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August 27, 2018 19:35
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| { | |
| "test": { | |
| "title": "S02T05", | |
| "slug": "S02T05", | |
| "description": "Přípravný test k státní maturitě.", | |
| "successfulLimit": 33, | |
| "tasks": [ | |
| { | |
| "slug": "S02T05U01", | |
| "title": "S02T05U01", | |
| "taskText": | |
| "Hladina řeky v místě A byla jednoho dne 22cm pod normálem. V následujících třech dnech postupně stoupala o 10cm, 6cm a 7cm. V dalších dvou dnech postupně klesala o 5cm a 13cm. ", | |
| "question": | |
| "Vyjádřete výslednou vzdálenost hladiny od normálu v místě A.", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "options": [ | |
| { "name": "opt1", "problem": "##15cm##" }, | |
| { "name": "opt2", "problem": "##-15cm##" }, | |
| { "name": "opt3", "problem": "##19cm##" }, | |
| { "name": "opt4", "problem": "##-19cm##" }, | |
| { "name": "opt5", "problem": "jiná hodnota" } | |
| ], | |
| "correctAnswer": ["opt5"] | |
| }, | |
| { | |
| "slug": "S02T05U02", | |
| "title": "S02T05U02", | |
| "question": | |
| "Uvnitř kterého jsou všechna řešení rovnice? $${x+4\\over{x-4}}+{x-5\\over{x+5}}={8\\over3}~~~x\\in\\mathbb{N}~~~[x_1=10]$$", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "options": [ | |
| { "name": "opt1", "problem": "##x_1=10;~x_2=14##" }, | |
| { "name": "opt2", "problem": "##x_1=10;~x_2=14##" }, | |
| { "name": "opt3", "problem": "##x=14##" }, | |
| { "name": "opt4", "problem": "##x=10##" }, | |
| { "name": "opt5", "problem": "jiná hodnota" } | |
| ], | |
| "correctAnswer": ["opt4"] | |
| }, | |
| { | |
| "slug": "S02T05U03", | |
| "title": "S02T05U03", | |
| "question": | |
| "Vypočtěte délku lomené čáry (vyznačena tučně) &&\\images\\tasks\\S02T05\\S02T05P03.jpg&&", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "options": [ | |
| { "name": "opt1", "problem": "##86m##" }, | |
| { "name": "opt2", "problem": "##78m##" }, | |
| { "name": "opt3", "problem": "##93m##" }, | |
| { "name": "opt4", "problem": "##102##" }, | |
| { "name": "opt5", "problem": "##106##" } | |
| ], | |
| "correctAnswer": ["opt3"] | |
| }, | |
| { | |
| "slug": "S02T05U04", | |
| "title": "S02T05U04", | |
| "taskText": | |
| "Směs o hmotnosti 28dkg obsahuje 3% nečistot. 80g jiné směsi obsahuje stejné množství nečistot.", | |
| "question": "Kolik % nečistot obsahuje druhá směs ?", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "options": [ | |
| { "name": "opt1", "problem": "##9,5%##" }, | |
| { "name": "opt2", "problem": "##10,5%##" }, | |
| { "name": "opt3", "problem": "##11,5%##" }, | |
| { "name": "opt4", "problem": "##10%##" }, | |
| { "name": "opt5", "problem": "##11%##" } | |
| ], | |
| "correctAnswer": ["opt2"] | |
| }, | |
| { | |
| "slug": "S02T05U05", | |
| "title": "S02T05U05", | |
| "taskText": | |
| "Pan Dvořák jel automobilem prvních 20km rychlostí ##80{km\\over{h}}##, dalších 30km rychlostí ##90{km\\over{h}}##, pak dalších 5km ##30{km\\over{h}}##.", | |
