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pufinek/S02T20

Created August 27, 2018 12:54
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S02T20
{
"test": {
"title": "S02T20",
"slug": "S02T20",
"description": "Maturita.",
"successfulLimit": 44,
"tasks": [
{
"slug": "S02T20U01",
"title": "S02T20U01",
"question":
"Průnikem množin ##\\{3;4;5\\}##a ##\\langle 4;6\\rangle##.",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##\\langle4;5\\rangle##" },
{ "name": "opt2", "problem": "##\\langle3;6\\rangle##" },
{ "name": "opt3", "problem": "##\\{4;5;6\\}##" },
{ "name": "opt4", "problem": "##\\{4;5\\}##" },
{ "name": "opt5", "problem": "##\\{5\\}##" }
],
"correctAnswer": ["opt4"]
},
{
"slug": "S02T20U02",
"title": "S02T20U02",
"question":
"Rozložte mnohočlen na součin mnohočlenů s nejmenšími možnými stupni.$$3a+b-3ab-b^2$$",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##-(3a+b)(b-1)##" },
{ "name": "opt2", "problem": "##(3a-b)(b-1)##" },
{ "name": "opt3", "problem": "##(3a+b)(b+1)##" },
{ "name": "opt4", "problem": "##-(3a-b)(b+1)##" },
{ "name": "opt5", "problem": "jiný výraz " }
],
"correctAnswer": ["opt1"]
},
{
"slug": "S02T20U03",
"title": "S02T20U03",
"question": "Nejmenší z uvedených čísel je :.",
"maxPoints": 2,
"type": "options",
"options": [
{
"name": "opt1",
"problem": "##300 000 000 \\cdot10^{-6}##"
},
{ "name": "opt2", "problem": "##30 000 \\cdot10^{-4}##" },
{ "name": "opt3", "problem": "##300 \\cdot10^{-1}##" },
{ "name": "opt4", "problem": "##0,03 \\cdot10^{5}##" },
{ "name": "opt5", "problem": "##0,000 3 \\cdot10^{6}##" }
],
"correctAnswer": ["opt2"]
},
{
"slug": "S02T20U04",
"title": "S02T20U04",
"taskText":
"Eva by sklidila jahody ze všech záhonů za 2 hodiny, Andule by to trvalo 3 hodiny.",
"question":
"Jak dlouho jim to bude trvat, když budou sklízet společně?.",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##5 hodin##" },
{ "name": "opt2", "problem": "##2,5 hodin##" },
{ "name": "opt3", "problem": "##1,5 hodin##" },
{ "name": "opt4", "problem": "##1 hodina a 12 minut##" },
{ "name": "opt5", "problem": "##1 hodina##" }
],
"correctAnswer": ["opt4"]
},
{
"slug": "S02T20U05",
"title": "S02T20U05",
"taskText":
"Vlak o délce 200m projíždí tunelem o délce 200m rychlostí 200km/h. Doba potřebná na projetí celého vlaku tunelem (tj. doba od vjetí lokomotivy do tunelu až po vyjetí posledního vagónu) je: ",
"question": ".",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##72s##" },
{ "name": "opt2", "problem": "##36s##" },
{ "name": "opt3", "problem": "##14,2s##" },
{ "name": "opt4", "problem": "##10,8s##" },
{ "name": "opt5", "problem": "##7,2s##" }
],
"correctAnswer": ["opt5"]
},
{
"slug": "S02T20U06",
"title": "S02T20U06",
"question": "Řešte: $$(y-2)^2=(y+1)(y-4)-{{3y-6}\\over2}$$.",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##K=\\{-10\\}##" },
{ "name": "opt2", "problem": "##K=\\{-8\\}##" },
{ "name": "opt3", "problem": "##K=\\{6\\}##" },
{ "name": "opt4", "problem": "##K=\\{10\\}##" },
{ "name": "opt5", "problem": "jiná hodnota" }
],
"correctAnswer": ["opt1"]
},
{
"slug": "S02T20U07",
"title": "S02T20U07",
"taskText":
