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March 19, 2018 21:16
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| { | |
| "test": { | |
| "title": "S02T12", | |
| "slug": "S02T12", | |
| "description": "Přípravný test k státní maturitě.", | |
| "successfulLimit": 33, | |
| "tasks": [ | |
| { | |
| "slug": "S02T12U01", | |
| "title": "S02T12U01", | |
| "question": | |
| "Zjednodušte pro ##x\\neq-{2\\over5}##, $${{3-x}\\over{5x+2}}+{{2x-5}\\over{-5x-2}}-{{3x-7}\\over{5x+2}}=$$", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a89fe4dbf5e07c5af6d5fa0"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##{-6x+7}\\over{5x+2}##" }, | |
| { "name": "opt2", "problem": "##{-6x+5}\\over{5x+2}##" }, | |
| { "name": "opt3", "problem": "##{-6x+15}\\over{5x+2}##" }, | |
| { "name": "opt4", "problem": "##{-6x-9}\\over{5x+2}##" }, | |
| { "name": "opt5", "problem": "jiná hodnota" } | |
| ], | |
| "correctAnswer": ["opt3"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T12U02", | |
| "title": "S02T12U02", | |
| "question": "{{x+5}\\over{x-5}}-{{3x-2}\\over{x^2-10x+25}}=", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "categories": ["5a89fe4dbf5e07c5af6d5fa0"], | |
| "options": [ | |
| { | |
| "name": "opt1", | |
| "problem": "##{x^2-3x-27}\\over{(x-5)^2}##" | |
| }, | |
| { | |
| "name": "opt2", | |
| "problem": "##{x^2-13x+27}\\over{(x-5)^2}##" | |
| }, | |
| { | |
| "name": "opt3", | |
| "problem": "##{x^2-3x-23}\\over{(x-5)^2}##" | |
| }, | |
| { | |
| "name": "opt4", | |
| "problem": "##{x^2-3x+23}\\over{(x-5)^2}##" | |
| }, | |
| { "name": "opt5", "problem": "jiná hodnota" } | |
| ], | |
| "correctAnswer": ["opt3"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T12U03", | |
| "title": "S02T12U03", | |
| "taskText": | |
| "Cyklista ujede na jedno šlápnutí ###5{1\\over2}##m.", | |
| "question": | |
| "Kolik kilometrů ujel, jestliže šlapal ##3\\over4## hodiny frekvencí 40 šlápnutí za minutu?", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a89fe67bf5e07c5af6d5fa1"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##11,8##km" }, | |
| { "name": "opt2", "problem": "##9,9##km" }, | |
| { "name": "opt3", "problem": "##18##km" }, | |
| { "name": "opt4", "problem": "##15,6##km" }, | |
| { "name": "opt5", "problem": "##8,3##km" } | |
| ], | |
| "correctAnswer": ["opt2"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T12U04", | |
| "title": "S02T12U04", | |
| "question": | |
| "Upravte na zlomek v základním tvaru: $$\\left({3{1\\over10}:{2{1\\over15}}}\\right):\\left({2,2-{1{3\\over5}}}\\right)=$$", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a89fddbbf5e07c5af6d5f99"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##7\\over2##" }, | |
| { "name": "opt2", "problem": "##3\\over2##" }, | |
| { "name": "opt3", "problem": "##1\\over2##" }, | |
| { "name": "opt4", "problem": "##5\\over2##" }, | |
| { "name": "opt5", "problem": "jiná hodnota" } | |
| ], | |
| "correctAnswer": ["opt4"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T12U05", | |
| "title": "S02T12U05", | |
| "taskText": | |
| "V průběhu let 1990-2000 ubylo v lese 80% jelenů a v letech 2001-2005 ještě ubylo 60% ze zbylých jelenů, takže jich nakonec zůstalo 20. ", | |
| "question": "Kolik jelenů bylo v lese v roce 1989?", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a8a0430bf5e07c5af6d5fa3"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##250##" }, | |
| { "name": "opt2", "problem": "##350##" }, | |
| { "name": "opt3", "problem": "##275##" }, | |
| { "name": "opt4", "problem": "##315##" }, | |
| { "name": "opt5", "problem": "##215##" } | |
| ], | |
| "correctAnswer": ["opt1"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T12U06", | |