| "question": "Jak dlouho trvala jízda ?", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "options": [ | |
| { "name": "opt1", "problem": "##55minut##" }, | |
| { "name": "opt2", "problem": "##1hodinu5minut##" }, | |
| { "name": "opt3", "problem": "##1hodinu##" }, | |
| { "name": "opt4", "problem": "##45minut##" }, | |
| { "name": "opt5", "problem": "jiná hodnota" } | |
| ], | |
| "correctAnswer": ["opt4"] | |
| }, | |
| { | |
| "slug": "S02T05U06", | |
| "title": "S02T05U06", | |
| "question": | |
| "Jaká je hmotnost olověné koule o průměru 82mm, jestliže hustota olova ##\\rho=11~340m^3##? ##(m=3,274kg)## ", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "options": [ | |
| { "name": "opt1", "problem": "##3~280g##" }, | |
| { "name": "opt2", "problem": "##26~190g##" }, | |
| { "name": "opt3", "problem": "##1~840g##" }, | |
| { "name": "opt4", "problem": "##14~730g##" }, | |
| { "name": "opt5", "problem": "jiná hodnota" } | |
| ], | |
| "correctAnswer": ["opt1"] | |
| }, | |
| { | |
| "slug": "S02T05U07", | |
| "title": "S02T05U07", | |
| "question": | |
| "Určete číslo ##y\\in\\mathbb{R}## tak,aby byla řešením dané soustavy, když pro ##x=5## $${\\sqrt{x+y}}+{\\sqrt{x-y}}=4$$", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "options": [ | |
| { "name": "opt1", "problem": "##y=3##" }, | |
| { "name": "opt2", "problem": "##y=5##" }, | |
| { "name": "opt3", "problem": "##y=8##" }, | |
| { "name": "opt4", "problem": "##y=7##" }, | |
| { "name": "opt5", "problem": "jiná hodnota " } | |
| ], | |
| "correctAnswer": ["opt5"] | |
| }, | |
| { | |
| "slug": "S02T05U08", | |
| "title": "S02T05U08", | |
| "question": | |
| "Zjednodušte : ##{{{m\\over3}+{27\\over{m}}+3}}\\over{{m\\over9}-{{81\\over{m^2}}}}##", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "options": [ | |
| { "name": "opt1", "problem": "##{m\\over{m^2+9m+81}}##" }, | |
| { "name": "opt2", "problem": "##{m\\over{m-3}}##" }, | |
| { "name": "opt3", "problem": "##{3m\\over{m-9}}##" }, | |
| { "name": "opt4", "problem": "##{3m\\over{m^2-9m+81}}##" }, | |
| { "name": "opt5", "problem": "jiná hodnota " } | |
| ], | |
| "correctAnswer": ["opt3"] | |
| }, | |
| { | |
| "slug": "S02T05U09", | |
| "title": "S02T05U09", | |
| "question": | |
| "Sestavte obecnou rovnici přímky, která prochází bodem B a je rovnoběžná s přímkou m. $$B[1;-2],~~m=KL,~~K[4;-3],L[-5;3]$$", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "options": [ | |
| { "name": "opt1", "problem": "##2x+3y+4=0##" }, | |
| { "name": "opt2", "problem": "##3x-2y+7=0##" }, | |
| { "name": "opt3", "problem": "##x-2y+5=0##" }, | |
| { "name": "opt4", "problem": "##3x-y+5=0##" }, | |
| { "name": "opt5", "problem": "jiná rovnice " } | |
| ], | |
| "correctAnswer": ["opt1"] | |
| }, | |
| { | |
| "slug": "S02T05U10", | |
| "title": "S02T05U10", | |
| "question": | |