"V trojúhelníku ##ABC## je ##S## střed strany ##AB## platí $$|AS|=|BS|=|CS|=10cm; |\\measuredangle ABC|=45°$$.",
"question": "Výška ##v_c## má délku :",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##\\sqrt{125}cm##" },
{ "name": "opt2", "problem": "##10cm##" },
{ "name": "opt3", "problem": "##9cm##" },
{ "name": "opt4", "problem": "##\\sqrt{75}cm##" },
{ "name": "opt5", "problem": "##8cm##" }
],
"correctAnswer": ["opt2"]
},
{
"slug": "S02T20U08",
"title": "S02T20U08",
"taskText":
"Čtyřčlenná rodina - otec, matka, syn a dcera - se chystá odjet čtyřmístným autem na chatu. Každé z obou dětí může sedět i na předním sedadle, řídit bude otec.",
"question": "Počet možných rozmístění všech osob v autě je :",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##2##" },
{ "name": "opt2", "problem": "##4##" },
{ "name": "opt3", "problem": "##6##" },
{ "name": "opt4", "problem": "##8##" },
{ "name": "opt5", "problem": "##12##" }
],
"correctAnswer": ["opt3"]
},
{
"slug": "S02T20U09",
"title": "S02T20U09",
"taskText": "Graf funkce ##y=1-x## je na obrázku.",
"maxPoints": 2,
"type": "options",
"options": [
{
"name": "opt1",
"problem": "&&\\images\\tasks\\S02T20\\S02T20P09A.jpg&&"
},
{
"name": "opt2",
"problem": "&&\\images\\tasks\\S02T20\\S02T20P09B.jpg&&"
},
{
"name": "opt3",
"problem": "&&\\images\\tasks\\S02T20\\S02T20P09C.jpg&&"
},
{
"name": "opt4",
"problem": "&&\\images\\tasks\\S02T20\\S02T20P09D.jpg&&"
},
{
"name": "opt5",
"problem": "Žádná z možností není správná "
}
],
"correctAnswer": ["opt1"]
},
{
"slug": "S02T20U10",
"title": "S02T20U10",
"question": "Řešte : $${{3x+6}\\over{x-2}}~~~~=1$$.",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##K=\\{-2\\}##" },
{ "name": "opt2", "problem": "##K=\\{-4\\}##" },
{ "name": "opt3", "problem": "##K=\\{0\\}##" },
{ "name": "opt4", "problem": "##K=\\{-1\\}##" },
{ "name": "opt5", "problem": "##K=\\{-3\\}##" }
],
"correctAnswer": ["opt2"]
},
{
"slug": "S02T20U11",
"title": "S02T20U11",
"question":
"Kolik celých čísel vyhovuje nerovnosti ##{x+1\\over {x-2}}~\\leq0##.",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##0##" },
{ "name": "opt2", "problem": "##1##" },
{ "name": "opt3", "problem": "##2##" },
{ "name": "opt4", "problem": "##3##" },
{ "name": "opt5", "problem": "##4##" }
],
"correctAnswer": ["opt4"]
},
{
"slug": "S02T20U12",
"title": "S02T20U12",
"taskText":
"Po modernizaci produkuje výrobní linka 8 750 lahví denně, tj. o 250% více než před modernizací. .",
"question": "Kolik lahví produkovala linka před modernizací ?.",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##1855##lahví" },
{ "name": "opt2", "problem": "##2500##lahví" },
{ "name": "opt3", "problem": "##5835##lahví" },
{ "name": "opt4", "problem": "##6250##lahví" },
{ "name": "opt5", "problem": "##8500##lahví" }
],
"correctAnswer": ["opt2"]
},
{
"slug": "S02T20U13",
"title": "S02T20U13",
"question":
"Jeden z kořenů rovnice ##4x^2+8x+3=0## leží v intervalu :",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##(-\\infty; -4\\rangle##" },
{ "name": "opt2", "problem": "##(-3;-2\\rangle##" },
{ "name": "opt3", "problem": "##(-1;0\\rangle##" },
{ "name": "opt4", "problem": "##(0;1\rangle##" },
