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pufinek/gist:66398a57f6ccc383c45cd46487e8626a

Created July 23, 2018 14:47
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S02T07
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gistfile1.txt
{
"test": {
"title": "S02T07",
"slug": "S02T07",
"description": "Přípravný test k státní maturitě.",
"cermat": false,
"successfulLimit": 44,
"tasks": [
{
"slug": "S02T07U01",
"title": "S02T07U01",
"taskText":
"Do válcovité plechovky o průměru 6cm zachytáváme kapající vodu. Za 70 minut bude plechovka naplněna z jedné třetiny.",
"question": "Za jak dlouho bude plechovka naplněna z jedné poloviny?",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "####" },
{ "name": "opt2", "problem": "####" },
{ "name": "opt3", "problem": "1,75 hodin" },
{ "name": "opt4", "problem": "####" },
{ "name": "opt5", "problem": "jiný " }
],
"correctAnswer": ["opt3"],
"solutions": [{}]
},
{
"slug": "S02T07U02",
"title": "S02T07U02",
"taskText": "Netučně.",
"question": "tučně.",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "####" },
{ "name": "opt2", "problem": "####" },
{ "name": "opt3", "problem": "####" },
{ "name": "opt4", "problem": "####" },
{ "name": "opt5", "problem": "jiný " }
],
"correctAnswer": ["opt!!"],
"solutions": [{}]
},
{
"slug": "S02T07U03",
"title": "S02T07U03",
"taskText": "Podlaha má rozměry 12x45cm.",
"question":
"Kolik čtvercových dlaždic o straně 50cm je potřeba na vydláždění?.",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "####" },
{ "name": "opt2", "problem": "####" },
{ "name": "opt3", "problem": "####" },
{ "name": "opt4", "problem": "##2160ks##" },
{ "name": "opt5", "problem": "jiný " }
],
"correctAnswer": ["opt4"],
"solutions": [{}]
},
{
"slug": "S02T07U04",
"title": "S02T07U04",
"taskText": "Výrobek byl zdražen o 18%. Zdražení činilo 819Kč.",
"question":
"Kolik korun by stál tento výrobek, kdyby byl naopak o 12% zlevněn?.",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##4004Kč##" },
{ "name": "opt2", "problem": "####" },
{ "name": "opt3", "problem": "####" },
{ "name": "opt4", "problem": "####" },
{ "name": "opt5", "problem": "jiný " }
],
"correctAnswer": ["opt1"],
"solutions": [{}]
},
{
"slug": "S02T07U05",
"title": "S02T07U05",
"question": "Vypočítej : $${{x^3+2x-x-2}\\over{x^3+x^2+2x}}=$$.",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##1-1\\overx##" },
{ "name": "opt2", "problem": "####" },
{ "name": "opt3", "problem": "####" },
{ "name": "opt4", "problem": "####" },
{ "name": "opt5", "problem": "jiný " }
],
"correctAnswer": ["opt1"],
"solutions": [{}]
},
{
"slug": "S02T07U06",
"title": "S02T07U06",
"question":
"Určete výraz, jehož logaritmováním dostanete $$2log x+log3-3log y-log2$$.",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "####" },
{ "name": "opt2", "problem": "####" },
{ "name": "opt3", "problem": "####" },
{ "name": "opt4", "problem": "##3x^2\\over2y^2##" },
{ "name": "opt5", "problem": "jiný " }
],
"correctAnswer": ["opt4"],
"solutions": [{}]
},
{
"slug": "S02T07U07",
"title": "S02T07U07",
"question":
"Vypočítej: $${{x\\over4}+{1\\over2}\\over{x\\over4}-{1\\over2}}={{x+{8\\over9}}\\over{x-{8\\over3}}}$$.",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "####" },