| "Hřiště je 80m dlouhé. Jaká bude jeho délka na plánku v měřítku 1:500?", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "options": [ | |
| { "name": "opt1", "problem": "##15cm##" }, | |
| { "name": "opt2", "problem": "##20cm##" }, | |
| { "name": "opt3", "problem": "##16cm##" }, | |
| { "name": "opt4", "problem": "##18cm##" }, | |
| { "name": "opt5", "problem": "jiná hodnota" } | |
| ], | |
| "correctAnswer": ["opt3"] | |
| }, | |
| { | |
| "slug": "S02T05U11", | |
| "title": "S02T05U11", | |
| "taskText": "&&\\images\\tasks\\S02T05\\S02T05P11.jpg&&", | |
| "question": | |
| "Pomocí vektorů ##\\vec{a}## a ##\\vec{b}## vyjádřete posunutí, které provádí ", | |
| "maxPoints": 4, | |
| "type": "options", | |
| "partPoints": [0, 1, 1, 2, 4], | |
| "options": [ | |
| { | |
| "name": "opt1", | |
| "problem": "z [1] do [2]", | |
| "part": "opt" | |
| }, | |
| { | |
| "name": "opt2", | |
| "problem": "z [2] do [3]", | |
| "part": "opt" | |
| }, | |
| { | |
| "name": "opt3", | |
| "problem": "z [3] do [4]", | |
| "part": "opt" | |
| }, | |
| { | |
| "name": "opt4", | |
| "problem": "z [1] do [4]", | |
| "part": "opt" | |
| }, | |
| { | |
| "name": "ans1", | |
| "problem": "##3\\vec{a}+\\vec{b}##", | |
| "part": "ans" | |
| }, | |
| { | |
| "name": "ans2", | |
| "problem": "##-5\\vec{a}+5\\vec{b}##", | |
| "part": "ans" | |
| }, | |
| { | |
| "name": "ans3", | |
| "problem": "##2\\vec{b}-4\\vec{a}##", | |
| "part": "ans" | |
| }, | |
| { | |
| "name": "ans4", | |
| "problem": "##-\\vec{b}+2\\vec{a}##", | |
| "part": "ans" | |
| }, | |
| { | |
| "name": "ans5", | |
| "problem": "##4\\vec{a}-2\\vec{b}##", | |
| "part": "ans" | |
| }, | |
| { | |
| "name": "ans6", | |
| "problem": "##-3\\vec{a}-\\vec{b}##", | |
| "part": "ans" | |
| } | |
| ], | |
| "correctAnswer": [ | |
| { "name": "opt1", "correct": "ans5" }, | |
| { "name": "opt2", "correct": "ans2" }, | |
| { "name": "opt3", "correct": "ans6" }, | |
| { "name": "opt4", "correct": "ans3" } | |
| ] | |
| }, | |
| { | |
| "slug": "S02T05U12", | |
| "title": "S02T05U12", | |
| "taskText": | |
| "Bude proveden nátěr bazénu na vnitřním povrchu ve dvou vrstvách. Spotřeba barvy na jednu vrstvu je ##0,5{kg\\over{m^2}}##.", | |
| "question": | |
| "Vypočtěte, kolik barvy bude potřeba na nátěr bazénu? &&\\images\\tasks\\S02T05\\S02T05P12.jpg&& ", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "options": [ | |
| { "name": "opt1", "problem": "přibližně 220kg barvy" }, | |
| { "name": "opt2", "problem": "přibližně 110kg barvy" }, | |
| { "name": "opt3", "problem": "přibližně 150kg barvy" }, | |
| { "name": "opt4", "problem": "přibližně 90kg barvy" }, | |
| { "name": "opt5", "problem": "jiné množství " } | |
| ], | |
| "correctAnswer": ["opt2"] | |
| }, | |
| { | |
| "slug": "S02T05U13", | |
| "title": "S02T05U13", | |
| "taskText": | |
| "Bude proveden nátěr bazénu na vnitřním povrchu ve dvou vrstvách. Spotřeba barvy na jednu vrstvu je ##0,5{kg\\over{m^2}}##. &&\\images\\tasks\\S02T05\\S02T05P12.jpg&&", | |