{ "name": "opt5", "problem": "##(2;3\rangle##" }
],
"correctAnswer": ["opt3"]
},
{
"slug": "S02T20U14",
"title": "S02T20U14",
"taskText":
"V pravidelném desetiúhalníku ##ABCDEFGHIJ## má úhel ##AJF## velikost:",
"question": "&&\\images\\tasks\\S02T20\\S02T20P14.jpg&&",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##81°##" },
{ "name": "opt2", "problem": "##85°##" },
{ "name": "opt3", "problem": "##90°##" },
{ "name": "opt4", "problem": "##91°##" },
{ "name": "opt5", "problem": "##100°##" }
],
"correctAnswer": ["opt3"]
},
{
"slug": "S02T20U15",
"title": "S02T20U15",
"question":
"Obsah trojúhelníku ohraničeného grafy funkcí $$y=|x|$$ a $$y=7$$ .",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##49##" },
{ "name": "opt2", "problem": "##2\\cdot49##" },
{ "name": "opt3", "problem": "##4\\cdot49##" },
{ "name": "opt4", "problem": "##49\\over4##" },
{ "name": "opt5", "problem": "##49\\over2##" }
],
"correctAnswer": ["opt1"]
},
{
"slug": "S02T20U16",
"title": "S02T20U16",
"taskText":
"Prvních pět členů posloupnosti, jejíž, ##n-tý## člen je $$cos{\\pi\\over2}+(-1)^{n+1}$$ , je.",
"question": ".",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##-1;1;-1;1;-1##" },
{ "name": "opt2", "problem": "##0;-1;0;1;0##" },
{ "name": "opt3", "problem": "##0;1;0;-1;0##" },
{ "name": "opt4", "problem": "##1;0;1;0;1##" },
{ "name": "opt5", "problem": "##1;-1;1;-1;1##" }
],
"correctAnswer": ["opt5"]
},
{
"slug": "S02T20U17",
"title": "S02T20U17",
"taskText": "&&\\images\\tasks\\S02T20\\S02T20P17.jpg&&",
"question":
"Počet přímek, na kterých leží hrany trojbokého hranolu ##ABCDEF## a které jsou mimoběžné s přímkou ##DF##, je:",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##8##" },
{ "name": "opt2", "problem": "##5##" },
{ "name": "opt3", "problem": "##3##" },
{ "name": "opt4", "problem": "##2##" },
{ "name": "opt5", "problem": "##1##" }
],
"correctAnswer": ["opt3"]
},
{
"slug": "S02T20U18",
"title": "S02T20U18",
"taskText":
"Na obrázku je graf podílu na příjmech z reklamy podle typu média v roce 1998. &&\\images\\tasks\\S02T20\\S02T20P18.jpg&&",
"question":
"Kolik % z veškerých příjmů z reklamy v roce 1998 činí příjmy za reklamy uveřejněné v rádiu a televizi ?",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "méně než ##43,4%##" },
{ "name": "opt2", "problem": "##43,4%##" },
{
"name": "opt3",
"problem": "více než 43,4% a méně než ##44,0##"
},
{ "name": "opt4", "problem": "##44,0%##" },
{ "name": "opt5", "problem": "více než 44,0%" }
],
"correctAnswer": ["opt5"]
},
{
"slug": "S02T20U19",
"title": "S02T20U19",
"taskText":
"Z dvanácti hráčů košíkové, kteří sedí na lavičce, jich má trenér pět poslat na hřiště..",
"question":
"Počet způsobů, kterými můžeme tuto pětici vybrat tak, aby v ní byl hráč A, je: ",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##{10\\choose 4}##" },
{ "name": "opt2", "problem": "##{11\\choose 5}##" },
{ "name": "opt3", "problem": "##{11\\choose 4}##" },
{ "name": "opt4", "problem": "##{12\\choose 4}##" },
{ "name": "opt5", "problem": "##{12\\choose 5}##" }
],
"correctAnswer": ["opt3"]
},
{
"slug": "S02T20U20",
"title": "S02T20U20",
"question":