| "title": "S02T12U06", | |
| "taskText": | |
| "Maminka rozdělila koláč mezi čtyři děti způsobem znázorněným diagramem. ", | |
| "question": | |
| "Zjistěte kolik procent koláče dostalo dítě s největším kusem. &&\\images\\tasks\\S02T12\\S02T12P06.jpg&&", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a89fdefbf5e07c5af6d5f9a"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##35%##" }, | |
| { "name": "opt2", "problem": "jiná hodnota" }, | |
| { "name": "opt3", "problem": "##38%##" }, | |
| { "name": "opt4", "problem": "##33%##" }, | |
| { "name": "opt5", "problem": "##42%##" } | |
| ], | |
| "correctAnswer": ["opt2"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T12U07", | |
| "title": "S02T12U07", | |
| "question": | |
| "Vyjádřete jako součin (podíl) mocnin s co nejmenším přirozeným základem mocninu: $${{20^{-4}}\\over{25^{-2}}}\\cdot{{2^7}\\over8^{-3}}=$$ ", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a89fe15bf5e07c5af6d5f9d"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##2^8\\cdot5##" }, | |
| { "name": "opt2", "problem": "##2^8##" }, | |
| { "name": "opt3", "problem": "##5^8##" }, | |
| { "name": "opt4", "problem": "##2^8\\cdot5^8##" }, | |
| { "name": "opt5", "problem": "##5^8\\cdot2##" } | |
| ], | |
| "correctAnswer": ["opt2"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T12U08", | |
| "title": "S02T12U08", | |
| "question": | |
| "Jak dlouhá je síť chodeb, kterou si na čtvercové zahrádce na obrázku vytvořil krtek? &&\\images\\tasks\\S02T12\\S02T12P08.jpg&&", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "categories": ["5a89fe67bf5e07c5af6d5fa1"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##150##m" }, | |
| { "name": "opt2", "problem": "##120##m" }, | |
| { "name": "opt3", "problem": "##100##m" }, | |
| { "name": "opt4", "problem": "##80##m" }, | |
| { "name": "opt5", "problem": "jiná hodnota " } | |
| ], | |
| "correctAnswer": ["opt3"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T12U09", | |
| "title": "S02T12U09", | |
| "question": "\\log(2x+10)=2\\cdot\\log(x+1)", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a8a0581bf5e07c5af6d5fb0"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##K=\\{3\\}##" }, | |
| { "name": "opt2", "problem": "##K=\\{5\\}##" }, | |
| { "name": "opt3", "problem": "##K=\\{9\\}##" }, | |
| { "name": "opt4", "problem": "##K=\\{7\\}##" }, | |
| { "name": "opt5", "problem": "jiná hodnota " } | |
| ], | |
| "correctAnswer": ["opt1"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T12U10", | |
| "title": "S02T12U10", | |
| "taskText": | |
| "Do 7.A chodí 32 žáků (18 děvčat a 14 chlapců). Průměrná výška děvčat je 154 cm, průměrná výška chlapců je 162 cm.", | |
| "question": "Jaká je průměrná výška žáka 7.A?", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a8a06eebf5e07c5af6d5fbf"], | |
| "options": [ | |
| { "name": "opt1", "problem": "155 cm" }, | |
| { | |
| "name": "opt2", | |
| "problem": "více než 150 cm, ale méně než 155 cm" | |
| }, | |
| { | |
| "name": "opt3", | |
| "problem": "více než 155 cm, ale méně než 160 cm" | |
| }, | |
| { "name": "opt4", "problem": "více než 160 cm" }, | |
| { "name": "opt5", "problem": "160 cm" } | |
| ], | |
| "correctAnswer": ["opt3"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T12U11", | |
| "title": "S02T12U11", | |
| "taskText": | |
| "Jirka vysadil více stromků než Milan, ale o 7 méně než Libor.", | |
| "question": | |
| "Kolik stromků vysadil Libor, jetliže dohromady vysadili 87 stromků?", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a8a0442bf5e07c5af6d5fa4"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##39##" }, | |
| { "name": "opt2", "problem": "##38##" }, | |