| "question": | |
| "Kolik Kč bude stát barva, jestliže ji nakoupíme v plechovkách po 4,5kg za 95Kč za plechovku.", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "options": [ | |
| { "name": "opt1", "problem": "více než 3 000Kč" }, | |
| { "name": "opt2", "problem": "v rozmezí 2500Kč a 3000Kč" }, | |
| { "name": "opt3", "problem": "v rozmezí 2000Kč a 2500Kč" }, | |
| { "name": "opt4", "problem": "v rozmezí 1500Kč a 2000Kč" }, | |
| { "name": "opt5", "problem": "méně než 1500Kč" } | |
| ], | |
| "correctAnswer": ["opt3"] | |
| }, | |
| { | |
| "slug": "S02T05U14", | |
| "title": "S02T05U14", | |
| "question": | |
| "Hodíme mincí třikrát po sobě. Určete kombinaci jevu a jeho pravděpodobnosti. Jaká je pravděpodobnost jevů: ", | |
| "maxPoints": 3, | |
| "partPoints": [0, 1, 2, 3], | |
| "type": "pairs", | |
| "options": [ | |
| { | |
| "name": "opt1", | |
| "problem": "Líc padne častěji než rub.", | |
| "part": "opt" | |
| }, | |
| { | |
| "name": "opt2", | |
| "problem": "Líc padne právě dvakrát", | |
| "part": "opt" | |
| }, | |
| { | |
| "name": "opt3", | |
| "problem": "Nejprve padne rub a pak líc", | |
| "part": "opt" | |
| }, | |
| { | |
| "name": "ans1", | |
| "problem": "##1\\over 6##", | |
| "part": "ans" | |
| }, | |
| { | |
| "name": "ans2", | |
| "problem": "##1\\over 2##", | |
| "part": "ans" | |
| }, | |
| { | |
| "name": "ans3", | |
| "problem": "##1\\over 4##", | |
| "part": "ans" | |
| }, | |
| { | |
| "name": "ans4", | |
| "problem": "##3\\over 8##", | |
| "part": "ans" | |
| } | |
| ], | |
| "correctAnswer": [ | |
| { "name": "opt1", "correct": "ans2" }, | |
| { "name": "opt2", "correct": "ans4" }, | |
| { "name": "opt3", "correct": "ans3" } | |
| ] | |
| }, | |
| { | |
| "slug": "S02T05U15", | |
| "title": "S02T05U15", | |
| "taskText": "&&\\images\\tasks\\S02T05\\S02T05P15.jpg&&", | |
| "question": | |
| "Spojte graf lineární funkce ##y=kx+q## z obrázku, který prochází bodem ##A=[-3;4]## k hodnotě ##k##. ", | |
| "maxPoints": 3, | |
| "type": "pairs", | |
| "options": [ | |
| { | |
| "name": "opt1", | |
| "problem": "fce z obrázku a)", | |
| "part": "opt" | |
| }, | |
| { | |
| "name": "opt2", | |
| "problem": "fce z obrázku b)", | |
| "part": "opt" | |
| }, | |
| { | |
| "name": "opt3", | |
| "problem": "fce z obrázku c)", | |
| "part": "opt" | |
| }, | |
| { | |
| "name": "ans1", | |
| "problem": "##k={3\\over4}##", | |
| "part": "ans" | |
| }, | |
| { | |
| "name": "ans2", | |
| "problem": "##k=-{2\\over5}##", | |
| "part": "ans" | |
| }, | |
| { "name": "ans3", "problem": "##k=0##", "part": "ans" }, | |
| { | |
| "name": "ans4", | |
| "problem": "##k=-{3\\over2}##", | |
| "part": "ans" | |
| }, | |
| { | |
| "name": "ans5", | |
| "problem": "##k=-{3\\over4}##", | |
| "part": "ans" | |
| }, | |
| { | |
| "name": "ans6", | |
| "problem": "##k={4\\over3}##", | |
| "part": "ans" | |
| } | |
| ], | |
| "correctAnswer": [ | |
| { "name": "opt1", "correct": "ans6" }, | |
