span class="mord text"><span class="mord mathrm cjk_fallback">周界</span></span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>=</mo><mn>2</mn><mi>π</mi><mo>×</mo><mtext>半徑</mtext></mrow><annotation encoding="application/x-tex">=2 \pi \times \text{半徑}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.68333em;"></span><span class="strut bottom" style="height: 0.76666em; vertical-align: -0.08333em;"></span><span class="base"><span class="mrel">=</span><span class="mord mathrm">2</span><span class="mord mathit" style="margin-right: 0.03588em;">π</span><span class="mbin">×</span><span class="mord text"><span class="mord mathrm cjk_fallback">半徑</span></span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>=</mo><mi>π</mi><msup><mi>r</mi><mn>2</mn></msup><mo>=</mo><mi>π</mi><mo>×</mo><mtext>直徑</mtext></mrow><annotation encoding="application/x-tex">=\pi r^2=\pi \times \text{直徑}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.814108em;"></span><span class="strut bottom" style="height: 0.897438em; vertical-align: -0.08333em;"></span><span class="base"><span class="mrel">=</span><span class="mord mathit" style="margin-right: 0.03588em;">π</span><span class="mord"><span class="mord mathit" style="margin-right: 0.02778em;">r</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span><span class="mrel">=</span><span class="mord mathit" style="margin-right: 0.03588em;">π</span><span class="mbin">×</span><span class="mord text"><span class="mord mathrm cjk_fallback">直徑</span></span></span></span></span></span><br> | |
| <img src="http://www.kkes.ilc.edu.tw/images/%E5%9C%93%E5%BD%A2.gif" alt="Image result for 圓形 é¢ç©"></li> | |
| </ol> | |
| <h3 id="習題（注意單位）">習題（注意單位）</h3> | |
| <ol> | |
| <li>邊長為7cm的正方形，其面積為？其周界為？</li> | |
| <li>長方形的長為17cm，高為11cm，其面積為？其周界為？</li> | |
| <li>平行四邊形的底邊為10cm，高為7cm，斜邊為8.5cm，其面積為？其周界為？</li> | |
| <li>梯形的上底為5cm，下底為7cm，高為10cm，左斜邊為12cm，右斜邊為13cm，其面積為？其周界為？</li> | |
| <li>圓形的<strong>直徑</strong>為 16cm，其面積為？其周界為？</li> | |
| </ol> | |
| <h3 id="試前練習-4">試前練習</h3> | |
| <ol> | |
| <li>邊長為9cm的正方形，其面積為？其周界為？</li> | |
| <li>長方形的長為15cm，高為7cm，其面積為？其周界為？</li> | |
| <li>平行四邊形的底邊為9cm，高為8cm，其面積為？</li> | |
| <li>梯形的上底為3cm，下底為5cm，高為8cm，其面積為？</li> | |
| <li>圓形的<strong>直徑</strong>為 6cm，其面積為？其周界為？</li> | |
| </ol> | |
| <h2 id="立體公式">立體公式</h2> | |
| <p><img src="http://www.assignmentpoint.com/wp-content/uploads/2017/07/Surface-Area-of-Cylinders-1.jpg" alt="Image result for cylinder surface area"><br> | |
| <img src="https://fthmb.tqn.com/aA4f0r_i0awPHh259PDN-cCFN6c=/768x0/filters:no_upscale():max_bytes(150000):strip_icc()/surface-area-2-589dda2f5f9b58819c872fb4.jpg" alt="Image result for cone surface area"><br> | |
| <img src="https://fthmb.tqn.com/cbp422eoJ-KHVFIP8Hkmdxkfi5M=/768x0/filters:no_upscale():max_bytes(150000):strip_icc()/surface-area-1-589dd97c3df78c47588a9b3a.jpg" alt="Image result for sphere surface area"></p> | |
| <h3 id="解釋-5">解釋</h3> | |
| <p><strong>底面積可以用上面平面公式搵番出黎喔</strong></p> | |
| <h4 id="體積">體積</h4> | |
| <ol> | |
| <li><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>柱體體積</mtext></mrow><annotation encoding="application/x-tex">\text{柱體體積}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.68333em;"></span><span class="strut bottom" style="height: 0.68333em; vertical-align: 0em;"></span><span class="base"><span class="mord text"><span class="mord mathrm cjk_fallback">柱體體積</span></span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>=</mo><mtext>底面積</mtext><mo>×</mo><mtext>高</mtext></mrow><annotation encoding="application/x-tex">=\text{底面積} \times \text{高}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.68333em;"></span><span class="strut bottom" style="height: 0.76666em; vertical-align: -0.08333em;"></span><span class="base"><span class="mrel">=</span><span class="mord text"><span class="mord mathrm cjk_fallback">底面積</span></span><span class="mbin">×</span><span class="mord text"><span class="mord mathrm cjk_fallback">高</span></span></span></span></span></span></li> | |
| <li><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>椎體體積</mtext></mrow><annotation encoding="application/x-tex">\text{椎體體積}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.68333em;"></span><span class="strut bottom" style="height: 0.68333em; vertical-align: 0em;"></span><span class="base"><span class="mord text"><span class="mord mathrm cjk_fallback">椎體體積</span></span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>=</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>×</mo><mtext>底面積</mtext><mo>×</mo><mtext>高</mtext></mrow><annotation encoding="application/x-tex">=\frac 1 3 \times \text{底面積} \times \text{高}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.845108em;"></span><span class="strut bottom" style="height: 1.19011em; vertical-align: -0.345em;"></span><span class="base"><span class="mrel">=</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.845108em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">3</span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.345em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mbin">×</span><span class="mord text"><span class="mord mathrm cjk_fallback">底面積</span></span><span class="mbin">×</span><span class="mord text"><span class="mord mathrm cjk_fallback">高</span></span></span></span></span></span></li> | |
| <li><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>球體體積</mtext></mrow><annotation encoding="application/x-tex">\text{球體體積}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.68333em;"></span><span class="strut bottom" style="height: 0.68333em; vertical-align: 0em;"></span><span class="base"><span class="mord text"><span class="mord mathrm cjk_fallback">球體體積</span></span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>=</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><mi>π</mi><mo>×</mo><msup><mtext>半徑</mtext><mn>3</mn></msup></mrow><annotation encoding="application/x-tex">=\frac 4 3 \pi \times \text{半徑}^3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.887338em;"></span><span class="strut bottom" style="height: 1.23234em; vertical-align: -0.345em;"></span><span class="base"><span class="mrel">=</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.845108em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">3</span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">4</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.345em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord mathit" style="margin-right: 0.03588em;">π</span><span class="mbin">×</span><span class="mord"><span class="mord text"><span class="mord mathrm cjk_fallback">半徑</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.887338em;"><span class="" style="top: -3.13623em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">3</span></span></span></span></span></span></span></span></span></span></span></span></li> | |
| </ol> | |
| <h4 id="表面積">表面積</h4> | |
| <ol> | |
| <li><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>柱體表面積</mtext></mrow><annotation encoding="application/x-tex">\text{柱體表面積}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.68333em;"></span><span class="strut bottom" style="height: 0.68333em; vertical-align: 0em;"></span><span class="base"><span class="mord text"><span class="mord mathrm cjk_fallback">柱體表面積</span></span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>=</mo><mtext>底面積</mtext><mo>×</mo><mn>2</mn><mo>+</mo><mtext>底周界</mtext><mo>×</mo><mtext>高</mtext></mrow><annotation encoding="application/x-tex">=\text{底面積} \times 2 + \text{底周界}\times \text{高}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.68333em;"></span><span class="strut bottom" style="height: 0.76666em; vertical-align: -0.08333em;"></span><span class="base"><span class="mrel">=</span><span class="mord text"><span class="mord mathrm cjk_fallback">底面積</span></span><span class="mbin">×</span><span class="mord mathrm">2</span><span class="mbin">+</span><span class="mord text"><span class="mord mathrm cjk_fallback">底周界</span></span><span class="mbin">×</span><span class="mord text"><span class="mord mathrm cjk_fallback">高</span></span></span></span></span></span><br> | |
| <strong>可以套用係圓形到架</strong></li> | |
| <li><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>圓柱體表面積</mtext></mrow><annotation encoding="application/x-tex">\text{圓柱體表面積}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.68333em;"></span><span class="strut bottom" style="height: 0.68333em; vertical-align: 0em;"></span><span class="base"><span class="mord text"><span class="mord mathrm cjk_fallback">圓柱體表面積</span></span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>=</mo><mi>π</mi><mo>×</mo><msup><mtext>半徑</mtext><mn>2</mn></msup><mo>×</mo><mn>2</mn><mo>+</mo><mn>2</mn><mi>π</mi><mo>×</mo><mtext>半徑</mtext><mo>×</mo><mtext>高</mtext></mrow><annotation encoding="application/x-tex">=\pi \times \text{半徑}^2 \times 2 + 2\pi \times \text{半徑} \times \text{高}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.887338em;"></span><span class="strut bottom" style="height: 0.970668em; vertical-align: -0.08333em;"></span><span class="base"><span class="mrel">=</span><span class="mord mathit" style="margin-right: 0.03588em;">π</span><span class="mbin">×</span><span class="mord"><span class="mord text"><span class="mord mathrm cjk_fallback">半徑</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.887338em;"><span class="" style="top: -3.13623em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span><span class="mbin">×</span><span class="mord mathrm">2</span><span class="mbin">+</span><span class="mord mathrm">2</span><span class="mord mathit" style="margin-right: 0.03588em;">π</span><span class="mbin">×</span><span class="mord text"><span class="mord mathrm cjk_fallback">半徑</span></span><span class="mbin">×</span><span class="mord text"><span class="mord mathrm cjk_fallback">高</span></span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>=</mo><mn>2</mn><mi>π</mi><msup><mi>r</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mi>π</mi><mi>r</mi><mi>h</mi></mrow><annotation encoding="application/x-tex">=2\pi r^2+2\pi rh</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.814108em;"></span><span class="strut bottom" style="height: 0.897438em; vertical-align: -0.08333em;"></span><span class="base"><span class="mrel">=</span><span class="mord mathrm">2</span><span class="mord mathit" style="margin-right: 0.03588em;">π</span><span class="mord"><span class="mord mathit" style="margin-right: 0.02778em;">r</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span><span class="mbin">+</span><span class="mord mathrm">2</span><span class="mord mathit" style="margin-right: 0.03588em;">π</span><span class="mord mathit" style="margin-right: 0.02778em;">r</span><span class="mord mathit">h</span></span></span></span></span></li> | |
| <li><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>椎體表面積</mtext><mo>=</mo><mtext>底面積</mtext><mo>+</mo><mtext>側面面積</mtext></mrow><annotation encoding="application/x-tex">\text{椎體表面積}=\text{底面積} + \text{側面面積}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.68333em;"></span><span class="strut bottom" style="height: 0.76666em; vertical-align: -0.08333em;"></span><span class="base"><span class="mord text"><span class="mord mathrm cjk_fallback">椎體表面積</span></span><span class="mrel">=</span><span class="mord text"><span class="mord mathrm cjk_fallback">底面積</span></span><span class="mbin">+</span><span class="mord text"><span class="mord mathrm cjk_fallback">側面面積</span></span></span></span></span></span></li> | |
| <li><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>圓椎體表面積</mtext></mrow><annotation encoding="application/x-tex">\text{圓椎體表面積}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.68333em;"></span><span class="strut bottom" style="height: 0.68333em; vertical-align: 0em;"></span><span class="base"><span class="mord text"><span class="mord mathrm cjk_fallback">圓椎體表面積</span></span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>=</mo><mi>π</mi><mo>×</mo><msup><mtext>半徑</mtext><mn>2</mn></msup><mo>+</mo><mi>π</mi><mo>×</mo><mtext>半徑</mtext><mo>×</mo><mtext>斜邊</mtext></mrow><annotation encoding="application/x-tex">=\pi \times \text{半徑}^2+\pi \times \text{半徑}\times \text{斜邊}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.887338em;"></span><span class="strut bottom" style="height: 0.970668em; vertical-align: -0.08333em;"></span><span class="base"><span class="mrel">=</span><span class="mord mathit" style="margin-right: 0.03588em;">π</span><span class="mbin">×</span><span class="mord"><span class="mord text"><span class="mord mathrm cjk_fallback">半徑</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.887338em;"><span class="" style="top: -3.13623em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span><span class="mbin">+</span><span class="mord mathit" style="margin-right: 0.03588em;">π</span><span class="mbin">×</span><span class="mord text"><span class="mord mathrm cjk_fallback">半徑</span></span><span class="mbin">×</span><span class="mord text"><span class="mord mathrm cjk_fallback">斜邊</span></span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>π</mi><msup><mi>r</mi><mn>2</mn></msup><mo>+</mo><mi>π</mi><mi>r</mi><mi>l</mi></mrow><annotation encoding="application/x-tex">\pi r^2+\pi rl</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.814108em;"></span><span class="strut bottom" style="height: 0.897438em; vertical-align: -0.08333em;"></span><span class="base"><span class="mord mathit" style="margin-right: 0.03588em;">π</span><span class="mord"><span class="mord mathit" style="margin-right: 0.02778em;">r</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span><span class="mbin">+</span><span class="mord mathit" style="margin-right: 0.03588em;">π</span><span class="mord mathit" style="margin-right: 0.02778em;">r</span><span class="mord mathit" style="margin-right: 0.01968em;">l</span></span></span></span></span><br> | |
| 圖係 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>l</mi><mo>=</mo><mi>s</mi></mrow><annotation encoding="application/x-tex">l=s</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.69444em;"></span><span class="strut bottom" style="height: 0.69444em; vertical-align: 0em;"></span><span class="base"><span class="mord mathit" style="margin-right: 0.01968em;">l</span><span class="mrel">=</span><span class="mord mathit">s</span></span></span></span></span></li> | |
| <li><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>斜邊</mtext></mrow><annotation encoding="application/x-tex">\text{斜邊}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.68333em;"></span><span class="strut bottom" style="height: 0.68333em; vertical-align: 0em;"></span><span class="base"><span class="mord text"><span class="mord mathrm cjk_fallback">斜邊</span></span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>=</mo><msqrt><mrow><msup><mtext>半徑</mtext><mn>2</mn></msup><mo>+</mo><msup><mtext>高</mtext><mn>2</mn></msup></mrow></msqrt></mrow><annotation encoding="application/x-tex">=\sqrt{\text{半徑}^2+\text{高}^2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 1.087em;"></span><span class="strut bottom" style="height: 1.24em; vertical-align: -0.152996em;"></span><span class="base"><span class="mrel">=</span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist svg-align" style="height: 1.087em;"><span class="" style="top: -3.2em;"><span class="pstrut" style="height: 3.2em;"></span><span class="mord" style="padding-left: 1em;"><span class="mord"><span class="mord text"><span class="mord mathrm cjk_fallback">半徑</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.887338em;"><span class="" style="top: -3.13623em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span><span class="mbin">+</span><span class="mord"><span class="mord text"><span class="mord mathrm cjk_fallback">高</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.887338em;"><span class="" style="top: -3.13623em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span></span></span><span class="" style="top: -3.047em;"><span class="pstrut" style="height: 3.2em;"></span><span class="hide-tail" style="min-width: 1.02em; height: 1.2em;"><svg width="400em" height="1.2em" viewBox="0 0 400000 1200" preserveAspectRatio="xMinYMin slice"><path d="M263 601c.667 0 18 39.667 52 119s68.167 | |