| { "name": "opt3", "problem": "##35##" }, | |
| { "name": "opt4", "problem": "##37##" }, | |
| { "name": "opt5", "problem": "##36##" } | |
| ], | |
| "correctAnswer": ["opt1"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T12U12", | |
| "title": "S02T12U12", | |
| "question": "##3^{5n-8}=9^{n-3}##", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "categories": ["5a8a0581bf5e07c5af6d5fb0"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##5\\over8##" }, | |
| { "name": "opt2", "problem": "##1\\over3##" }, | |
| { "name": "opt3", "problem": "##2\\over3##" }, | |
| { "name": "opt4", "problem": "##1\\over6##" }, | |
| { "name": "opt5", "problem": "jiná hodnota" } | |
| ], | |
| "correctAnswer": ["opt3"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T12U13", | |
| "title": "S02T12U13", | |
| "cermat": true, | |
| "taskText": "&&\\images\\tasks\\S02T12\\S02T12P13.png&&", | |
| "question": | |
| "S využitím grafu funkce ##y=2x+3; x\\in\\mathbb{R}## přiřaďte grafy funkcí !", | |
| "maxPoints": 3, | |
| "partPoints": [0, 1, 2, 3], | |
| "type": "pairs", | |
| "categories": ["5a8a051cbf5e07c5af6d5fac"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##y=2x-3##", "part": "opt" }, | |
| { "name": "opt2", "problem": "##y=-2x+3##", "part": "opt" }, | |
| { "name": "opt3", "problem": "##y=-2x-3##", "part": "opt" }, | |
| { | |
| "name": "ans1", | |
| "problem": | |
| "&&\\images\\tasks\\S02T12\\S02T12P13i.png&& ", | |
| "part": "ans" | |
| }, | |
| { | |
| "name": "ans2", | |
| "problem": | |
| "&&\\images\\tasks\\S02T12\\S02T12P13h.png&&", | |
| "part": "ans" | |
| }, | |
| { | |
| "name": "ans3", | |
| "problem": | |
| "&&\\images\\tasks\\S02T12\\S02T12P13g.png&&", | |
| "part": "ans" | |
| }, | |
| { | |
| "name": "ans4", | |
| "problem": | |
| "&&\\images\\tasks\\S02T12\\S02T12P13m.png&&", | |
| "part": "ans" | |
| } | |
| ], | |
| "correctAnswer": [ | |
| { "name": "opt1", "correct": "ans3" }, | |
| { "name": "opt2", "correct": "ans1" }, | |
| { "name": "opt3", "correct": "ans4" } | |
| ], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T12U14", | |
| "title": "S02T12U14", | |
| "question": | |
| "Řešte v ##\\mathbb{R}##, výsledek zapište intervalem ##\\left({1\\over3}\\right)^x\\lt3##", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a8a04c3bf5e07c5af6d5faa"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##(-\\infty;3)##" }, | |
| { "name": "opt2", "problem": "##(3;\\infty)##" }, | |
| { "name": "opt3", "problem": "##(-\\infty;1)##" }, | |
| { "name": "opt4", "problem": "##(1;\\infty)##" }, | |
| { "name": "opt5", "problem": "jiný interval " } | |
| ], | |
| "correctAnswer": ["opt5"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T12U15", | |
| "title": "S02T12U15", | |
| "question": | |
| "V množině ##\\mathbb{Z}## řešte rovnici: $$x\\cdot{{(x+3)!}\\over{(x+2)}!}~~{~+x^2}=14$$", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "categories": ["59eba2813ed54d1200c8d3f8"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##K=\\{4\\}##" }, | |
| { "name": "opt2", "problem": "##K=\\{-4\\}####" }, | |
| { "name": "opt3", "problem": "##K=\\{-2\\}####" }, | |
| { "name": "opt4", "problem": "##K=\\{2\\}####" }, | |
| { "name": "opt5", "problem": "nemá řešení " } | |
| ], | |
| "correctAnswer": ["opt4"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T12U16", | |
| "title": "S02T12U16", | |
| "question": | |
| "Určete druhý člen aritmetické posloupnosti ##(a_n)^{\\infty}n=1##, je-li dáno $$a_1+a_6=16$$, $$a_3+a_5=19$$", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "categories": ["5a8a05f3bf5e07c5af6d5fb5"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##a_2={3\\over2}##" }, | |
| { "name": "opt2", "problem": "##a_2=4##" }, | |