{ "name": "opt2", "problem": "##K=\\{0;{4\\over3},\\}##" },
{ "name": "opt3", "problem": "####" },
{ "name": "opt4", "problem": "####" },
{ "name": "opt5", "problem": "jiný " }
],
"correctAnswer": ["opt2"],
"solutions": [{}]
},
{
"slug": "S02T07U08",
"title": "S02T07U08",
"question":
"Řešte nerovnici: $${{2x-3}\\over5}+{{3x-4}\\over6}\\lt{{9x-5}\\over10}$$.",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##x\\lt3##" },
{ "name": "opt2", "problem": "##\\mathbb{R}##" },
{ "name": "opt3", "problem": "##K=\\{\\emptyset\\}##" },
{ "name": "opt4", "problem": "##(-\\infty;0)##" },
{ "name": "opt5", "problem": "jiný " }
],
"correctAnswer": ["opt3"],
"solutions": [{}]
},
{
"slug": "S02T07U09",
"title": "S02T07U09",
"question":
"Jak široké je mezikruží, jehož obsah je ##248 cm^2## a vnitřní průměr ##16cm##?",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "####" },
{ "name": "opt2", "problem": "####" },
{ "name": "opt3", "problem": "####" },
{ "name": "opt4", "problem": "##3,96cm##" },
{ "name": "opt5", "problem": "jiný " }
],
"correctAnswer": ["opt4"],
"solutions": [{}]
},
{
"slug": "S02T07U10",
"title": "S02T07U10",
"taskText":
"Ve dvouciferném čísle je součet obou cifer 7. Vyměníme-li v něm cifry, dostaneme číslo o 27 větší než číslo původní",
"question": "Určete původní číslo.",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "####" },
{ "name": "opt2", "problem": "##25##" },
{ "name": "opt3", "problem": "####" },
{ "name": "opt4", "problem": "####" },
{ "name": "opt5", "problem": "jiný " }
],
"correctAnswer": ["opt2"],
"solutions": [{}]
},
{
"slug": "S02T07U11",
"title": "S02T07U11",
"question": "Řešte nerovnici s neznámou ##3^{x+5}\\lt 1##.",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##(-\\infty;-5)##" },
{ "name": "opt2", "problem": "####" },
{ "name": "opt3", "problem": "####" },
{ "name": "opt4", "problem": "####" },
{ "name": "opt5", "problem": "jiný " }
],
"correctAnswer": ["opt1"],
"solutions": [{}]
},
{
"slug": "S02T07U12",
"title": "S02T07U12",
"taskText":"Určete první člen aritmetické posloupnosti kde: ",
"question":
"$$a_1+a_4+a_6=71$$, $$a_5-a_2-a_3=2$$",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "####" },
{ "name": "opt2", "problem": "####" },
{ "name": "opt3", "problem": "####" },
{ "name": "opt4", "problem": "##a_1=5##" },
{ "name": "opt5", "problem": "jiný " }
],
"correctAnswer": ["opt4"],
"solutions": [{}]
},
{
"slug": "S02T07U13",
"title": "S02T07U13",
"question":
"Ve kterém nejmenším intervalu celých čísel jsou logaritmy ##log_28; log_3{1\\over27}; log_216; log_{0,5}1; log0,001; log_20,5 ##.",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##\\langle-3;4\\rangle##" },
{ "name": "opt2", "problem": "####" },
{ "name": "opt3", "problem": "####" },
{ "name": "opt4", "problem": "####" },
{ "name": "opt5", "problem": "jiný " }
],
"correctAnswer": ["opt1"],
"solutions": [{}]
},
{
"slug": "S02T07U14",
"title": "S02T07U14",
"taskText":
"Vstupenka na koncert byla pro dospělou osobu ##a Kč, a\\neq 1## pro děti 1Kč.",
"question":