| 158.667 102.5 238 51.833 119.333 52.5 120C810 373.333 980.667 17.667 982 11 | |
| c4.667-7.333 11-11 19-11h398999v40H1012.333L741 607c-38.667 80.667-84 175-136 | |
| 283s-89.167 185.333-111.5 232-33.833 70.333-34.5 71c-4.667 4.667-12.333 7-23 | |
| 7l-12-1-109-253c-72.667-168-109.333-252-110-252-10.667 8-22 16.667-34 26-22 | |
| 17.333-33.333 26-34 26l-26-26 76-59 76-60zM1001 0h398999v40H1012z"></path></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.152996em;"></span></span></span></span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>=</mo><msqrt><mrow><msup><mi>r</mi><mn>2</mn></msup><mo>+</mo><msup><mi>h</mi><mn>2</mn></msup></mrow></msqrt></mrow><annotation encoding="application/x-tex">=\sqrt{r^2+h^2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.913389em;"></span><span class="strut bottom" style="height: 1.04em; vertical-align: -0.126611em;"></span><span class="base"><span class="mrel">=</span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist svg-align" style="height: 0.913389em;"><span class="" style="top: -3em;"><span class="pstrut" style="height: 3em;"></span><span class="mord" style="padding-left: 0.833em;"><span class="mord"><span class="mord mathit" style="margin-right: 0.02778em;">r</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.740108em;"><span class="" style="top: -2.989em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span><span class="mbin">+</span><span class="mord"><span class="mord mathit">h</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.740108em;"><span class="" style="top: -2.989em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span></span></span><span class="" style="top: -2.87339em;"><span class="pstrut" style="height: 3em;"></span><span class="hide-tail" style="min-width: 0.853em; height: 1em;"><svg width="400em" height="1em" viewBox="0 0 400000 1000" preserveAspectRatio="xMinYMin slice"><path d="M95 622c-2.667 0-7.167-2.667-13.5 | |
| -8S72 604 72 600c0-2 .333-3.333 1-4 1.333-2.667 23.833-20.667 67.5-54s | |
| 65.833-50.333 66.5-51c1.333-1.333 3-2 5-2 4.667 0 8.667 3.333 12 10l173 | |
| 378c.667 0 35.333-71 104-213s137.5-285 206.5-429S812 17.333 812 14c5.333 | |
| -9.333 12-14 20-14h399166v40H845.272L620 507 385 993c-2.667 4.667-9 7-19 | |
| 7-6 0-10-1-12-3L160 575l-65 47zM834 0h399166v40H845z"></path></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.126611em;"></span></span></span></span></span></span></span></span><br> | |
| <strong>畢氏定理</strong></li> | |
| <li><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>球體表面積</mtext></mrow><annotation encoding="application/x-tex">\text{球體表面積}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.68333em;"></span><span class="strut bottom" style="height: 0.68333em; vertical-align: 0em;"></span><span class="base"><span class="mord text"><span class="mord mathrm cjk_fallback">球體表面積</span></span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>=</mo><mn>4</mn><mi>π</mi><mo>×</mo><msup><mtext>半徑</mtext><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">=4 \pi \times \text{半徑}^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.887338em;"></span><span class="strut bottom" style="height: 0.970668em; vertical-align: -0.08333em;"></span><span class="base"><span class="mrel">=</span><span class="mord mathrm">4</span><span class="mord mathit" style="margin-right: 0.03588em;">π</span><span class="mbin">×</span><span class="mord"><span class="mord text"><span class="mord mathrm cjk_fallback">半徑</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.887338em;"><span class="" style="top: -3.13623em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>=</mo><mn>4</mn><mi>π</mi><msup><mi>r</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">=4\pi r^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.814108em;"></span><span class="strut bottom" style="height: 0.814108em; vertical-align: 0em;"></span><span class="base"><span class="mrel">=</span><span class="mord mathrm">4</span><span class="mord mathit" style="margin-right: 0.03588em;">π</span><span class="mord"><span class="mord mathit" style="margin-right: 0.02778em;">r</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span></span></span></span></span></li> | |
| </ol> | |
| <h3 id="習題-4">習題</h3> | |
| <p>以下題目需找出體積及表面積</p> | |
| <ol> | |
| <li>邊長 4cm 的正方體</li> | |
| <li>長 7cm，闊 5cm，高 3cm 的長方體</li> | |
| <li>半徑 5cm，高 7cm，(a)圓柱體，(b)圓錐體</li> | |
| </ol> | |
| <h3 id="試前練習-5">試前練習</h3> | |
| <p>以下題目需找出體積及表面積</p> | |
| <ol> | |
| <li>邊長 2cm 的正方體</li> | |
| <li>長 520cm，闊 13cm，高 14cm 的長方體</li> | |
| <li>半徑 3cm，高 4cm，(a)圓柱體，(b)圓錐體</li> | |
| </ol> | |
| <h2 id="對稱">對稱</h2> | |
| <h3 id="解釋-6">解釋</h3> | |
| <p><img src="https://mathspace-production-media.mathspace.co/media/upload/2015-06-20-21_00_11-_cube-plane2.svg-inkscape.png" alt="Image result for axis of rotational symmetry"></p> | |
| <ol> | |
| <li>旋轉對稱軸：係個立體中間穿一條線</li> | |
| <li>對稱面：係中間斬一下，然後兩邊一樣</li> | |
| </ol> | |
| <h3 id="習題-5">習題</h3> | |
| <p>對上圖而言</p> | |
| <ol> | |
| <li>找出多兩條對稱軸</li> | |
| <li>找出多兩塊對稱面</li> | |
| </ol> | |
| <h3 id="試前練習-6">試前練習</h3> | |
| <p>對上圖而言</p> | |
| <ol> | |
| <li>畫出多三條對稱軸</li> | |
| <li>畫出多三塊對稱面</li> | |
| </ol> | |
| <h2 id="因式分解">因式分解</h2> | |
| <h3 id="示例">示例</h3> | |
| <p>以下是逐步用calc機程式解決因式分解的問題</p> | |
| <h4 id="一個字母，最多2次方">一個字母，最多2次方</h4> | |
| <ol> | |
| <li>題目係 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>−</mo><mn>6</mn><mi>x</mi><mo>+</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow><annotation encoding="application/x-tex">-6x+2x^2+4</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.814108em;"></span><span class="strut bottom" style="height: 0.897438em; vertical-align: -0.08333em;"></span><span class="base"><span class="mord">−</span><span class="mord mathrm">6</span><span class="mord mathit">x</span><span class="mbin">+</span><span class="mord mathrm">2</span><span class="mord"><span class="mord mathit">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span><span class="mbin">+</span><span class="mord mathrm">4</span></span></span></span></span></li> | |
| <li>以<span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.43056em;"></span><span class="strut bottom" style="height: 0.43056em; vertical-align: 0em;"></span><span class="base"><span class="mord mathit">x</span></span></span></span></span>嘅指數（即係右上角嗰個）大至少咁排，<br> | |
| 變做 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>6</mn><mi>x</mi><mo>+</mo><mn>4</mn></mrow><annotation encoding="application/x-tex">2x^2-6x+4</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.814108em;"></span><span class="strut bottom" style="height: 0.897438em; vertical-align: -0.08333em;"></span><span class="base"><span class="mord mathrm">2</span><span class="mord"><span class="mord mathit">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span><span class="mbin">−</span><span class="mord mathrm">6</span><span class="mord mathit">x</span><span class="mbin">+</span><span class="mord mathrm">4</span></span></span></span></span></li> | |
| <li>禁 program 1，<br> | |
| 首先入 2，然後 -6，跟住 4，<br> | |
| <strong>注意正負號呀</strong></li> | |
| <li>首先會出兩個數字，唔駛理佢</li> | |
| <li>然後按照下面嘅順序寫答案出嚟</li> | |
| </ol> | |
| <table> | |
| <thead> | |
| <tr> | |
| <th>次序</th> | |
| <th>數字</th> | |
| <th>答案</th> | |
| <th>解說</th> | |
| </tr> | |
| </thead> | |
| <tbody> | |
| <tr> | |
| <td>1</td> | |
| <td>1</td> | |
| <td><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>(</mo><mi>x</mi></mrow><annotation encoding="application/x-tex">(x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.75em;"></span><span class="strut bottom" style="height: 1em; vertical-align: -0.25em;"></span><span class="base"><span class="mopen">(</span><span class="mord mathit">x</span></span></span></span></span></td> | |
| <td>個數字係1所以唔駛寫出嚟</td> | |
| </tr> | |
| <tr> | |
| <td>2</td> | |
| <td>-2</td> | |
| <td><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>(</mo><mi>x</mi><mo>−</mo><mn>2</mn><mo>)</mo></mrow><annotation encoding="application/x-tex">(x-2)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.75em;"></span><span class="strut bottom" style="height: 1em; vertical-align: -0.25em;"></span><span class="base"><span class="mopen">(</span><span class="mord mathit">x</span><span class="mbin">−</span><span class="mord mathrm">2</span><span class="mclose">)</span></span></span></span></span></td> | |
| <td>無x嘅項，注意正負號</td> | |
| </tr> | |
| <tr> | |
| <td>3</td> | |
| <td>1</td> | |
| <td><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>(</mo><mi>x</mi><mo>−</mo><mn>2</mn><mo>)</mo><mo>(</mo><mi>x</mi></mrow><annotation encoding="application/x-tex">(x-2)(x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.75em;"></span><span class="strut bottom" style="height: 1em; vertical-align: -0.25em;"></span><span class="base"><span class="mopen">(</span><span class="mord mathit">x</span><span class="mbin">−</span><span class="mord mathrm">2</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord mathit">x</span></span></span></span></span></td> | |
| <td>個數字係1所以唔駛寫出嚟</td> | |
| </tr> | |
| <tr> | |
| <td>4</td> | |
| <td>-1</td> | |
| <td><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>(</mo><mi>x</mi><mo>−</mo><mn>2</mn><mo>)</mo><mo>(</mo><mi>x</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><annotation encoding="application/x-tex">(x-2)(x-1)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.75em;"></span><span class="strut bottom" style="height: 1em; vertical-align: -0.25em;"></span><span class="base"><span class="mopen">(</span><span class="mord mathit">x</span><span class="mbin">−</span><span class="mord mathrm">2</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord mathit">x</span><span class="mbin">−</span><span class="mord mathrm">1</span><span class="mclose">)</span></span></span></span></span></td> | |
| <td>無x嘅項，注意正負號</td> | |
| </tr> | |
| <tr> | |
| <td>5</td> | |
| <td>2</td> | |
| <td><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>2</mn><mo>(</mo><mi>x</mi><mo>−</mo><mn>2</mn><mo>)</mo><mo>(</mo><mi>x</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><annotation encoding="application/x-tex">2(x-2)(x-1)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.75em;"></span><span class="strut bottom" style="height: 1em; vertical-align: -0.25em;"></span><span class="base"><span class="mord mathrm">2</span><span class="mopen">(</span><span class="mord mathit">x</span><span class="mbin">−</span><span class="mord mathrm">2</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord mathit">x</span><span class="mbin">−</span><span class="mord mathrm">1</span><span class="mclose">)</span></span></span></span></span></td> | |
| <td>最後嘅數係2，所以就要成條式乘返2，如果係1就唔使寫出黎</td> | |
| </tr> | |
| </tbody> | |
| </table><h4 id="一個字母，最多2次方，無咗中間個項">一個字母，最多2次方，無咗中間個項</h4> | |
| <ol> | |
| <li>題目係 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>8</mn><mo>−</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">8-2x^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.814108em;"></span><span class="strut bottom" style="height: 0.897438em; vertical-align: -0.08333em;"></span><span class="base"><span class="mord mathrm">8</span><span class="mbin">−</span><span class="mord mathrm">2</span><span class="mord"><span class="mord mathit">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span></span></span></span></span></li> | |
| <li>以<span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.43056em;"></span><span class="strut bottom" style="height: 0.43056em; vertical-align: 0em;"></span><span class="base"><span class="mord mathit">x</span></span></span></span></span>嘅指數（即係右上角嗰個）大至少咁排，<br> | |
| 變做 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>−</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn></mrow><annotation encoding="application/x-tex">-2x^2+8</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.814108em;"></span><span class="strut bottom" style="height: 0.897438em; vertical-align: -0.08333em;"></span><span class="base"><span class="mord">−</span><span class="mord mathrm">2</span><span class="mord"><span class="mord mathit">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span><span class="mbin">+</span><span class="mord mathrm">8</span></span></span></span></span></li> | |
| <li>因為冇咗中間果個 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.43056em;"></span><span class="strut bottom" style="height: 0.43056em; vertical-align: 0em;"></span><span class="base"><span class="mord mathit">x</span></span></span></span></span> 項，所以為正式起見<br> | |
| 加返個 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>+</mo><mn>0</mn><mi>x</mi></mrow><annotation encoding="application/x-tex">+0x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.64444em;"></span><span class="strut bottom" style="height: 0.72777em; vertical-align: -0.08333em;"></span><span class="base"><span class="mord">+</span><span class="mord mathrm">0</span><span class="mord mathit">x</span></span></span></span></span> 項俾佢<br> | |
| 變做 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>−</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>0</mn><mi>x</mi><mo>+</mo><mn>8</mn></mrow><annotation encoding="application/x-tex">-2x^2+0x+8</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.814108em;"></span><span class="strut bottom" style="height: 0.897438em; vertical-align: -0.08333em;"></span><span class="base"><span class="mord">−</span><span class="mord mathrm">2</span><span class="mord"><span class="mord mathit">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span><span class="mbin">+</span><span class="mord mathrm">0</span><span class="mord mathit">x</span><span class="mbin">+</span><span class="mord mathrm">8</span></span></span></span></span></li> | |
| <li>可以照跟返上面個方法入program啦</li> | |
| </ol> | |
| <h4 id="兩個字母，最多二次方">兩個字母，最多二次方</h4> | |
| <ol> | |
| <li>題目係 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>−</mo><mn>6</mn><mi>x</mi><mi>y</mi><mo>+</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><msup><mi>y</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">-6xy+2x^2+4y^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.814108em;"></span><span class="strut bottom" style="height: 1.00855em; vertical-align: -0.19444em;"></span><span class="base"><span class="mord">−</span><span class="mord mathrm">6</span><span class="mord mathit">x</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mbin">+</span><span class="mord mathrm">2</span><span class="mord"><span class="mord mathit">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span><span class="mbin">+</span><span class="mord mathrm">4</span><span class="mord"><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span></span></span></span></span></li> | |
| <li>以<span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.43056em;"></span><span class="strut bottom" style="height: 0.43056em; vertical-align: 0em;"></span><span class="base"><span class="mord mathit">x</span></span></span></span></span>（求其一個字母）嘅指數（即係右上角嗰個）大至少咁排，<br> | |
| 無，嗰個term即係指數當0<br> | |