"Počet řešení rovnice ##{1\\choose 3}^{x^2}=3^{x^2}## je :.",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##0##" },
{ "name": "opt2", "problem": "##1##" },
{ "name": "opt3", "problem": "##2##" },
{ "name": "opt4", "problem": "##3##" },
{ "name": "opt5", "problem": "##4## " }
],
"correctAnswer": ["opt2"]
},
{
"slug": "S02T20U21",
"title": "S02T20U21",
"question": "Vypočítejte vzdálenost bodů ##A(5;3), B(2;-1)##.",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##\\sqrt{24}##" },
{ "name": "opt2", "problem": "##\\sqrt{22}##" },
{ "name": "opt3", "problem": "##\\sqrt{18}##" },
{ "name": "opt4", "problem": "##\\sqrt{26}##" },
{ "name": "opt5", "problem": "jiná hodnota " }
],
"correctAnswer": ["opt5"]
},
{
"slug": "S02T20U22",
"title": "S02T20U22",
"taskText":
"Máme k dispozicic 36 dobrých výrobků a 4 zmetky. Vybereme namátkou 9 výrobků.",
"question":
"Jaká je pravděpodobnost, že vybereme jen ty dobré výrobky?",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##25%##" },
{ "name": "opt2", "problem": "##34,4%##" },
{ "name": "opt3", "problem": "##90%##" },
{ "name": "opt4", "problem": "##48%##" },
{ "name": "opt5", "problem": "jiná " }
],
"correctAnswer": ["opt2"]
},
{
"slug": "S02T20U23",
"title": "S02T20U23",
"question":
"Napište obecnou rovnici přímky, která je určena bodem ##M[-2;3]## a je kolmá k přímce ##2x-3y-6=0##.",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##3x+2y=0##" },
{ "name": "opt2", "problem": "##3x-2y-2=0##" },
{ "name": "opt3", "problem": "##-3x-2y+3=0##" },
{ "name": "opt4", "problem": "##-3x+2y+1=0##" },
{ "name": "opt5", "problem": "žádná z uvedených " }
],
"correctAnswer": ["opt1"]
},
{
"slug": "S02T20U24",
"title": "S02T20U24",
"question": "Vypočítej: $$log_x=2\\cdot log3+3\\cdot log_2$$.",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##17##" },
{ "name": "opt2", "problem": "##48##" },
{ "name": "opt3", "problem": "##36##" },
{ "name": "opt4", "problem": "##72##" },
{ "name": "opt5", "problem": "jiná hodnota " }
],
"correctAnswer": ["opt4"]
},
{
"slug": "S02T20U25",
"title": "S02T20U25",
"taskText":
"V lednu bylo v podniku vyrobeno 20 kusů zmetků. Počet zmetků se pravidelně zmenšuje o 2 kusy za měsíc.",
"question": "Za kolik měsíců bude všech zmetků 98?.",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##6##" },
{ "name": "opt2", "problem": "##7##" },
{ "name": "opt3", "problem": "##8##" },
{ "name": "opt4", "problem": "##9##" },
{ "name": "opt5", "problem": "jiný počet" }
],
"correctAnswer": ["opt2"]
},
{
"slug": "S02T20U26",
"title": "S02T20U26",
"taskText":
"Dodavatel zaplatil po odpočítání slevy za fakturu 8 920 Kč. Faktura zněla na 10 200 Kč.",
"question": "Vypočítejte procento slevy.",
"maxPoints": 2,
"type": "options",
"options": [
{
"name": "opt1",
"problem": "více než ##12%##a méně než ##14%##"
},
{ "name": "opt2", "problem": "méně než ##8%##" },
{
"name": "opt3",
"problem": "méně než ##10,5%## a více než ##8%##"
},
{
"name": "opt4",
"problem": "více než ##10,5%## a méně než 12%"
},
{ "name": "opt5", "problem": "více než ##14%##" }
],
"correctAnswer": ["opt1"]
}
]
}
}
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