| { "name": "opt2", "correct": "ans4" }, | |
| { "name": "opt3", "correct": "ans2" } | |
| ] | |
| }, | |
| { | |
| "slug": "S02T05U16", | |
| "title": "S02T05U16", | |
| "taskText": | |
| "Odečteme-li totéž číslo od čísel 9; 15; 27; dostaneme první tři členy geometrické posloupnosti.", | |
| "question": "Určete šestý člen této posloupnosti.", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "options": [ | |
| { "name": "opt1", "problem": "##150##" }, | |
| { "name": "opt2", "problem": "##160##" }, | |
| { "name": "opt3", "problem": "##192##" }, | |
| { "name": "opt4", "problem": "##243##" }, | |
| { "name": "opt5", "problem": "##384##" } | |
| ], | |
| "correctAnswer": ["opt3"] | |
| }, | |
| { | |
| "slug": "S02T05U17", | |
| "title": "S02T05U17", | |
| "question": | |
| "Vypočítej: ##{\\sqrt[3]{a\\over{\\sqrt{b^2}}}}\\cdot{\\sqrt{b\\over{\\sqrt[3]{a}}}}## ", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "options": [ | |
| { "name": "opt1", "problem": "##\\sqrt[6]{a}##" }, | |
| { "name": "opt2", "problem": "##a^6##" }, | |
| { "name": "opt3", "problem": "##\\sqrt[6]{b}##" }, | |
| { "name": "opt4", "problem": "##b^6##" }, | |
| { "name": "opt5", "problem": "##\\sqrt[6]{ab}##" } | |
| ], | |
| "correctAnswer": ["opt5"] | |
| }, | |
| { | |
| "slug": "S02T05U18", | |
| "title": "S02T05U18", | |
| "question": | |
| "K danému grafu vyberte správný funkční předpis. &&\\images\\tasks\\S02T05\\S02T05P18.jpg&&", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "options": [ | |
| { | |
| "name": "opt1", | |
| "problem": "##y=\\left({1\\over2}\\right)^x-1##" | |
| }, | |
| { | |
| "name": "opt2", | |
| "problem": "##y=\\left({1\\over2}\\right)^{x-1}##" | |
| }, | |
| { | |
| "name": "opt3", | |
| "problem": "##y=\\log_{1\\over2}(x-1)##" | |
| }, | |
| { "name": "opt4", "problem": "##y={1\\over{x}}-1##" }, | |
| { "name": "opt5", "problem": "##y=\\log_{1\\over2}(x+1)##" } | |
| ], | |
| "correctAnswer": ["opt3"] | |
| }, | |
| { | |
| "slug": "S02T05U19", | |
| "title": "S02T05U19", | |
| "question": | |
| "Určete odchylku přímek ##a,b## $$a:2x-2y+1=0$$, $$b:x=-1-t~~y=4+t~~t\\in\\mathbb{R}$$", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "options": [ | |
| { "name": "opt1", "problem": "##45°##" }, | |
| { "name": "opt2", "problem": "##90°##" }, | |
| { "name": "opt3", "problem": "##25°##" }, | |
| { "name": "opt4", "problem": "##80°##" }, | |
| { "name": "opt5", "problem": "##65°## " } | |
| ], | |
| "correctAnswer": ["opt2"] | |
| }, | |
| { | |
| "slug": "S02T05U20", | |
| "title": "S02T05U20", | |
| "question": | |
| "Vypočtěte obsah rovnoběžníku ABCD, je-li dáno ##|AB|=57cm,~|AC|=66cm,~|\\measuredangle{ABC}|=57°40´##", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "options": [ | |
| { "name": "opt1", "problem": "##3640~cm^2##" }, | |
| { "name": "opt2", "problem": "##4230~cm^2##" }, | |
| { "name": "opt3", "problem": "##3270~cm^2##" }, | |
| { "name": "opt4", "problem": "##4440~cm^2##" }, | |