| 變做 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>6</mn><mi>x</mi><mi>y</mi><mo>+</mo><mn>4</mn><msup><mi>y</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">2x^2-6xy+4y^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.814108em;"></span><span class="strut bottom" style="height: 1.00855em; vertical-align: -0.19444em;"></span><span class="base"><span class="mord mathrm">2</span><span class="mord"><span class="mord mathit">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span><span class="mbin">−</span><span class="mord mathrm">6</span><span class="mord mathit">x</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mbin">+</span><span class="mord mathrm">4</span><span class="mord"><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span></span></span></span></span></li> | |
| <li>禁 program 1，<br> | |
| 首先入 2，然後 -6，跟住 4，<br> | |
| <strong>注意正負號呀</strong></li> | |
| <li>首先會出兩個數字，唔駛理佢</li> | |
| <li>然後按照下面嘅順序寫答案出嚟</li> | |
| </ol> | |
| <table> | |
| <thead> | |
| <tr> | |
| <th>次序</th> | |
| <th>數字</th> | |
| <th>答案</th> | |
| <th>解說</th> | |
| </tr> | |
| </thead> | |
| <tbody> | |
| <tr> | |
| <td>1</td> | |
| <td>1</td> | |
| <td><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>(</mo><mi>x</mi></mrow><annotation encoding="application/x-tex">(x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.75em;"></span><span class="strut bottom" style="height: 1em; vertical-align: -0.25em;"></span><span class="base"><span class="mopen">(</span><span class="mord mathit">x</span></span></span></span></span></td> | |
| <td>x項，個數字係1所以唔駛寫出嚟</td> | |
| </tr> | |
| <tr> | |
| <td>2</td> | |
| <td>-2</td> | |
| <td><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>(</mo><mi>x</mi><mo>−</mo><mn>2</mn><mi>y</mi><mo>)</mo></mrow><annotation encoding="application/x-tex">(x-2y)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.75em;"></span><span class="strut bottom" style="height: 1em; vertical-align: -0.25em;"></span><span class="base"><span class="mopen">(</span><span class="mord mathit">x</span><span class="mbin">−</span><span class="mord mathrm">2</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mclose">)</span></span></span></span></span></td> | |
| <td>y項，注意正負號</td> | |
| </tr> | |
| <tr> | |
| <td>3</td> | |
| <td>1</td> | |
| <td><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>(</mo><mi>x</mi><mo>−</mo><mn>2</mn><mi>y</mi><mo>)</mo><mo>(</mo><mi>x</mi></mrow><annotation encoding="application/x-tex">(x-2y)(x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.75em;"></span><span class="strut bottom" style="height: 1em; vertical-align: -0.25em;"></span><span class="base"><span class="mopen">(</span><span class="mord mathit">x</span><span class="mbin">−</span><span class="mord mathrm">2</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord mathit">x</span></span></span></span></span></td> | |
| <td>x項，個數字係1所以唔駛寫出嚟</td> | |
| </tr> | |
| <tr> | |
| <td>4</td> | |
| <td>-1</td> | |
| <td><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>(</mo><mi>x</mi><mo>−</mo><mn>2</mn><mi>y</mi><mo>)</mo><mo>(</mo><mi>x</mi><mo>−</mo><mi>y</mi><mo>)</mo></mrow><annotation encoding="application/x-tex">(x-2y)(x-y)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.75em;"></span><span class="strut bottom" style="height: 1em; vertical-align: -0.25em;"></span><span class="base"><span class="mopen">(</span><span class="mord mathit">x</span><span class="mbin">−</span><span class="mord mathrm">2</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord mathit">x</span><span class="mbin">−</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mclose">)</span></span></span></span></span></td> | |
| <td>y項，注意正負號</td> | |
| </tr> | |
| <tr> | |
| <td>5</td> | |
| <td>2</td> | |
| <td><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>2</mn><mo>(</mo><mi>x</mi><mo>−</mo><mn>2</mn><mi>y</mi><mo>)</mo><mo>(</mo><mi>x</mi><mo>−</mo><mi>y</mi><mo>)</mo></mrow><annotation encoding="application/x-tex">2(x-2y)(x-y)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.75em;"></span><span class="strut bottom" style="height: 1em; vertical-align: -0.25em;"></span><span class="base"><span class="mord mathrm">2</span><span class="mopen">(</span><span class="mord mathit">x</span><span class="mbin">−</span><span class="mord mathrm">2</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord mathit">x</span><span class="mbin">−</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mclose">)</span></span></span></span></span></td> | |
| <td>最後嘅數係2，所以就要成條式乘返2，如果係1就唔使寫出黎</td> | |
| </tr> | |
| </tbody> | |
| </table><h4 id="二個字母，最多2次方，無咗中間個項">二個字母，最多2次方，無咗中間個項</h4> | |
| <ol> | |
| <li>題目係 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>8</mn><msup><mi>y</mi><mn>2</mn></msup><mo>−</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">8y^2-2x^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.814108em;"></span><span class="strut bottom" style="height: 1.00855em; vertical-align: -0.19444em;"></span><span class="base"><span class="mord mathrm">8</span><span class="mord"><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span><span class="mbin">−</span><span class="mord mathrm">2</span><span class="mord"><span class="mord mathit">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span></span></span></span></span></li> | |
| <li>以<span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.43056em;"></span><span class="strut bottom" style="height: 0.43056em; vertical-align: 0em;"></span><span class="base"><span class="mord mathit">x</span></span></span></span></span>（求其一個字母）嘅指數（即係右上角嗰個）大至少咁排，<br> | |
| 變做 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>−</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><msup><mi>y</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">-2x^2+8y^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.814108em;"></span><span class="strut bottom" style="height: 1.00855em; vertical-align: -0.19444em;"></span><span class="base"><span class="mord">−</span><span class="mord mathrm">2</span><span class="mord"><span class="mord mathit">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span><span class="mbin">+</span><span class="mord mathrm">8</span><span class="mord"><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span></span></span></span></span></li> | |
| <li>因為冇咗中間果個 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.43056em;"></span><span class="strut bottom" style="height: 0.43056em; vertical-align: 0em;"></span><span class="base"><span class="mord mathit">x</span></span></span></span></span> 項，所以為正式起見<br> | |
| 加返個 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>+</mo><mn>0</mn><mi>x</mi><mi>y</mi></mrow><annotation encoding="application/x-tex">+0xy</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.64444em;"></span><span class="strut bottom" style="height: 0.83888em; vertical-align: -0.19444em;"></span><span class="base"><span class="mord">+</span><span class="mord mathrm">0</span><span class="mord mathit">x</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span></span></span></span></span> 項俾佢<br> | |
| 變做 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>−</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>0</mn><mi>x</mi><mi>y</mi><mo>+</mo><mn>8</mn><msup><mi>y</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">-2x^2+0xy+8y^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.814108em;"></span><span class="strut bottom" style="height: 1.00855em; vertical-align: -0.19444em;"></span><span class="base"><span class="mord">−</span><span class="mord mathrm">2</span><span class="mord"><span class="mord mathit">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span><span class="mbin">+</span><span class="mord mathrm">0</span><span class="mord mathit">x</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mbin">+</span><span class="mord mathrm">8</span><span class="mord"><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span></span></span></span></span></li> | |
| <li>可以照跟返上面個方法入program啦</li> | |
| </ol> | |
| <h3 id="習題-6">習題</h3> | |
| <p>因式分解以下算式</p> | |
| <ol> | |
| <li><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>−</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>4</mn></mrow><annotation encoding="application/x-tex">-2x+12x^2-4</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.814108em;"></span><span class="strut bottom" style="height: 0.897438em; vertical-align: -0.08333em;"></span><span class="base"><span class="mord">−</span><span class="mord mathrm">2</span><span class="mord mathit">x</span><span class="mbin">+</span><span class="mord mathrm">1</span><span class="mord mathrm">2</span><span class="mord"><span class="mord mathit">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span><span class="mbin">−</span><span class="mord mathrm">4</span></span></span></span></span></li> | |
| <li><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>−</mo><mn>2</mn><mi>x</mi><mi>y</mi><mo>+</mo><mn>1</mn><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>4</mn><msup><mi>y</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">-2xy+12x^2-4y^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.814108em;"></span><span class="strut bottom" style="height: 1.00855em; vertical-align: -0.19444em;"></span><span class="base"><span class="mord">−</span><span class="mord mathrm">2</span><span class="mord mathit">x</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mbin">+</span><span class="mord mathrm">1</span><span class="mord mathrm">2</span><span class="mord"><span class="mord mathit">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span><span class="mbin">−</span><span class="mord mathrm">4</span><span class="mord"><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span></span></span></span></span></li> | |
| <li><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>−</mo><mn>2</mn><mn>7</mn><mo>+</mo><mn>1</mn><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">-27+12x^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.814108em;"></span><span class="strut bottom" style="height: 0.897438em; vertical-align: -0.08333em;"></span><span class="base"><span class="mord">−</span><span class="mord mathrm">2</span><span class="mord mathrm">7</span><span class="mbin">+</span><span class="mord mathrm">1</span><span class="mord mathrm">2</span><span class="mord"><span class="mord mathit">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span></span></span></span></span></li> | |
| <li><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>−</mo><mn>2</mn><mn>7</mn><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">-27y^2+12x^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.814108em;"></span><span class="strut bottom" style="height: 1.00855em; vertical-align: -0.19444em;"></span><span class="base"><span class="mord">−</span><span class="mord mathrm">2</span><span class="mord mathrm">7</span><span class="mord"><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span><span class="mbin">+</span><span class="mord mathrm">1</span><span class="mord mathrm">2</span><span class="mord"><span class="mord mathit">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span></span></span></span></span></li> | |
| </ol> | |
| <h3 id="試前練習-7">試前練習</h3> | |
| <ol> | |
| <li><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>−</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>4</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>2</mn><mn>0</mn></mrow><annotation encoding="application/x-tex">-2x+4x^2-20</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.814108em;"></span><span class="strut bottom" style="height: 0.897438em; vertical-align: -0.08333em;"></span><span class="base"><span class="mord">−</span><span class="mord mathrm">2</span><span class="mord mathit">x</span><span class="mbin">+</span><span class="mord mathrm">4</span><span class="mord"><span class="mord mathit">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span><span class="mbin">−</span><span class="mord mathrm">2</span><span class="mord mathrm">0</span></span></span></span></span></li> | |
| <li><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>−</mo><mn>2</mn><mi>x</mi><mi>y</mi><mo>+</mo><mn>4</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>2</mn><mn>0</mn><msup><mi>y</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">-2xy+4x^2-20y^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.814108em;"></span><span class="strut bottom" style="height: 1.00855em; vertical-align: -0.19444em;"></span><span class="base"><span class="mord">−</span><span class="mord mathrm">2</span><span class="mord mathit">x</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mbin">+</span><span class="mord mathrm">4</span><span class="mord"><span class="mord mathit">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span><span class="mbin">−</span><span class="mord mathrm">2</span><span class="mord mathrm">0</span><span class="mord"><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span></span></span></span></span></li> | |
| <li><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>−</mo><mn>5</mn><mn>0</mn><mo>+</mo><mn>1</mn><mn>8</mn><msup><mi>x</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">-50+18x^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.814108em;"></span><span class="strut bottom" style="height: 0.897438em; vertical-align: -0.08333em;"></span><span class="base"><span class="mord">−</span><span class="mord mathrm">5</span><span class="mord mathrm">0</span><span class="mbin">+</span><span class="mord mathrm">1</span><span class="mord mathrm">8</span><span class="mord"><span class="mord mathit">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span></span></span></span></span></li> | |
| <li><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>−</mo><mn>5</mn><msup><mn>0</mn><mn>2</mn></msup><mo>+</mo><mn>1</mn><mn>8</mn><msup><mi>x</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">-50^2+18x^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.814108em;"></span><span class="strut bottom" style="height: 0.897438em; vertical-align: -0.08333em;"></span><span class="base"><span class="mord">−</span><span class="mord mathrm">5</span><span class="mord"><span class="mord mathrm">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span><span class="mbin">+</span><span class="mord mathrm">1</span><span class="mord mathrm">8</span><span class="mord"><span class="mord mathit">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span></span></span></span></span></li> | |
| </ol> | |
| <h2 id="調換主項">調換主項</h2> | |
| <h3 id="示例-1">示例</h3> | |
| <h4 id="分數類">分數類</h4> | |
| <table> | |
| <thead> | |
| <tr> | |
| <th>解說</th> | |
| <th>步驟</th> | |
| </tr> | |
| </thead> | |
| <tbody> | |
| <tr> | |
| <td>題目，答案以<span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.43056em;"></span><span class="strut bottom" style="height: 0.43056em; vertical-align: 0em;"></span><span class="base"><span class="mord mathit">x</span></span></span></span></span>為主項</td> | |