| { "name": "opt3", "problem": "##a_2={7\\over2}##" }, | |
| { "name": "opt4", "problem": "##a_2={5\\over2}##" }, | |
| { "name": "opt5", "problem": "##a_2=2##" } | |
| ], | |
| "correctAnswer": ["opt3"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T12U17", | |
| "title": "S02T12U17", | |
| "question": | |
| "Určete počet všech čtyřciferných přirozených čísel sestavených pouze z čísel 1;3;5;8;9.", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["59eba2813ed54d1200c8d3f8"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##5!##" }, | |
| { "name": "opt2", "problem": "##5!-4!##" }, | |
| { "name": "opt3", "problem": "##5!-1##" }, | |
| { "name": "opt4", "problem": "##{5\\choose4}##" }, | |
| { "name": "opt5", "problem": "jiný počet " } | |
| ], | |
| "correctAnswer": ["opt1"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T12U18", | |
| "title": "S02T12U18", | |
| "question": "Ke grafům přiřaďte odpovídající obor hodnot.", | |
| "maxPoints": 4, | |
| "partPoints": [0, 1, 2, 3, 4], | |
| "type": "pairs", | |
| "categories": ["5a8a051cbf5e07c5af6d5fac"], | |
| "options": [ | |
| { | |
| "name": "opt1", | |
| "problem": | |
| "&&\\images\\tasks\\S02T12\\S02T12P18b.jpg&&", | |
| "part": "opt" | |
| }, | |
| { | |
| "name": "opt2", | |
| "problem": | |
| "&&\\images\\tasks\\S02T12\\S02T12P18a.jpg&&", | |
| "part": "opt" | |
| }, | |
| { | |
| "name": "opt3", | |
| "problem": | |
| "&&\\images\\tasks\\S02T12\\S02T12P18c.jpg&&", | |
| "part": "opt" | |
| }, | |
| { | |
| "name": "ans1", | |
| "problem": "##\\langle-2;2\\rangle##", | |
| "part": "ans" | |
| }, | |
| { | |
| "name": "ans2", | |
| "problem": "##\\langle0;2\\rangle##", | |
| "part": "ans" | |
| }, | |
| { | |
| "name": "ans3", | |
| "problem": "##\\langle0;2)##", | |
| "part": "ans" | |
| }, | |
| { "name": "ans4", "problem": "##(-2;0)##", "part": "ans" }, | |
| { "name": "ans5", "problem": "##(0;2)##", "part": "ans" } | |
| ], | |
| "correctAnswer": [ | |
| { "name": "opt1", "correct": "ans3" }, | |
| { "name": "opt2", "correct": "ans1" }, | |
| { "name": "opt3", "correct": "ans5" } | |
| ], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T12U19", | |
| "title": "S02T12U19", | |
| "taskText": | |
| "Trojúhelník ABC je určen vrcholy ##A[-1;0]~B[2;5]~C[4;1]##.", | |
| "question": "Určete velikost úhlu při vrcholu B.", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a8a061ebf5e07c5af6d5fb7"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##57°31´##" }, | |
| { "name": "opt2", "problem": "##51°31´##" }, | |
| { "name": "opt3", "problem": "##48°31´##" }, | |
| { "name": "opt4", "problem": "##43°31´##" }, | |
| { "name": "opt5", "problem": "jiný úhel" } | |
| ], | |
| "correctAnswer": ["opt1"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T12U20", | |
| "title": "S02T12U20", | |
| "question": | |
| "Na kladné ose ##y## určete bod ##A## tak, aby měl od bodu ##B[-6;-5]## vzdálenost ##d=10##.", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a8a0680bf5e07c5af6d5fbc"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##A[0;2]##" }, | |
| { "name": "opt2", "problem": "##A[0;3]##" }, | |
| { "name": "opt3", "problem": "##A[0;4]##" }, | |
| { "name": "opt4", "problem": "##A[0;5]##" }, | |
| { "name": "opt5", "problem": "##A[0;6]##" } | |
| ], | |
| "correctAnswer": ["opt2"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T12U21", | |
| "title": "S02T12U21", | |
| "question": | |
| "Z grafu funkce sinus s periodou ##4\\pi## pro ##Df=\\lt0;4\\pi)## určete intervaly ve kterých je tato funkce rostoucí.", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "categories": ["5a8a0532bf5e07c5af6d5fad"], | |
| "options": [ | |
| { | |
| "name": "opt1", | |