"Kolik bylo na koncertě dospělích, dostavilo-li se celkem 320 posluchačů a na vstupném se vybralo 520Kč?",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "####" },
{ "name": "opt2", "problem": "##x={200\\over a-1}##" },
{ "name": "opt3", "problem": "####" },
{ "name": "opt4", "problem": "####" },
{ "name": "opt5", "problem": "jiný " }
],
"correctAnswer": ["opt2"],
"solutions": [{}]
},
{
"slug": "S02T07U15",
"title": "S02T07U15",
"taskText":
"Pekárna zpracovala první den ##4{1\\over4}## pytlů mouky, druhý den o 0,75 pytlů méně než první den, a třetí o ##2{4\\over5}## pytlů méně než první a druhý den dohromady.",
"question":
"Kolik pytlů mouky zpracovala pekárna za všechny tři dny celkem?.",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##12,7##pytlů" },
{ "name": "opt2", "problem": "####" },
{ "name": "opt3", "problem": "####" },
{ "name": "opt4", "problem": "####" },
{ "name": "opt5", "problem": "jiný " }
],
"correctAnswer": ["opt1"],
"solutions": [{}]
},
{
"slug": "S02T07U16",
"title": "S02T07U16",
"question":
"Urči úrokovou sazbu jednoduchého úročení, jestliže po čtvrt roce vzrostl kapitál 6000Kč o 75Kč.",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "####" },
{ "name": "opt2", "problem": "####" },
{ "name": "opt3", "problem": "####" },
{ "name": "opt4", "problem": "5%" },
{ "name": "opt5", "problem": "jiný " }
],
"correctAnswer": ["opt4"],
"solutions": [{}]
},
{
"slug": "S02T07U17",
"title": "S02T07U17",
"question":
"Zjednodušte: ##{{(n+1)}!\\over{n!}}~~~~~-{n!\\over{(n-1)!}}~~~=##.",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "####" },
{ "name": "opt2", "problem": "##1##" },
{ "name": "opt3", "problem": "####" },
{ "name": "opt4", "problem": "####" },
{ "name": "opt5", "problem": "jiný " }
],
"correctAnswer": ["opt2"],
"solutions": [{}]
},
{
"slug": "S02T07U18",
"title": "S02T07U18",
"question":
"Určete obvod trojúhelníku daného body ##A[3;-2], B[4;0], C[-3; 1]##.",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "####" },
{ "name": "opt2", "problem": "####" },
{ "name": "opt3", "problem": "####" },
{ "name": "opt4", "problem": "##\\sqrt{5}\\cdot (4+\\sqrt{10})##" },
{ "name": "opt5", "problem": "jiný " }
],
"correctAnswer": ["opt4"],
"solutions": [{}]
},
{
"slug": "S02T07U19",
"title": "S02T07U19",
"question":
"Určete obsah trojúhelníku se stranami ##a=7m,~b=5m,~c=8m##.",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##17,3m^2##" },
{ "name": "opt2", "problem": "####" },
{ "name": "opt3", "problem": "####" },
{ "name": "opt4", "problem": "####" },
{ "name": "opt5", "problem": "jiný " }
],
"correctAnswer": ["opt1"],
"solutions": [{}]
},
{
"slug": "S02T07U20",
"title": "S02T07U20",
"taskText":
"Strany obdélníku jsou 12 a 8cm. M se dělí v poměru 3:2. ##{|CM|\\over{|MB|}}={3\\over2} \\\\##. &&\\images\\tasks\\S02T07\\S02T07P20.jpg&&",
"question": "Jaký je obvod vyšrafované části?",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "####" },
{ "name": "opt2", "problem": "##43,2cm##" },
{ "name": "opt3", "problem": "####" },
{ "name": "opt4", "problem": "####" },
{ "name": "opt5", "problem": "jiný " }
],
"correctAnswer": ["opt2"],
"solutions": [{}]
},
{
"slug": "S02T07U21",
"title": "S02T07U21",
"taskText":