| <td><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mfrac><mrow><mn>3</mn><mi>a</mi></mrow><mrow><mn>2</mn><mi>x</mi><mo>+</mo><mn>3</mn><mi>y</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn><mi>b</mi></mrow><mrow><mn>3</mn><mi>x</mi><mo>+</mo><mn>5</mn><mi>y</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac {3a} {2x+3y}=\frac {2b} {3x+5y}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.880108em;"></span><span class="strut bottom" style="height: 1.36122em; vertical-align: -0.481108em;"></span><span class="base"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.845108em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathrm mtight">2</span><span class="mord mathit mtight">x</span><span class="mbin mtight">+</span><span class="mord mathrm mtight">3</span><span class="mord mathit mtight" style="margin-right: 0.03588em;">y</span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathrm mtight">3</span><span class="mord mathit mtight">a</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.481108em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mrel">=</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.880108em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathrm mtight">3</span><span class="mord mathit mtight">x</span><span class="mbin mtight">+</span><span class="mord mathrm mtight">5</span><span class="mord mathit mtight" style="margin-right: 0.03588em;">y</span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathrm mtight">2</span><span class="mord mathit mtight">b</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.481108em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></td> | |
| </tr> | |
| <tr> | |
| <td>將兩邊嘅分母（如有）乘返去另外一面到</td> | |
| <td><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>3</mn><mi>a</mi><mrow><mo fence="true">(</mo><mn>3</mn><mi>x</mi><mo>+</mo><mn>5</mn><mi>y</mi><mo fence="true">)</mo></mrow><mo>=</mo><mn>2</mn><mi>b</mi><mrow><mo fence="true">(</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>3</mn><mi>y</mi><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">3a\left(3x+5y\right)=2b\left(2x+3y\right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.75em;"></span><span class="strut bottom" style="height: 1em; vertical-align: -0.25em;"></span><span class="base"><span class="mord mathrm">3</span><span class="mord mathit">a</span><span class="minner"><span class="mopen delimcenter" style="top: 0em;">(</span><span class="mord mathrm">3</span><span class="mord mathit">x</span><span class="mbin">+</span><span class="mord mathrm">5</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mclose delimcenter" style="top: 0em;">)</span></span><span class="mrel">=</span><span class="mord mathrm">2</span><span class="mord mathit">b</span><span class="minner"><span class="mopen delimcenter" style="top: 0em;">(</span><span class="mord mathrm">2</span><span class="mord mathit">x</span><span class="mbin">+</span><span class="mord mathrm">3</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mclose delimcenter" style="top: 0em;">)</span></span></span></span></span></span></td> | |
| </tr> | |
| <tr> | |
| <td>拆括號 can be skipped</td> | |
| <td><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>3</mn><mi>a</mi><mo>(</mo><mn>3</mn><mi>x</mi><mo>)</mo><mo>+</mo><mn>3</mn><mi>a</mi><mo>(</mo><mn>5</mn><mi>y</mi><mo>)</mo><mo>=</mo><mn>2</mn><mi>b</mi><mo>(</mo><mn>2</mn><mi>x</mi><mo>)</mo><mo>+</mo><mn>2</mn><mi>b</mi><mo>(</mo><mn>3</mn><mi>y</mi><mo>)</mo></mrow><annotation encoding="application/x-tex">3a(3x)+3a(5y)=2b(2x)+2b(3y)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.75em;"></span><span class="strut bottom" style="height: 1em; vertical-align: -0.25em;"></span><span class="base"><span class="mord mathrm">3</span><span class="mord mathit">a</span><span class="mopen">(</span><span class="mord mathrm">3</span><span class="mord mathit">x</span><span class="mclose">)</span><span class="mbin">+</span><span class="mord mathrm">3</span><span class="mord mathit">a</span><span class="mopen">(</span><span class="mord mathrm">5</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mclose">)</span><span class="mrel">=</span><span class="mord mathrm">2</span><span class="mord mathit">b</span><span class="mopen">(</span><span class="mord mathrm">2</span><span class="mord mathit">x</span><span class="mclose">)</span><span class="mbin">+</span><span class="mord mathrm">2</span><span class="mord mathit">b</span><span class="mopen">(</span><span class="mord mathrm">3</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mclose">)</span></span></span></span></span></td> | |
| </tr> | |
| <tr> | |
| <td>乘埋</td> | |
| <td><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>9</mn><mi>a</mi><mi>x</mi><mo>+</mo><mn>1</mn><mn>5</mn><mi>a</mi><mi>y</mi><mo>=</mo><mn>4</mn><mi>b</mi><mi>x</mi><mo>+</mo><mn>6</mn><mi>b</mi><mi>y</mi></mrow><annotation encoding="application/x-tex">9ax+15ay=4bx+6by</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.69444em;"></span><span class="strut bottom" style="height: 0.88888em; vertical-align: -0.19444em;"></span><span class="base"><span class="mord mathrm">9</span><span class="mord mathit">a</span><span class="mord mathit">x</span><span class="mbin">+</span><span class="mord mathrm">1</span><span class="mord mathrm">5</span><span class="mord mathit">a</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mrel">=</span><span class="mord mathrm">4</span><span class="mord mathit">b</span><span class="mord mathit">x</span><span class="mbin">+</span><span class="mord mathrm">6</span><span class="mord mathit">b</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span></span></span></span></span></td> | |
| </tr> | |
| <tr> | |
| <td>無 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.43056em;"></span><span class="strut bottom" style="height: 0.43056em; vertical-align: 0em;"></span><span class="base"><span class="mord mathit">x</span></span></span></span></span> 嘅項調去右面，有 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.43056em;"></span><span class="strut bottom" style="height: 0.43056em; vertical-align: 0em;"></span><span class="base"><span class="mord mathit">x</span></span></span></span></span> 嘅調去另外一面</td> | |
| <td><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>9</mn><mi>a</mi><mi>x</mi><mo>−</mo><mn>4</mn><mi>b</mi><mi>x</mi><mo>=</mo><mn>6</mn><mi>b</mi><mi>y</mi><mo>−</mo><mn>1</mn><mn>5</mn><mi>a</mi><mi>y</mi></mrow><annotation encoding="application/x-tex">9ax-4bx=6by-15ay</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.69444em;"></span><span class="strut bottom" style="height: 0.88888em; vertical-align: -0.19444em;"></span><span class="base"><span class="mord mathrm">9</span><span class="mord mathit">a</span><span class="mord mathit">x</span><span class="mbin">−</span><span class="mord mathrm">4</span><span class="mord mathit">b</span><span class="mord mathit">x</span><span class="mrel">=</span><span class="mord mathrm">6</span><span class="mord mathit">b</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mbin">−</span><span class="mord mathrm">1</span><span class="mord mathrm">5</span><span class="mord mathit">a</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span></span></span></span></span></td> | |
| </tr> | |
| <tr> | |
| <td>兩面抽因子</td> | |
| <td><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>x</mi><mo>(</mo><mn>9</mn><mi>a</mi><mo>−</mo><mn>4</mn><mi>b</mi><mo>)</mo><mo>=</mo><mn>3</mn><mi>y</mi><mo>(</mo><mn>2</mn><mi>b</mi><mo>−</mo><mn>5</mn><mi>a</mi><mo>)</mo></mrow><annotation encoding="application/x-tex">x(9a-4b)=3y(2b-5a)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.75em;"></span><span class="strut bottom" style="height: 1em; vertical-align: -0.25em;"></span><span class="base"><span class="mord mathit">x</span><span class="mopen">(</span><span class="mord mathrm">9</span><span class="mord mathit">a</span><span class="mbin">−</span><span class="mord mathrm">4</span><span class="mord mathit">b</span><span class="mclose">)</span><span class="mrel">=</span><span class="mord mathrm">3</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mopen">(</span><span class="mord mathrm">2</span><span class="mord mathit">b</span><span class="mbin">−</span><span class="mord mathrm">5</span><span class="mord mathit">a</span><span class="mclose">)</span></span></span></span></span></td> | |
| </tr> | |
| <tr> | |
| <td>將有x嗰面嘅其他嘢調過去另外嗰面</td> | |
| <td><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>x</mi><mo>=</mo><mfrac><mrow><mn>3</mn><mi>y</mi><mo>(</mo><mn>2</mn><mi>b</mi><mo>−</mo><mn>5</mn><mi>a</mi><mo>)</mo></mrow><mrow><mo>(</mo><mn>9</mn><mi>a</mi><mo>−</mo><mn>4</mn><mi>b</mi><mo>)</mo></mrow></mfrac></mrow><annotation encoding="application/x-tex">x=\frac{3y(2b-5a)}{(9a-4b)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 1.01em;"></span><span class="strut bottom" style="height: 1.53em; vertical-align: -0.52em;"></span><span class="base"><span class="mord mathit">x</span><span class="mrel">=</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 1.01em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathrm mtight">9</span><span class="mord mathit mtight">a</span><span class="mbin mtight">−</span><span class="mord mathrm mtight">4</span><span class="mord mathit mtight">b</span><span class="mclose mtight">)</span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.485em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathrm mtight">3</span><span class="mord mathit mtight" style="margin-right: 0.03588em;">y</span><span class="mopen mtight">(</span><span class="mord mathrm mtight">2</span><span class="mord mathit mtight">b</span><span class="mbin mtight">−</span><span class="mord mathrm mtight">5</span><span class="mord mathit mtight">a</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.52em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></td> | |
| </tr> | |
| </tbody> | |
| </table><h4 id="個主項原本係另外一個">個主項原本係另外一個</h4> | |
| <h5 id="方法一，唔係次次都用得架">方法一，唔係次次都用得架</h5> | |
| <p><s><strong>只適用於得一面先有x個陣，而且啲 x term 可以group埋一齊</strong></s> 無必要都係唔好用，你唔熟好易錯</p> | |
| <table> | |
| <thead> | |
| <tr> | |
| <th>解說</th> | |
| <th>步驟</th> | |
| </tr> | |
| </thead> | |
| <tbody> | |
| <tr> | |
| <td>題目，答案以<span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.43056em;"></span><span class="strut bottom" style="height: 0.43056em; vertical-align: 0em;"></span><span class="base"><span class="mord mathit">x</span></span></span></span></span>為主項</td> | |
| <td><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>2</mn><mi>y</mi><mo>=</mo><mi>a</mi><mo>+</mo><mfrac><mi>b</mi><mi>x</mi></mfrac><mo>+</mo><mfrac><mi>c</mi><mi>x</mi></mfrac></mrow><annotation encoding="application/x-tex">2y=a+\frac b x +\frac c x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.880108em;"></span><span class="strut bottom" style="height: 1.22511em; vertical-align: -0.345em;"></span><span class="base"><span class="mord mathrm">2</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mrel">=</span><span class="mord mathit">a</span><span class="mbin">+</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.880108em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathit mtight">x</span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathit mtight">b</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.345em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mbin">+</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.695392em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathit mtight">x</span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathit mtight">c</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.345em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></td> | |
| </tr> | |
| <tr> | |
| <td>將啲有x嘅term合埋一齊</td> | |
| <td><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>2</mn><mi>y</mi><mo>=</mo><mi>a</mi><mo>+</mo><mfrac><mrow><mi>b</mi><mo>+</mo><mi>c</mi></mrow><mi>x</mi></mfrac></mrow><annotation encoding="application/x-tex">2y=a+\frac{b+c}x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.880108em;"></span><span class="strut bottom" style="height: 1.22511em; vertical-align: -0.345em;"></span><span class="base"><span class="mord mathrm">2</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mrel">=</span><span class="mord mathit">a</span><span class="mbin">+</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.880108em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathit mtight">x</span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathit mtight">b</span><span class="mbin mtight">+</span><span class="mord mathit mtight">c</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.345em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></td> | |
| </tr> | |
| <tr> | |
| <td>無 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.43056em;"></span><span class="strut bottom" style="height: 0.43056em; vertical-align: 0em;"></span><span class="base"><span class="mord mathit">x</span></span></span></span></span> 嘅項調去右面，有 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.43056em;"></span><span class="strut bottom" style="height: 0.43056em; vertical-align: 0em;"></span><span class="base"><span class="mord mathit">x</span></span></span></span></span> 嘅調去另外一面</td> | |
| <td><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>2</mn><mi>y</mi><mo>−</mo><mi>a</mi><mo>=</mo><mfrac><mrow><mi>b</mi><mo>+</mo><mi>c</mi></mrow><mi>x</mi></mfrac></mrow><annotation encoding="application/x-tex">2y-a=\frac {b+c} x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.880108em;"></span><span class="strut bottom" style="height: 1.22511em; vertical-align: -0.345em;"></span><span class="base"><span class="mord mathrm">2</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mbin">−</span><span class="mord mathit">a</span><span class="mrel">=</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.880108em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathit mtight">x</span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathit mtight">b</span><span class="mbin mtight">+</span><span class="mord mathit mtight">c</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.345em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></td> | |
| </tr> | |
| <tr> | |
| <td>將有x嗰面嘅其他嘢調過去另外嗰面</td> | |
| <td><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>x</mi><mo>=</mo><mfrac><mrow><mi>b</mi><mo>+</mo><mi>c</mi></mrow><mrow><mn>2</mn><mi>y</mi><mo>−</mo><mi>a</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">x=\frac{b+c}{2y-a}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.880108em;"></span><span class="strut bottom" style="height: 1.36122em; vertical-align: -0.481108em;"></span><span class="base"><span class="mord mathit">x</span><span class="mrel">=</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.880108em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathrm mtight">2</span><span class="mord mathit mtight" style="margin-right: 0.03588em;">y</span><span class="mbin mtight">−</span><span class="mord mathit mtight">a</span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathit mtight">b</span><span class="mbin mtight">+</span><span class="mord mathit mtight">c</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.481108em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></td> | |
| </tr> | |
| </tbody> | |
| </table><h5 id="方法二，煩啲，但係通常都用到">方法二，煩啲，但係通常都用到</h5> | |
| <table> | |
| <thead> | |
| <tr> | |
| <th>解說</th> | |
| <th>步驟</th> | |
| </tr> | |
| </thead> | |
| <tbody> | |
| <tr> | |
| <td>題目，答案以<span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.43056em;"></span><span class="strut bottom" style="height: 0.43056em; vertical-align: 0em;"></span><span class="base"><span class="mord mathit">x</span></span></span></span></span>為主項</td> | |