| { "name": "opt5", "problem": "jiná hodnota " } | |
| ], | |
| "correctAnswer": ["opt1"] | |
| }, | |
| { | |
| "slug": "S02T05U21", | |
| "title": "S02T05U21", | |
| "question": | |
| "Je-li ##\\sin{x}=0,8##, pak##\\cos{x}## je roven :", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "options": [ | |
| { "name": "opt1", "problem": "##{\\pi\\over2}-0,8##" }, | |
| { "name": "opt2", "problem": "##1\\over5##" }, | |
| { "name": "opt3", "problem": "##3\\over5##" }, | |
| { "name": "opt4", "problem": "##{\\pi\\over2}+0,8##" }, | |
| { "name": "opt5", "problem": "##88,2##" } | |
| ], | |
| "correctAnswer": ["opt3"] | |
| }, | |
| { | |
| "slug": "S02T05U22", | |
| "title": "S02T05U22", | |
| "taskText": | |
| "Ve špičte projede po cestě průměrně 22 aut za 12 min. Bla bla Bla ...", | |
| "question": "Bla bla bla", | |
| "maxPoints": 1, | |
| "type": "write", | |
| "correctAnswer": ["12"] | |
| }, | |
| { | |
| "slug": "S02T05U23", | |
| "title": "S02T05U23", | |
| "taskText": "Nějaké zadání", | |
| "question": "Bla bla", | |
| "maxPoints": 1, | |
| "type": "write", | |
| "options": [ | |
| { "name": "opt1", "problem": "" }, | |
| { "name": "opt2", "problem": "" }, | |
| { "name": "opt3", "problem": "" }, | |
| { "name": "opt4", "problem": "" }, | |
| { "name": "opt5", "problem": "" } | |
| ], | |
| "correctAnswer": ["opt5"] | |
| }, | |
| { | |
| "slug": "S02T05U24", | |
| "title": "S02T05U24", | |
| "taskText": "##1+6+11+..........+x=970##", | |
| "question": | |
| "Máme aritmetickou posloupnost. Určete poslední hodnotu posloupnosti, kterou jsme přičetli před dosažením cílového součtu.", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "options": [ | |
| { "name": "opt1", "problem": "##91##" }, | |
| { "name": "opt2", "problem": "##96##" }, | |
| { "name": "opt3", "problem": "##81##" }, | |
| { "name": "opt4", "problem": "##101##" }, | |
| { "name": "opt5", "problem": "jiná hodnota" } | |
| ], | |
| "correctAnswer": ["opt2"] | |
| }, | |
| { | |
| "slug": "S02T05U25", | |
| "title": "S02T05U25", | |
| "taskText": "##1+6+11+..........+x=970##", | |
| "question": | |
| "Máme aritmetickou posloupnost. Kolik hodnot jsme sečetli než jsme získali požadovaný součet? Zapiště pouze počet.", | |
| "maxPoints": 1, | |
| "type": "write", | |
| "correctAnswer": ["20"] | |
| }, | |
| { | |
| "slug": "S02T05U26", | |
| "title": "S02T05U26", | |
| "question": | |
| "Řešte rovnici s neznámou ##x\\in{R}## $$\\log_3{{6x-2}\\over{x-3}}=2$$", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "options": [ | |
| { "name": "opt1", "problem": "##8{1\\over3}##" }, | |
| { "name": "opt2", "problem": "##5{1\\over3}##" }, | |
| { "name": "opt3", "problem": "##8{2\\over3}##" }, | |
| { "name": "opt4", "problem": "##5{2\\over3}##" }, | |
| { "name": "opt5", "problem": "jiná hodnota " } | |
| ], | |
| "correctAnswer": ["opt1"] | |
| } | |
| ] | |
| } | |
| } |
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