| "problem": | |
| "##\\langle0;\\pi\\rangle\\cup\\langle3\\pi;4\\pi\\rangle##" | |
| }, | |
| { | |
| "name": "opt2", | |
| "problem": | |
| "##\\langle{\\pi\\over2};{3\\over2}\\pi\\rangle##" | |
| }, | |
| { | |
| "name": "opt3", | |
| "problem": | |
| "##\\langle0;{\\pi\\over2}\\rangle\\cup\\langle{3\\over2}\\pi;2\\pi\\rangle##" | |
| }, | |
| { | |
| "name": "opt4", | |
| "problem": "##\\langle\\pi;3\\pi\\rangle##" | |
| }, | |
| { "name": "opt5", "problem": "jiný interval" } | |
| ], | |
| "correctAnswer": ["opt5"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T12U22", | |
| "title": "S02T12U22", | |
| "question": | |
| "V kvádru ABCDEFGH, kde |AB|=3cm, |BC|=3cm, |AE|=5cm určete odchylku přímek EG a BC.", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a8a065cbf5e07c5af6d5fbb"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##60°##" }, | |
| { "name": "opt2", "problem": "##90°##" }, | |
| { "name": "opt3", "problem": "##45°##" }, | |
| { "name": "opt4", "problem": "##75°##" }, | |
| { "name": "opt5", "problem": "##55°##" } | |
| ], | |
| "correctAnswer": ["opt3"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T12U23", | |
| "title": "S02T12U23", | |
| "question": | |
| "Určete diferenci aritmetické posloupnosti, je-li ##a_{10}=6;~a_{14}=4##.", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a8a05babf5e07c5af6d5fb2"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##d=-2##" }, | |
| { "name": "opt2", "problem": "##d=4##" }, | |
| { "name": "opt3", "problem": "##d=-4##" }, | |
| { "name": "opt4", "problem": "jiná hodnota" }, | |
| { "name": "opt5", "problem": "##d=2##" } | |
| ], | |
| "correctAnswer": ["opt4"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T12U24", | |
| "title": "S02T12U24", | |
| "question": | |
| "Určete vzdálenost bodu M od přímky p, je-li dáno: ##M[2;1];p:3x+4y-12=0##", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a8a0688bf5e07c5af6d5fbd"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##4##" }, | |
| { "name": "opt2", "problem": "##5##" }, | |
| { "name": "opt3", "problem": "##2##" }, | |
| { "name": "opt4", "problem": "##3##" }, | |
| { "name": "opt5", "problem": "jiná hodnota " } | |
| ], | |
| "correctAnswer": ["opt3"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T12U25", | |
| "title": "S02T12U25", | |
| "question": | |
| "Určete definiční obor funkce ##f:y=\\sqrt{x-2}+\\sqrt{5-x}##", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "categories": ["5a89fe95bf5e07c5af6d5fa2"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##2\\lt{x}\\lt5##" }, | |
| { "name": "opt2", "problem": "##2\\leq{x}\\leq5##" }, | |
| { "name": "opt3", "problem": "##\\langle5;\\infty)##" }, | |
| { "name": "opt4", "problem": "##(-\\infty;2)##" }, | |
| { "name": "opt5", "problem": "##(2;\\infty)##" } | |
| ], | |
| "correctAnswer": ["opt2"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T12U26", | |
| "title": "S02T12U26", | |
| "taskText": | |
| "Brouček leze po plášti rotačního válce od bodu A do bodu B.", | |
| "question": | |
| "Jaká je délka nejkratší cesty, jestliže ##r=1## a ##h=6##? &&\\images\\tasks\\S02T12\\S02T12P26.jpg&&", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "categories": ["5a8a061ebf5e07c5af6d5fb7"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##\\sqrt{\\pi^2+36}##" }, | |
| { "name": "opt2", "problem": "##7##" }, | |
| { | |
| "name": "opt3", | |
| "problem": "##{2\\cdot}\\sqrt{\\pi^2+9}##" | |
| }, | |
| { "name": "opt4", "problem": "##{2\\cdot}\\sqrt{10}##" }, | |
| { "name": "opt5", "problem": "##8##" } | |
| ], | |
| "correctAnswer": ["opt1"], | |
| "solutions": [{}] | |
| } | |
| ] | |
| } | |
| } |
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