| <td><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>2</mn><mi>y</mi><mo>=</mo><mi>a</mi><mo>+</mo><mfrac><mi>b</mi><mi>x</mi></mfrac><mo>+</mo><mfrac><mi>c</mi><mi>x</mi></mfrac></mrow><annotation encoding="application/x-tex">2y=a+\frac b x +\frac c x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.880108em;"></span><span class="strut bottom" style="height: 1.22511em; vertical-align: -0.345em;"></span><span class="base"><span class="mord mathrm">2</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mrel">=</span><span class="mord mathit">a</span><span class="mbin">+</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.880108em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathit mtight">x</span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathit mtight">b</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.345em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mbin">+</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.695392em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathit mtight">x</span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathit mtight">c</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.345em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></td> | |
| </tr> | |
| <tr> | |
| <td>將兩邊嘅分母（如有）乘返去另外一面到</td> | |
| <td><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>2</mn><mi>y</mi><mi>x</mi><mo>=</mo><mi>a</mi><mi>x</mi><mo>+</mo><mi>b</mi><mo>+</mo><mi>c</mi></mrow><annotation encoding="application/x-tex">2yx=ax+b+c</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.69444em;"></span><span class="strut bottom" style="height: 0.88888em; vertical-align: -0.19444em;"></span><span class="base"><span class="mord mathrm">2</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mord mathit">x</span><span class="mrel">=</span><span class="mord mathit">a</span><span class="mord mathit">x</span><span class="mbin">+</span><span class="mord mathit">b</span><span class="mbin">+</span><span class="mord mathit">c</span></span></span></span></span></td> | |
| </tr> | |
| <tr> | |
| <td>無 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.43056em;"></span><span class="strut bottom" style="height: 0.43056em; vertical-align: 0em;"></span><span class="base"><span class="mord mathit">x</span></span></span></span></span> 嘅項調去右面，有 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.43056em;"></span><span class="strut bottom" style="height: 0.43056em; vertical-align: 0em;"></span><span class="base"><span class="mord mathit">x</span></span></span></span></span> 嘅調去另外一面</td> | |
| <td><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>2</mn><mi>y</mi><mi>x</mi><mo>−</mo><mi>a</mi><mi>x</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>c</mi></mrow><annotation encoding="application/x-tex">2yx-ax=b+c</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.69444em;"></span><span class="strut bottom" style="height: 0.88888em; vertical-align: -0.19444em;"></span><span class="base"><span class="mord mathrm">2</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mord mathit">x</span><span class="mbin">−</span><span class="mord mathit">a</span><span class="mord mathit">x</span><span class="mrel">=</span><span class="mord mathit">b</span><span class="mbin">+</span><span class="mord mathit">c</span></span></span></span></span></td> | |
| </tr> | |
| <tr> | |
| <td>兩面抽因子</td> | |
| <td><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>x</mi><mo>(</mo><mn>2</mn><mi>y</mi><mo>−</mo><mi>a</mi><mo>)</mo><mo>=</mo><mi>b</mi><mo>+</mo><mi>c</mi></mrow><annotation encoding="application/x-tex">x(2y-a)=b+c</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.75em;"></span><span class="strut bottom" style="height: 1em; vertical-align: -0.25em;"></span><span class="base"><span class="mord mathit">x</span><span class="mopen">(</span><span class="mord mathrm">2</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mbin">−</span><span class="mord mathit">a</span><span class="mclose">)</span><span class="mrel">=</span><span class="mord mathit">b</span><span class="mbin">+</span><span class="mord mathit">c</span></span></span></span></span></td> | |
| </tr> | |
| <tr> | |
| <td>將有x嗰面嘅其他嘢調過去另外嗰面</td> | |
| <td><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>x</mi><mo>=</mo><mfrac><mrow><mi>b</mi><mo>+</mo><mi>c</mi></mrow><mrow><mn>2</mn><mi>y</mi><mo>−</mo><mi>a</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">x=\frac{b+c}{2y-a}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.880108em;"></span><span class="strut bottom" style="height: 1.36122em; vertical-align: -0.481108em;"></span><span class="base"><span class="mord mathit">x</span><span class="mrel">=</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.880108em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathrm mtight">2</span><span class="mord mathit mtight" style="margin-right: 0.03588em;">y</span><span class="mbin mtight">−</span><span class="mord mathit mtight">a</span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathit mtight">b</span><span class="mbin mtight">+</span><span class="mord mathit mtight">c</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.481108em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></td> | |
| </tr> | |
| </tbody> | |
| </table><h3 id="習題-7">習題</h3> | |
| <ol> | |
| <li><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mfrac><mrow><mi>a</mi></mrow><mrow><mn>3</mn><mo>+</mo><mi>b</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>5</mn><mo>+</mo><mn>7</mn><mi>b</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac {a}{3+b}=\frac{3}{5+7b}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.845108em;"></span><span class="strut bottom" style="height: 1.24844em; vertical-align: -0.403331em;"></span><span class="base"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.695392em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathrm mtight">3</span><span class="mbin mtight">+</span><span class="mord mathit mtight">b</span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathit mtight">a</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.403331em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mrel">=</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.845108em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathrm mtight">5</span><span class="mbin mtight">+</span><span class="mord mathrm mtight">7</span><span class="mord mathit mtight">b</span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathrm mtight">3</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.403331em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span> ( <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>b</mi></mrow><annotation encoding="application/x-tex">b</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.69444em;"></span><span class="strut bottom" style="height: 0.69444em; vertical-align: 0em;"></span><span class="base"><span class="mord mathit">b</span></span></span></span></span> 為主項)</li> | |
| <li><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>a</mi><mi>y</mi><mo>=</mo><mn>3</mn><mo>+</mo><mfrac><mn>5</mn><mi>x</mi></mfrac><mo>+</mo><mfrac><mi>b</mi><mrow><mn>2</mn><mi>x</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">ay=3+\frac 5 x +\frac b {2x}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.880108em;"></span><span class="strut bottom" style="height: 1.22511em; vertical-align: -0.345em;"></span><span class="base"><span class="mord mathit">a</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mrel">=</span><span class="mord mathrm">3</span><span class="mbin">+</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.845108em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathit mtight">x</span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">5</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.345em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mbin">+</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.880108em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathrm mtight">2</span><span class="mord mathit mtight">x</span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathit mtight">b</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.345em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span> ( <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.43056em;"></span><span class="strut bottom" style="height: 0.43056em; vertical-align: 0em;"></span><span class="base"><span class="mord mathit">x</span></span></span></span></span> 為主項)</li> | |
| </ol> | |
| <h3 id="試前練習-8">試前練習</h3> | |
| <ol> | |
| <li><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mfrac><mrow><mn>2</mn><mi>a</mi></mrow><mrow><mn>5</mn><mo>+</mo><mn>3</mn><mi>b</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>4</mn></mrow><mrow><mn>9</mn><mo>+</mo><mn>8</mn><mi>b</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac {2a}{5+3b}=\frac{4}{9+8b}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.845108em;"></span><span class="strut bottom" style="height: 1.24844em; vertical-align: -0.403331em;"></span><span class="base"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.845108em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathrm mtight">5</span><span class="mbin mtight">+</span><span class="mord mathrm mtight">3</span><span class="mord mathit mtight">b</span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathrm mtight">2</span><span class="mord mathit mtight">a</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.403331em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mrel">=</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.845108em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathrm mtight">9</span><span class="mbin mtight">+</span><span class="mord mathrm mtight">8</span><span class="mord mathit mtight">b</span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathrm mtight">4</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.403331em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span> ( <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>b</mi></mrow><annotation encoding="application/x-tex">b</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.69444em;"></span><span class="strut bottom" style="height: 0.69444em; vertical-align: 0em;"></span><span class="base"><span class="mord mathit">b</span></span></span></span></span> 為主項)</li> | |
| <li><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>2</mn><mi>a</mi><mi>y</mi><mo>=</mo><mn>5</mn><mo>+</mo><mfrac><mn>7</mn><mrow><mn>3</mn><mi>x</mi></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>2</mn><mi>b</mi></mrow><mrow><mn>2</mn><mi>x</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">2ay=5+\frac 7 {3x} +\frac {2b} {2x}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.880108em;"></span><span class="strut bottom" style="height: 1.22511em; vertical-align: -0.345em;"></span><span class="base"><span class="mord mathrm">2</span><span class="mord mathit">a</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mrel">=</span><span class="mord mathrm">5</span><span class="mbin">+</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.845108em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathrm mtight">3</span><span class="mord mathit mtight">x</span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">7</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.345em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mbin">+</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.880108em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathrm mtight">2</span><span class="mord mathit mtight">x</span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathrm mtight">2</span><span class="mord mathit mtight">b</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.345em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span> ( <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.43056em;"></span><span class="strut bottom" style="height: 0.43056em; vertical-align: 0em;"></span><span class="base"><span class="mord mathit">x</span></span></span></span></span> 為主項)</li> | |
| </ol> | |
| <h2 id="解方程">解方程</h2> | |
| <h3 id="示例-2">示例</h3> | |
| <p>以下例子使用計算機程式二解二元一次方程</p> | |
| <table> | |
| <thead> | |
| <tr> | |
| <th>解釋</th> | |
| <th>步驟</th> | |
| </tr> | |
| </thead> | |
| <tbody> | |
| <tr> | |
| <td>原題目</td> | |
| <td><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>[</mo><mn>2</mn><mo>(</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>)</mo><mo>=</mo><mn>3</mn><mo>(</mo><mn>5</mn><mi>y</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>]</mo></mrow><annotation encoding="application/x-tex">[2(x+3)=3(5y+1)]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.75em;"></span><span class="strut bottom" style="height: 1em; vertical-align: -0.25em;"></span><span class="base"><span class="mopen">[</span><span class="mord mathrm">2</span><span class="mopen">(</span><span class="mord mathit">x</span><span class="mbin">+</span><span class="mord mathrm">3</span><span class="mclose">)</span><span class="mrel">=</span><span class="mord mathrm">3</span><span class="mopen">(</span><span class="mord mathrm">5</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mbin">+</span><span class="mord mathrm">1</span><span class="mclose">)</span><span class="mclose">]</span></span></span></span></span> <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>[</mo><mn>3</mn><mo>(</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>=</mo><mi>y</mi><mo>+</mo><mn>3</mn><mo>]</mo></mrow><annotation encoding="application/x-tex">[3(2x+1)=y+3]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.75em;"></span><span class="strut bottom" style="height: 1em; vertical-align: -0.25em;"></span><span class="base"><span class="mopen">[</span><span class="mord mathrm">3</span><span class="mopen">(</span><span class="mord mathrm">2</span><span class="mord mathit">x</span><span class="mbin">+</span><span class="mord mathrm">1</span><span class="mclose">)</span><span class="mrel">=</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mbin">+</span><span class="mord mathrm">3</span><span class="mclose">]</span></span></span></span></span></td> | |
| </tr> | |
| <tr> | |
| <td>拆括號</td> | |
| <td><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>[</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>6</mn><mo>=</mo><mn>1</mn><mn>5</mn><mi>y</mi><mo>+</mo><mn>3</mn><mo>]</mo></mrow><annotation encoding="application/x-tex">[2x+6=15y+3]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.75em;"></span><span class="strut bottom" style="height: 1em; vertical-align: -0.25em;"></span><span class="base"><span class="mopen">[</span><span class="mord mathrm">2</span><span class="mord mathit">x</span><span class="mbin">+</span><span class="mord mathrm">6</span><span class="mrel">=</span><span class="mord mathrm">1</span><span class="mord mathrm">5</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mbin">+</span><span class="mord mathrm">3</span><span class="mclose">]</span></span></span></span></span> <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>[</mo><mn>6</mn><mi>x</mi><mo>+</mo><mn>3</mn><mo>=</mo><mi>y</mi><mo>+</mo><mn>3</mn><mo>]</mo></mrow><annotation encoding="application/x-tex">[6x+3=y+3]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.75em;"></span><span class="strut bottom" style="height: 1em; vertical-align: -0.25em;"></span><span class="base"><span class="mopen">[</span><span class="mord mathrm">6</span><span class="mord mathit">x</span><span class="mbin">+</span><span class="mord mathrm">3</span><span class="mrel">=</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mbin">+</span><span class="mord mathrm">3</span><span class="mclose">]</span></span></span></span></span></td> | |
| </tr> | |
| <tr> | |
| <td>有xy嘅擺左邊 冇xy嘅擺右邊 然後計好加減</td> | |