"Pan Novák má dvě možnosti, jak nakoupit zásobu jablek: 1) koupí je v blízkém obchodě v ceně 32Kč/kg, 2) zajede do zemědělského podniku, kde 1kg stojí 18Kč, za dopravu ale zaplatí 200Kč.",
"question": "Určete hranici výhodnosti obou možností nákupu jablek.",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##14,3kg##" },
{ "name": "opt2", "problem": "####" },
{ "name": "opt3", "problem": "####" },
{ "name": "opt4", "problem": "####" },
{ "name": "opt5", "problem": "jiný " }
],
"correctAnswer": ["opt1"],
"solutions": [{}]
},
{
"slug": "S02T07U22",
"title": "S02T07U22",
"question":
"O kolik je bod ##A[2;7]## vzdálenější od přímky ##p:3x-4y-14=0## než bod ##B[0;0]?##.",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "####" },
{ "name": "opt2", "problem": "##4,4##" },
{ "name": "opt3", "problem": "####" },
{ "name": "opt4", "problem": "####" },
{ "name": "opt5", "problem": "jiný " }
],
"correctAnswer": ["opt2"],
"solutions": [{}]
},
{
"slug": "S02T07U23",
"title": "S02T07U23",
"question": "K funkcím přiřaďte graf.",
"maxPoints": 3,
"partPoints": [3, 2, 1, 1, 0],
"type": "pairs",
"options": [
{ "name": "opt1", "problem": "##y=(x-5)^4##", "part": "opt" },
{ "name": "opt2", "problem": "##y=2+3x##", "part": "opt" },
{ "name": "opt3", "problem": "##y={10\\over x}##", "part": "opt" },
{ "name": "opt4", "problem": "##y=4^{x-1}##", "part": "opt" },
{ "name": "ans1", "problem": "přímka", "part": "ans" },
{ "name": "ans2", "problem": "exponenciála", "part": "ans" },
{ "name": "ans3", "problem": "kružnice", "part": "ans" },
{ "name": "ans4", "problem": "parabola", "part": "ans" },
{ "name": "ans5", "problem": "hyperbola", "part": "ans" },
{ "name": "ans6", "problem": "elipsa", "part": "ans" }
],
"correctAnswer": [
{ "name": "opt1", "correct": "ans4" },
{ "name": "opt2", "correct": "ans1" },
{ "name": "opt3", "correct": "ans5" },
{ "name": "opt4", "correct": "ans2" }
],
"solutions": [{}]
},
{
"slug": "S02T07U24",
"title": "S02T07U24",
"question":
"Jaká je pravděpodobnost, že při prvním hodu čtyřmi mincemi padne 2x líc a při druhém hodu 3x líc?.",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "####" },
{ "name": "opt2", "problem": "####" },
{ "name": "opt3", "problem": "####" },
{ "name": "opt4", "problem": "##3\\over32##" },
{ "name": "opt5", "problem": "jiný " }
],
"correctAnswer": ["opt4"],
"solutions": [{}]
},
{
"slug": "S02T07U25",
"title": "S02T07U25",
"taskText":
"??? ",
"question": "???",
"maxPoints": 1,
"type": "options",
"options": [
{ "name": "opt1", "problem": "####" },
{ "name": "opt2", "problem": "####" },
{ "name": "opt3", "problem": "####" },
{ "name": "opt4", "problem": "####" },
{ "name": "opt5", "problem": "jiný " }
],
"correctAnswer": ["opt1"],
"solutions": [{}]
},
{
"slug": "S02T07U26",
"title": "S02T07U26",
"question":
"Vypočítejte povrch krychle, jejichž tělesová uhlopříčka je ##21cm##.",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "####" },
{ "name": "opt2", "problem": "##882~cm^2##" },
{ "name": "opt3", "problem": "####" },
{ "name": "opt4", "problem": "####" },
{ "name": "opt5", "problem": "jiná hodnota " }
],
"correctAnswer": ["opt2"],
"solutions": [{}]
}
]
}
}
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