| <td><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>[</mo><mn>2</mn><mi>x</mi><mo>−</mo><mn>1</mn><mn>5</mn><mi>y</mi><mo>=</mo><mn>3</mn><mo>−</mo><mn>6</mn><mo>=</mo><mo>−</mo><mn>3</mn><mo>]</mo></mrow><annotation encoding="application/x-tex">[2x-15y=3-6=-3]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.75em;"></span><span class="strut bottom" style="height: 1em; vertical-align: -0.25em;"></span><span class="base"><span class="mopen">[</span><span class="mord mathrm">2</span><span class="mord mathit">x</span><span class="mbin">−</span><span class="mord mathrm">1</span><span class="mord mathrm">5</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mrel">=</span><span class="mord mathrm">3</span><span class="mbin">−</span><span class="mord mathrm">6</span><span class="mrel">=</span><span class="mord">−</span><span class="mord mathrm">3</span><span class="mclose">]</span></span></span></span></span> <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>[</mo><mn>6</mn><mi>x</mi><mo>−</mo><mi>y</mi><mo>=</mo><mn>0</mn><mo>]</mo></mrow><annotation encoding="application/x-tex">[6x-y=0]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.75em;"></span><span class="strut bottom" style="height: 1em; vertical-align: -0.25em;"></span><span class="base"><span class="mopen">[</span><span class="mord mathrm">6</span><span class="mord mathit">x</span><span class="mbin">−</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mrel">=</span><span class="mord mathrm">0</span><span class="mclose">]</span></span></span></span></span></td> | |
| </tr> | |
| <tr> | |
| <td>首先入咗第一條式先 依次序係 2 -15 -3</td> | |
| <td><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>2</mn><mi>x</mi><mo>−</mo><mn>1</mn><mn>5</mn><mi>y</mi><mo>=</mo><mo>−</mo><mn>3</mn></mrow><annotation encoding="application/x-tex">2x-15y=-3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.64444em;"></span><span class="strut bottom" style="height: 0.83888em; vertical-align: -0.19444em;"></span><span class="base"><span class="mord mathrm">2</span><span class="mord mathit">x</span><span class="mbin">−</span><span class="mord mathrm">1</span><span class="mord mathrm">5</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mrel">=</span><span class="mord">−</span><span class="mord mathrm">3</span></span></span></span></span></td> | |
| </tr> | |
| <tr> | |
| <td>然後入3次0</td> | |
| <td></td> | |
| </tr> | |
| <tr> | |
| <td>最後入第二條式 依次序係 6 -1 0</td> | |
| <td><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>6</mn><mi>x</mi><mo>−</mo><mi>y</mi><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">6x-y=0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.64444em;"></span><span class="strut bottom" style="height: 0.83888em; vertical-align: -0.19444em;"></span><span class="base"><span class="mord mathrm">6</span><span class="mord mathit">x</span><span class="mbin">−</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mrel">=</span><span class="mord mathrm">0</span></span></span></span></span></td> | |
| </tr> | |
| <tr> | |
| <td>第1個輸出係x嘅值</td> | |
| <td><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>x</mi><mo>=</mo><mn>3</mn><mi mathvariant="normal">/</mi><mn>8</mn><mn>8</mn></mrow><annotation encoding="application/x-tex">x=3/88</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.75em;"></span><span class="strut bottom" style="height: 1em; vertical-align: -0.25em;"></span><span class="base"><span class="mord mathit">x</span><span class="mrel">=</span><span class="mord mathrm">3</span><span class="mord mathrm">/</span><span class="mord mathrm">8</span><span class="mord mathrm">8</span></span></span></span></span></td> | |
| </tr> | |
| <tr> | |
| <td>第二個輸出係y嘅值</td> | |
| <td><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>y</mi><mo>=</mo><mn>9</mn><mi mathvariant="normal">/</mi><mn>4</mn><mn>4</mn></mrow><annotation encoding="application/x-tex">y=9/44</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.75em;"></span><span class="strut bottom" style="height: 1em; vertical-align: -0.25em;"></span><span class="base"><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mrel">=</span><span class="mord mathrm">9</span><span class="mord mathrm">/</span><span class="mord mathrm">4</span><span class="mord mathrm">4</span></span></span></span></span></td> | |
| </tr> | |
| </tbody> | |
| </table><p>當一邊係同x有關嘅分母，另外一面y有關嘅分母</p> | |
| <table> | |
| <thead> | |
| <tr> | |
| <th>解釋</th> | |
| <th>步驟</th> | |
| </tr> | |
| </thead> | |
| <tbody> | |
| <tr> | |
| <td>原題目</td> | |
| <td><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>[</mo><mfrac><mn>2</mn><mrow><mo>(</mo><mn>5</mn><mi>y</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mfrac><mo>=</mo><mfrac><mn>3</mn><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>)</mo></mrow></mfrac><mo>]</mo></mrow><annotation encoding="application/x-tex">[\frac2{(5y+1)}=\frac 3{(x+3)}]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.845108em;"></span><span class="strut bottom" style="height: 1.36511em; vertical-align: -0.52em;"></span><span class="base"><span class="mopen">[</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.845108em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathrm mtight">5</span><span class="mord mathit mtight" style="margin-right: 0.03588em;">y</span><span class="mbin mtight">+</span><span class="mord mathrm mtight">1</span><span class="mclose mtight">)</span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.52em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mrel">=</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.845108em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathit mtight">x</span><span class="mbin mtight">+</span><span class="mord mathrm mtight">3</span><span class="mclose mtight">)</span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">3</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.52em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose">]</span></span></span></span></span> <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>[</mo><mfrac><mn>3</mn><mrow><mi>y</mi><mo>+</mo><mn>3</mn></mrow></mfrac><mo>=</mo><mfrac><mn>1</mn><mrow><mo>(</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mfrac><mo>]</mo></mrow><annotation encoding="application/x-tex">[\frac 3{y+3}=\frac 1 {(2x+1)}]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.845108em;"></span><span class="strut bottom" style="height: 1.36511em; vertical-align: -0.52em;"></span><span class="base"><span class="mopen">[</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.845108em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathit mtight" style="margin-right: 0.03588em;">y</span><span class="mbin mtight">+</span><span class="mord mathrm mtight">3</span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">3</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.481108em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mrel">=</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.845108em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathrm mtight">2</span><span class="mord mathit mtight">x</span><span class="mbin mtight">+</span><span class="mord mathrm mtight">1</span><span class="mclose mtight">)</span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.52em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose">]</span></span></span></span></span></td> | |
| </tr> | |
| <tr> | |
| <td>將啲分母調返過去另外一邊</td> | |
| <td><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>[</mo><mn>2</mn><mo>(</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>)</mo><mo>=</mo><mn>3</mn><mo>(</mo><mn>5</mn><mi>y</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>]</mo></mrow><annotation encoding="application/x-tex">[2(x+3)=3(5y+1)]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.75em;"></span><span class="strut bottom" style="height: 1em; vertical-align: -0.25em;"></span><span class="base"><span class="mopen">[</span><span class="mord mathrm">2</span><span class="mopen">(</span><span class="mord mathit">x</span><span class="mbin">+</span><span class="mord mathrm">3</span><span class="mclose">)</span><span class="mrel">=</span><span class="mord mathrm">3</span><span class="mopen">(</span><span class="mord mathrm">5</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mbin">+</span><span class="mord mathrm">1</span><span class="mclose">)</span><span class="mclose">]</span></span></span></span></span> <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>[</mo><mn>3</mn><mo>(</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>=</mo><mi>y</mi><mo>+</mo><mn>3</mn><mo>]</mo></mrow><annotation encoding="application/x-tex">[3(2x+1)=y+3]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.75em;"></span><span class="strut bottom" style="height: 1em; vertical-align: -0.25em;"></span><span class="base"><span class="mopen">[</span><span class="mord mathrm">3</span><span class="mopen">(</span><span class="mord mathrm">2</span><span class="mord mathit">x</span><span class="mbin">+</span><span class="mord mathrm">1</span><span class="mclose">)</span><span class="mrel">=</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mbin">+</span><span class="mord mathrm">3</span><span class="mclose">]</span></span></span></span></span></td> | |
| </tr> | |
| <tr> | |
| <td>可以用返上面果個方法做</td> | |
| <td></td> | |
| </tr> | |
| </tbody> | |
| </table><h3 id="習題-8">習題</h3> | |
| <ol> | |
| <li><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>2</mn><mi>x</mi><mo>+</mo><mn>5</mn><mi>y</mi><mo>−</mo><mn>7</mn><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">2x+5y-7=0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.64444em;"></span><span class="strut bottom" style="height: 0.83888em; vertical-align: -0.19444em;"></span><span class="base"><span class="mord mathrm">2</span><span class="mord mathit">x</span><span class="mbin">+</span><span class="mord mathrm">5</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mbin">−</span><span class="mord mathrm">7</span><span class="mrel">=</span><span class="mord mathrm">0</span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>3</mn><mi>x</mi><mo>−</mo><mn>4</mn><mi>y</mi><mo>=</mo><mn>3</mn><mo>−</mo><mn>5</mn><mi>x</mi></mrow><annotation encoding="application/x-tex">3x-4y=3-5x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.64444em;"></span><span class="strut bottom" style="height: 0.83888em; vertical-align: -0.19444em;"></span><span class="base"><span class="mord mathrm">3</span><span class="mord mathit">x</span><span class="mbin">−</span><span class="mord mathrm">4</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mrel">=</span><span class="mord mathrm">3</span><span class="mbin">−</span><span class="mord mathrm">5</span><span class="mord mathit">x</span></span></span></span></span></li> | |
| <li><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>3</mn><mo>(</mo><mi>x</mi><mo>+</mo><mn>2</mn><mi>y</mi><mo>)</mo><mo>=</mo><mn>5</mn><mo>(</mo><mi>y</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><annotation encoding="application/x-tex">3(x+2y)=5(y+1)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.75em;"></span><span class="strut bottom" style="height: 1em; vertical-align: -0.25em;"></span><span class="base"><span class="mord mathrm">3</span><span class="mopen">(</span><span class="mord mathit">x</span><span class="mbin">+</span><span class="mord mathrm">2</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mclose">)</span><span class="mrel">=</span><span class="mord mathrm">5</span><span class="mopen">(</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mbin">+</span><span class="mord mathrm">1</span><span class="mclose">)</span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>2</mn><mo>(</mo><mi>x</mi><mo>+</mo><mn>5</mn><mo>)</mo><mo>=</mo><mn>7</mn><mo>(</mo><mn>3</mn><mi>y</mi><mo>+</mo><mn>8</mn><mo>)</mo></mrow><annotation encoding="application/x-tex">2(x+5)=7(3y+8)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.75em;"></span><span class="strut bottom" style="height: 1em; vertical-align: -0.25em;"></span><span class="base"><span class="mord mathrm">2</span><span class="mopen">(</span><span class="mord mathit">x</span><span class="mbin">+</span><span class="mord mathrm">5</span><span class="mclose">)</span><span class="mrel">=</span><span class="mord mathrm">7</span><span class="mopen">(</span><span class="mord mathrm">3</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mbin">+</span><span class="mord mathrm">8</span><span class="mclose">)</span></span></span></span></span></li> | |
| <li><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mfrac><mn>2</mn><mrow><mn>3</mn><mi>x</mi><mo>+</mo><mi>y</mi></mrow></mfrac><mo>=</mo><mfrac><mn>5</mn><mrow><mn>2</mn><mi>y</mi><mo>+</mo><mn>1</mn></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac 2 {3x+y}=\frac 5 {2y+1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.845108em;"></span><span class="strut bottom" style="height: 1.32622em; vertical-align: -0.481108em;"></span><span class="base"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.845108em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathrm mtight">3</span><span class="mord mathit mtight">x</span><span class="mbin mtight">+</span><span class="mord mathit mtight" style="margin-right: 0.03588em;">y</span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.481108em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mrel">=</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.845108em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathrm mtight">2</span><span class="mord mathit mtight" style="margin-right: 0.03588em;">y</span><span class="mbin mtight">+</span><span class="mord mathrm mtight">1</span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">5</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.481108em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mfrac><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mn>3</mn></mfrac><mo>=</mo><mfrac><mrow><mi>y</mi><mo>+</mo><mn>2</mn></mrow><mn>7</mn></mfrac></mrow><annotation encoding="application/x-tex">\frac {x+1} 3=\frac {y+2} 7</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.897216em;"></span><span class="strut bottom" style="height: 1.24222em; vertical-align: -0.345em;"></span><span class="base"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.845108em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">3</span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathit mtight">x</span><span class="mbin mtight">+</span><span class="mord mathrm mtight">1</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.345em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mrel">=</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.897216em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">7</span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.44611em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathit mtight" style="margin-right: 0.03588em;">y</span><span class="mbin mtight">+</span><span class="mord mathrm mtight">2</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.345em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></li> | |
| </ol> | |
| <h3 id="試前練習-9">試前練習</h3> | |
| <ol> | |
| <li><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>3</mn><mi>x</mi><mo>+</mo><mn>7</mn><mi>y</mi><mo>−</mo><mn>5</mn><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">3x+7y-5=0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.64444em;"></span><span class="strut bottom" style="height: 0.83888em; vertical-align: -0.19444em;"></span><span class="base"><span class="mord mathrm">3</span><span class="mord mathit">x</span><span class="mbin">+</span><span class="mord mathrm">7</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mbin">−</span><span class="mord mathrm">5</span><span class="mrel">=</span><span class="mord mathrm">0</span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>x</mi><mo>−</mo><mn>2</mn><mi>y</mi><mo>=</mo><mn>7</mn><mo>−</mo><mn>3</mn><mi>x</mi></mrow><annotation encoding="application/x-tex">x-2y=7-3x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.64444em;"></span><span class="strut bottom" style="height: 0.83888em; vertical-align: -0.19444em;"></span><span class="base"><span class="mord mathit">x</span><span class="mbin">−</span><span class="mord mathrm">2</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mrel">=</span><span class="mord mathrm">7</span><span class="mbin">−</span><span class="mord mathrm">3</span><span class="mord mathit">x</span></span></span></span></span></li> | |
| <li><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>7</mn><mo>(</mo><mn>5</mn><mi>x</mi><mo>+</mo><mn>2</mn><mi>y</mi><mo>)</mo><mo>=</mo><mn>2</mn><mo>(</mo><mn>3</mn><mi>y</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><annotation encoding="application/x-tex">7(5x+2y)=2(3y+1)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.75em;"></span><span class="strut bottom" style="height: 1em; vertical-align: -0.25em;"></span><span class="base"><span class="mord mathrm">7</span><span class="mopen">(</span><span class="mord mathrm">5</span><span class="mord mathit">x</span><span class="mbin">+</span><span class="mord mathrm">2</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mclose">)</span><span class="mrel">=</span><span class="mord mathrm">2</span><span class="mopen">(</span><span class="mord mathrm">3</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mbin">+</span><span class="mord mathrm">1</span><span class="mclose">)</span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>3</mn><mo>(</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>7</mn><mo>)</mo><mo>=</mo><mn>5</mn><mo>(</mo><mn>2</mn><mi>y</mi><mo>+</mo><mn>9</mn><mo>)</mo></mrow><annotation encoding="application/x-tex">3(2x+7)=5(2y+9)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.75em;"></span><span class="strut bottom" style="height: 1em; vertical-align: -0.25em;"></span><span class="base"><span class="mord mathrm">3</span><span class="mopen">(</span><span class="mord mathrm">2</span><span class="mord mathit">x</span><span class="mbin">+</span><span class="mord mathrm">7</span><span class="mclose">)</span><span class="mrel">=</span><span class="mord mathrm">5</span><span class="mopen">(</span><span class="mord mathrm">2</span><span class="mord mathit" style="margin-right: 0.03588em;">y</span><span class="mbin">+</span><span class="mord mathrm">9</span><span class="mclose">)</span></span></span></span></span></li> | |
| <li><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mfrac><mn>2</mn><mrow><mn>5</mn><mi>x</mi><mo>+</mo><mn>2</mn><mi>y</mi></mrow></mfrac><mo>=</mo><mfrac><mn>7</mn><mrow><mn>3</mn><mi>y</mi><mo>+</mo><mn>1</mn></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac 2 {5x+2y}=\frac 7 {3y+1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.845108em;"></span><span class="strut bottom" style="height: 1.32622em; vertical-align: -0.481108em;"></span><span class="base"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.845108em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathrm mtight">5</span><span class="mord mathit mtight">x</span><span class="mbin mtight">+</span><span class="mord mathrm mtight">2</span><span class="mord mathit mtight" style="margin-right: 0.03588em;">y</span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.481108em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mrel">=</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.845108em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathrm mtight">3</span><span class="mord mathit mtight" style="margin-right: 0.03588em;">y</span><span class="mbin mtight">+</span><span class="mord mathrm mtight">1</span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">7</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.481108em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mfrac><mrow><mn>2</mn><mi>y</mi><mo>+</mo><mn>9</mn></mrow><mn>3</mn></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn><mi>x</mi><mo>+</mo><mn>7</mn></mrow><mn>5</mn></mfrac></mrow><annotation encoding="application/x-tex">\frac {2y+9} 3=\frac {2x+7} 5</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.897216em;"></span><span class="strut bottom" style="height: 1.24222em; vertical-align: -0.345em;"></span><span class="base"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.897216em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">3</span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.44611em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathrm mtight">2</span><span class="mord mathit mtight" style="margin-right: 0.03588em;">y</span><span class="mbin mtight">+</span><span class="mord mathrm mtight">9</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.345em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mrel">=</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.845108em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">5</span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathrm mtight">2</span><span class="mord mathit mtight">x</span><span class="mbin mtight">+</span><span class="mord mathrm mtight">7</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.345em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></li> | |
| </ol> | |
| <h2 id="機率">機率</h2> | |
| <h3 id="解釋-7">解釋</h3> | |
| <ol> | |
| <li>基礎公式：<span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mfrac><mrow><mtext>符合條件的結果數</mtext></mrow><mrow><mtext>總結果數</mtext></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{\text{符合條件的結果數}}{\text{總結果數}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.872331em;"></span><span class="strut bottom" style="height: 1.21733em; vertical-align: -0.345em;"></span><span class="base"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.872331em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mathrm cjk_fallback mtight">總結果數</span></span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mathrm cjk_fallback mtight">符合條件的結果數</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.345em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></li> | |
| <li>不是vs是：<span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>不符合某條件的機率</mtext><mo>=</mo><mn>1</mn><mo>−</mo><mtext>符合某條件的機率</mtext></mrow><annotation encoding="application/x-tex">\text{不符合某條件的機率}=1-\text{符合某條件的機率}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.68333em;"></span><span class="strut bottom" style="height: 0.76666em; vertical-align: -0.08333em;"></span><span class="base"><span class="mord text"><span class="mord mathrm cjk_fallback">不符合某條件的機率</span></span><span class="mrel">=</span><span class="mord mathrm">1</span><span class="mbin">−</span><span class="mord text"><span class="mord mathrm cjk_fallback">符合某條件的機率</span></span></span></span></span></span></li> | |
| <li>抽完<strong>放返落去</strong>：<span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msup><mrow><mo fence="true">(</mo><mfrac><mrow><mtext>抽一次符合／不符合條件的結果數</mtext></mrow><mrow><mtext>抽一次總結果數</mtext></mrow></mfrac><mo fence="true">)</mo></mrow><mtext>次數</mtext></msup></mrow><annotation encoding="application/x-tex">\left(\frac{\text{抽一次符合／不符合條件的結果數}}{\text{抽一次總結果數}}\right)^\text{次數}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 1.10356em;"></span><span class="strut bottom" style="height: 1.45357em; vertical-align: -0.35001em;"></span><span class="base"><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top: 0em;"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.872331em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mathrm cjk_fallback mtight">抽一次總結果數</span></span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mathrm cjk_fallback mtight">抽一次符合／不符合條件的結果數</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.345em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top: 0em;"><span class="delimsizing size1">)</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 1.10356em;"><span class="" style="top: -3.32523em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord text mtight"><span class="mord mathrm cjk_fallback mtight">次數</span></span></span></span></span></span></span></span></span></span></span></span></span></li> | |
| <li>抽完<strong>唔放返落去</strong>，抽極都抽唔中：<span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mrow><mo fence="true">(</mo><mfrac><mrow><mtext>抽一次抽唔中的結果數</mtext></mrow><mrow><mtext>抽一次總結果數</mtext></mrow></mfrac><mo fence="true">)</mo></mrow><mrow><mo fence="true">(</mo><mfrac><mrow><mtext>抽一次抽唔中的結果數</mtext></mrow><mrow><mtext>抽一次總結果數</mtext><mo>−</mo><mn>1</mn></mrow></mfrac><mo fence="true">)</mo></mrow><mrow><mo fence="true">(</mo><mfrac><mrow><mtext>抽一次抽唔中的結果數</mtext></mrow><mrow><mtext>抽一次總結果數</mtext><mo>−</mo><mn>2</mn></mrow></mfrac><mo fence="true">)</mo></mrow><mo>⋯</mo><mo>⋯</mo></mrow><annotation encoding="application/x-tex">\left(\frac{\text{抽一次抽唔中的結果數}}{\text{抽一次總結果數}}\right)\left(\frac{\text{抽一次抽唔中的結果數}}{\text{抽一次總結果數}-1}\right)\left(\frac{\text{抽一次抽唔中的結果數}}{\text{抽一次總結果數}-2}\right) \cdots\cdots</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.872331em;"></span><span class="strut bottom" style="height: 1.27566em; vertical-align: -0.403331em;"></span><span class="base"><span class="minner"><span class="mopen delimcenter" style="top: 0em;"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.872331em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mathrm cjk_fallback mtight">抽一次總結果數</span></span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mathrm cjk_fallback mtight">抽一次抽唔中的結果數</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.345em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top: 0em;"><span class="delimsizing size1">)</span></span></span><span class="minner"><span class="mopen delimcenter" style="top: 0em;"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.872331em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mathrm cjk_fallback mtight">抽一次總結果數</span></span><span class="mbin mtight">−</span><span class="mord mathrm mtight">1</span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mathrm cjk_fallback mtight">抽一次抽唔中的結果數</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.403331em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top: 0em;"><span class="delimsizing size1">)</span></span></span><span class="minner"><span class="mopen delimcenter" style="top: 0em;"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.872331em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mathrm cjk_fallback mtight">抽一次總結果數</span></span><span class="mbin mtight">−</span><span class="mord mathrm mtight">2</span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mathrm cjk_fallback mtight">抽一次抽唔中的結果數</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.403331em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top: 0em;"><span class="delimsizing size1">)</span></span></span><span class="minner">⋯</span><span class="minner">⋯</span></span></span></span></span><br> | |
| 抽幾多次就有幾多個項，例如抽兩次就 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mrow><mo fence="true">(</mo><mfrac><mrow><mtext>抽一次抽唔中的結果數</mtext></mrow><mrow><mtext>抽一次總結果數</mtext></mrow></mfrac><mo fence="true">)</mo></mrow><mrow><mo fence="true">(</mo><mfrac><mrow><mtext>抽一次抽唔中的結果數</mtext></mrow><mrow><mtext>抽一次總結果數</mtext><mo>−</mo><mn>1</mn></mrow></mfrac><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">\left(\frac{\text{抽一次抽唔中的結果數}}{\text{抽一次總結果數}}\right)\left(\frac{\text{抽一次抽唔中的結果數}}{\text{抽一次總結果數}-1}\right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.872331em;"></span><span class="strut bottom" style="height: 1.27566em; vertical-align: -0.403331em;"></span><span class="base"><span class="minner"><span class="mopen delimcenter" style="top: 0em;"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.872331em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mathrm cjk_fallback mtight">抽一次總結果數</span></span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mathrm cjk_fallback mtight">抽一次抽唔中的結果數</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.345em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top: 0em;"><span class="delimsizing size1">)</span></span></span><span class="minner"><span class="mopen delimcenter" style="top: 0em;"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.872331em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mathrm cjk_fallback mtight">抽一次總結果數</span></span><span class="mbin mtight">−</span><span class="mord mathrm mtight">1</span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mathrm cjk_fallback mtight">抽一次抽唔中的結果數</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.403331em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top: 0em;"><span class="delimsizing size1">)</span></span></span></span></span></span></span></li> | |
| <li>抽完<strong>唔放返落去</strong>，不斷抽中：<span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mrow><mo fence="true">(</mo><mfrac><mrow><mtext>抽一次抽中的結果數</mtext></mrow><mrow><mtext>抽一次總結果數</mtext></mrow></mfrac><mo fence="true">)</mo></mrow><mrow><mo fence="true">(</mo><mfrac><mrow><mtext>抽一次抽中的結果數-1</mtext></mrow><mrow><mtext>抽一次總結果數</mtext><mo>−</mo><mn>1</mn></mrow></mfrac><mo fence="true">)</mo></mrow><mrow><mo fence="true">(</mo><mfrac><mrow><mtext>抽一次抽中的結果數-2</mtext></mrow><mrow><mtext>抽一次總結果數</mtext><mo>−</mo><mn>2</mn></mrow></mfrac><mo fence="true">)</mo></mrow><mo>⋯</mo><mo>⋯</mo></mrow><annotation encoding="application/x-tex">\left(\frac{\text{抽一次抽中的結果數}}{\text{抽一次總結果數}}\right)\left(\frac{\text{抽一次抽中的結果數-1}}{\text{抽一次總結果數}-1}\right)\left(\frac{\text{抽一次抽中的結果數-2}}{\text{抽一次總結果數}-2}\right) \cdots\cdots</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.872331em;"></span><span class="strut bottom" style="height: 1.27566em; vertical-align: -0.403331em;"></span><span class="base"><span class="minner"><span class="mopen delimcenter" style="top: 0em;"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.872331em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mathrm cjk_fallback mtight">抽一次總結果數</span></span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mathrm cjk_fallback mtight">抽一次抽中的結果數</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.345em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top: 0em;"><span class="delimsizing size1">)</span></span></span><span class="minner"><span class="mopen delimcenter" style="top: 0em;"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.872331em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mathrm cjk_fallback mtight">抽一次總結果數</span></span><span class="mbin mtight">−</span><span class="mord mathrm mtight">1</span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mathrm cjk_fallback mtight">抽一次抽中的結果數</span><span class="mord mathrm mtight">-1</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.403331em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top: 0em;"><span class="delimsizing size1">)</span></span></span><span class="minner"><span class="mopen delimcenter" style="top: 0em;"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.872331em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mathrm cjk_fallback mtight">抽一次總結果數</span></span><span class="mbin mtight">−</span><span class="mord mathrm mtight">2</span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mathrm cjk_fallback mtight">抽一次抽中的結果數</span><span class="mord mathrm mtight">-2</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.403331em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top: 0em;"><span class="delimsizing size1">)</span></span></span><span class="minner">⋯</span><span class="minner">⋯</span></span></span></span></span><br> | |
| 抽幾多次就有幾多個項，例如抽兩次就 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mrow><mo fence="true">(</mo><mfrac><mrow><mtext>抽一次抽中的結果數</mtext></mrow><mrow><mtext>抽一次總結果數</mtext></mrow></mfrac><mo fence="true">)</mo></mrow><mrow><mo fence="true">(</mo><mfrac><mrow><mtext>抽一次抽中的結果數</mtext><mo>−</mo><mn>1</mn></mrow><mrow><mtext>抽一次總結果數</mtext><mo>−</mo><mn>1</mn></mrow></mfrac><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">\left(\frac{\text{抽一次抽中的結果數}}{\text{抽一次總結果數}}\right)\left(\frac{\text{抽一次抽中的結果數}-1}{\text{抽一次總結果數}-1}\right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.872331em;"></span><span class="strut bottom" style="height: 1.27566em; vertical-align: -0.403331em;"></span><span class="base"><span class="minner"><span class="mopen delimcenter" style="top: 0em;"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.872331em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mathrm cjk_fallback mtight">抽一次總結果數</span></span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mathrm cjk_fallback mtight">抽一次抽中的結果數</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.345em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top: 0em;"><span class="delimsizing size1">)</span></span></span><span class="minner"><span class="mopen delimcenter" style="top: 0em;"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.872331em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mathrm cjk_fallback mtight">抽一次總結果數</span></span><span class="mbin mtight">−</span><span class="mord mathrm mtight">1</span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mathrm cjk_fallback mtight">抽一次抽中的結果數</span></span><span class="mbin mtight">−</span><span class="mord mathrm mtight">1</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.403331em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top: 0em;"><span class="delimsizing size1">)</span></span></span></span></span></span></span></li> | |
| </ol> | |
| <h3 id="習題-9">習題</h3> | |
| <p>以下題目中，白球3個，黃球5個，紅球7個</p> | |
| <ol> | |
| <li>抽中白波嘅機率</li> | |
| <li>抽唔中白波嘅機率</li> | |
| <li>抽完之後放返落去，抽4次，都係紅波嘅機會率</li> | |
| <li>抽完之後唔放返落去，抽4次，都係紅波嘅機會率</li> | |
| <li>抽完之後唔放返落去，抽4次，都唔係紅波嘅機會率</li> | |
| </ol> | |
| <h3 id="試前練習-10">試前練習</h3> | |
| <p>以下題目中，白球6個，黃球8個，紅球13個</p> | |
| <ol> | |
| <li>抽中白波嘅機率</li> | |
| <li>抽唔中白波嘅機率</li> | |
| <li>抽完之後放返落去，抽4次，都係紅波嘅機會率</li> | |
| <li>抽完之後唔放返落去，抽4次，都係紅波嘅機會率</li> | |
| <li>抽完之後唔放返落去，抽4次，都唔係紅波嘅機會率</li> | |
| </ol> | |
| <h2 id="座標">座標</h2> | |
| <h3 id="解釋-8">解釋</h3> | |
| <ol> | |
| <li>斜率：<span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mfrac><mrow><mtext>第一點嘅y座標</mtext><mo>−</mo><mtext>第二點嘅y座標</mtext></mrow><mrow><mtext>第一點嘅x座標</mtext><mo>−</mo><mtext>第二點嘅x座標</mtext></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{\text{第一點嘅y座標}-\text{第二點嘅y座標}}{\text{第一點嘅x座標}-\text{第二點嘅x座標}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.924439em;"></span><span class="strut bottom" style="height: 1.32777em; vertical-align: -0.403331em;"></span><span class="base"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.924439em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mathrm cjk_fallback mtight">第一點嘅</span><span class="mord mathrm mtight">x</span><span class="mord mathrm cjk_fallback mtight">座標</span></span><span class="mbin mtight">−</span><span class="mord text mtight"><span class="mord mathrm cjk_fallback mtight">第二點嘅</span><span class="mord mathrm mtight">x</span><span class="mord mathrm cjk_fallback mtight">座標</span></span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.44611em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mathrm cjk_fallback mtight">第一點嘅</span><span class="mord mathrm mtight">y</span><span class="mord mathrm cjk_fallback mtight">座標</span></span><span class="mbin mtight">−</span><span class="mord text mtight"><span class="mord mathrm cjk_fallback mtight">第二點嘅</span><span class="mord mathrm mtight">y</span><span class="mord mathrm cjk_fallback mtight">座標</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.403331em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span><br> | |
| <img src="http://www.mathwarehouse.com/algebra/linear_equation/images/slope-of-a-line/simple/slope-formula-simple.png" alt="Image result for slope"></li> | |
| <li>距離：<span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msqrt><mrow><msup><mrow><mo fence="true">(</mo><mtext>第一點嘅y座標</mtext><mo>−</mo><mtext>第二點嘅y座標</mtext><mo fence="true">)</mo></mrow><mn>2</mn></msup><mo>+</mo><msup><mrow><mo fence="true">(</mo><mtext>第一點嘅x座標</mtext><mo>−</mo><mtext>第二點嘅x座標</mtext><mo fence="true">)</mo></mrow><mn>2</mn></msup></mrow></msqrt></mrow><annotation encoding="application/x-tex">\sqrt{\left(\text{第一點嘅y座標}-\text{第二點嘅y座標}\right)^2+\left(\text{第一點嘅x座標}-\text{第二點嘅x座標}\right)^2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 1.337em;"></span><span class="strut bottom" style="height: 1.84em; vertical-align: -0.502996em;"></span><span class="base"><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist svg-align" style="height: 1.337em;"><span class="" style="top: -3.8em;"><span class="pstrut" style="height: 3.8em;"></span><span class="mord" style="padding-left: 1em;"><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top: 0em;">(</span><span class="mord text"><span class="mord mathrm cjk_fallback">第一點嘅</span><span class="mord mathrm">y</span><span class="mord mathrm cjk_fallback">座標</span></span><span class="mbin">−</span><span class="mord text"><span class="mord mathrm cjk_fallback">第二點嘅</span><span class="mord mathrm">y</span><span class="mord mathrm cjk_fallback">座標</span></span><span class="mclose delimcenter" style="top: 0em;">)</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.954008em;"><span class="" style="top: -3.2029em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span><span class="mbin">+</span><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top: 0em;">(</span><span class="mord text"><span class="mord mathrm cjk_fallback">第一點嘅</span><span class="mord mathrm">x</span><span class="mord mathrm cjk_fallback">座標</span></span><span class="mbin">−</span><span class="mord text"><span class="mord mathrm cjk_fallback">第二點嘅</span><span class="mord mathrm">x</span><span class="mord mathrm cjk_fallback">座標</span></span><span class="mclose delimcenter" style="top: 0em;">)</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.954008em;"><span class="" style="top: -3.2029em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span></span></span><span class="" style="top: -3.297em;"><span class="pstrut" style="height: 3.8em;"></span><span class="hide-tail" style="min-width: 1.02em; height: 1.8em;"><svg width="400em" height="1.8em" viewBox="0 0 400000 1800" preserveAspectRatio="xMinYMin slice"><path d="M1001 0h398999v40H1013.084S929.667 308 749 | |
| 880s-277 876.333-289 913c-4.667 4.667-12.667 7-24 7h-12c-1.333-3.333-3.667 | |
| -11.667-7-25-35.333-125.333-106.667-373.333-214-744-10 12-21 25-33 39l-32 39 | |
| c-6-5.333-15-14-27-26l25-30c26.667-32.667 52-63 76-91l52-60 208 722c56-175.333 | |
| 126.333-397.333 211-666s153.833-488.167 207.5-658.5C944.167 129.167 975 32.667 | |
| 983 10c4-6.667 10-10 18-10zm0 0h398999v40H1013z"></path></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.502996em;"></span></span></span></span></span></span></span></span><br> | |
| <img src="https://files.askiitians.com/cdn1/images/2014714-162824642-1952-1.jpg" alt="Image result for shortest distance"></li> | |
| <li>三點嘅面積：畫個圖出嚟先，跟住睇下有無兩點連埋係打橫或者打直嘅，個條線做底，然後剩低個點同條線嘅距離做高</li> | |
| <li>線同點嘅最短距離：係個點到，畫一條同條題目線垂直嘅線去題目線到，畫出嚟嗰條線就係最短距離<br> | |
| <img src="http://i1303.photobucket.com/albums/ag142/ignatz_mouse/line0_zpsf8fbf404.png" alt="Image result for shortest distance"></li> | |
| <li><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>中點嘅x座標</mtext><mo>=</mo><mfrac><mrow><mtext>第一點嘅x座標</mtext><mo>+</mo><mtext>第二點嘅x座標</mtext></mrow><mn>2</mn></mfrac></mrow><annotation encoding="application/x-tex">\text{中點嘅x座標}=\frac{\text{第一點嘅x座標}+\text{第二點嘅x座標}}2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.872331em;"></span><span class="strut bottom" style="height: 1.21733em; vertical-align: -0.345em;"></span><span class="base"><span class="mord text"><span class="mord mathrm cjk_fallback">中點嘅</span><span class="mord mathrm">x</span><span class="mord mathrm cjk_fallback">座標</span></span><span class="mrel">=</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.872331em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.394em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mathrm cjk_fallback mtight">第一點嘅</span><span class="mord mathrm mtight">x</span><span class="mord mathrm cjk_fallback mtight">座標</span></span><span class="mbin mtight">+</span><span class="mord text mtight"><span class="mord mathrm cjk_fallback mtight">第二點嘅</span><span class="mord mathrm mtight">x</span><span class="mord mathrm cjk_fallback mtight">座標</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.345em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span><br> | |
| <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>中點嘅y座標</mtext><mo>=</mo><mfrac><mrow><mtext>第一點嘅y座標</mtext><mo>+</mo><mtext>第二點嘅y座標</mtext></mrow><mn>2</mn></mfrac></mrow><annotation encoding="application/x-tex">\text{中點嘅y座標}=\frac{\text{第一點嘅y座標}+\text{第二點嘅y座標}}2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.924439em;"></span><span class="strut bottom" style="height: 1.26944em; vertical-align: -0.345em;"></span><span class="base"><span class="mord text"><span class="mord mathrm cjk_fallback">中點嘅</span><span class="mord mathrm">y</span><span class="mord mathrm cjk_fallback">座標</span></span><span class="mrel">=</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.924439em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line hide-tail" style="height: 0.04em;"><svg width="400em" height="400em" viewBox="0 0 400000 400000" preserveAspectRatio="xMinYMin slice"><path d="M0 0 h400000 v400000 h-400000z M0 0 h400000 v400000 h-400000z"></path></svg></span></span><span class="" style="top: -3.44611em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mathrm cjk_fallback mtight">第一點嘅</span><span class="mord mathrm mtight">y</span><span class="mord mathrm cjk_fallback mtight">座標</span></span><span class="mbin mtight">+</span><span class="mord text mtight"><span class="mord mathrm cjk_fallback mtight">第二點嘅</span><span class="mord mathrm mtight">y</span><span class="mord mathrm cjk_fallback mtight">座標</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.345em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></li> | |
| <li>判斷垂直：<span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mtext>斜率</mtext><mn>1</mn></msub><mo>×</mo><msub><mtext>斜率</mtext><mn>2</mn></msub><mo>=</mo><mo>−</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">\text{斜率}_1\times\text{斜率}_2=-1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.68333em;"></span><span class="strut bottom" style="height: 0.83333em; vertical-align: -0.15em;"></span><span class="base"><span class="mord"><span class="mord text"><span class="mord mathrm cjk_fallback">斜率</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.301108em;"><span class="" style="top: -2.55em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.15em;"></span></span></span></span></span><span class="mbin">×</span><span class="mord"><span class="mord text"><span class="mord mathrm cjk_fallback">斜率</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.301108em;"><span class="" style="top: -2.55em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.15em;"></span></span></span></span></span><span class="mrel">=</span><span class="mord">−</span><span class="mord mathrm">1</span></span></span></span></span></li> | |
| <li>判斷平行：<span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mtext>斜率</mtext><mn>1</mn></msub><mo>=</mo><msub><mtext>斜率</mtext><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">\text{斜率}_1=\text{斜率}_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.68333em;"></span><span class="strut bottom" style="height: 0.83333em; vertical-align: -0.15em;"></span><span class="base"><span class="mord"><span class="mord text"><span class="mord mathrm cjk_fallback">斜率</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.301108em;"><span class="" style="top: -2.55em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.15em;"></span></span></span></span></span><span class="mrel">=</span><span class="mord"><span class="mord text"><span class="mord mathrm cjk_fallback">斜率</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.301108em;"><span class="" style="top: -2.55em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.15em;"></span></span></span></span></span></span></span></span></span></li> | |
| </ol> | |
| <h3 id="習題-10">習題</h3> | |
| <p>見1617卷一乙部q8</p> | |
| <h3 id="試前練習-11">試前練習</h3> | |
| <p>見1516卷一乙部q8</p> | |
| <h2 id="mc-calc-機大法">MC calc 機大法</h2> | |
| <ol> | |
| <li>先入 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>π</mi></mrow><annotation encoding="application/x-tex">\pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.43056em;"></span><span class="strut bottom" style="height: 0.43056em; vertical-align: 0em;"></span><span class="base"><span class="mord mathit" style="margin-right: 0.03588em;">π</span></span></span></span></span> 做 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>X</mi></mrow><annotation encoding="application/x-tex">X</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.68333em;"></span><span class="strut bottom" style="height: 0.68333em; vertical-align: 0em;"></span><span class="base"><span class="mord mathit" style="margin-right: 0.07847em;">X</span></span></span></span></span>，shift -> <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>π</mi></mrow><annotation encoding="application/x-tex">\pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.43056em;"></span><span class="strut bottom" style="height: 0.43056em; vertical-align: 0em;"></span><span class="base"><span class="mord mathit" style="margin-right: 0.03588em;">π</span></span></span></span></span> -> shift -> RCL -> X</li> | |
| <li>再入 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>e</mi></mrow><annotation encoding="application/x-tex">e</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.43056em;"></span><span class="strut bottom" style="height: 0.43056em; vertical-align: 0em;"></span><span class="base"><span class="mord mathit">e</span></span></span></span></span> 做 <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>Y</mi></mrow><annotation encoding="application/x-tex">Y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.68333em;"></span><span class="strut bottom" style="height: 0.68333em; vertical-align: 0em;"></span><span class="base"><span class="mord mathit" style="margin-right: 0.22222em;">Y</span></span></span></span></span>，shift -> <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>e</mi></mrow><annotation encoding="application/x-tex">e</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.43056em;"></span><span class="strut bottom" style="height: 0.43056em; vertical-align: 0em;"></span><span class="base"><span class="mord mathit">e</span></span></span></span></span> -> shift -> RCL -> Y</li> | |
| <li>先試題目俾個條式</li> | |
| <li>再逐個啲選項佢</li> | |
| </ol> | |
| <ul> | |
| <li>記得善用括號／分數，有需要嘅話可以分子分母分開計</li> | |
| <li>要調用 X：alpha -> X ，調用 Y：alpha -> Y</li> | |
| </ul> | |
| </div> | |
| </div> | |
| </body> | |
| </html> |
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