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pufinek/S02T19

Created July 23, 2018 14:48
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S02T19
{
"test": {
"title": "S02T19",
"slug": "S02T19",
"description": "Přípravný test k státní maturitě.",
"successfulLimit": 44,
"cermat":false,
"tasks": [
{
"slug": "S02T19U01",
"title": "S02T19U01",
"taskText": "Strana jednoho čtverečku je 1cm.",
"question":
"Kolikrát je obsah čtverce A´B´C´D´ menší než ABCD? &&\\images\\tasks\\S02T19\\S02T19P01.jpg&&",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##\\sqrt8##" },
{ "name": "opt2", "problem": "##\\sqrt2##" },
{ "name": "opt3", "problem": "##1\\over2##" },
{ "name": "opt4", "problem": "##2##" },
{ "name": "opt5", "problem": "##1##" }
],
"correctAnswer": ["opt4"],
"solutions": [{}]
},
{
"slug": "S02T19U02",
"title": "S02T19U02",
"question":
"O kolik dvanáctin je číslo pět třetin menší, než číslo pět polovin?",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##13##" },
{ "name": "opt2", "problem": "##8##" },
{ "name": "opt3", "problem": "##18##" },
{ "name": "opt4", "problem": "##10##" },
{ "name": "opt5", "problem": "##12##" }
],
"correctAnswer": ["opt4"],
"solutions": [{}]
},
{
"slug": "S02T19U03",
"title": "S02T19U03",
"question":
"Za jak dlouho natře natěrač plot vysoký 3m a dlouhý 20m, jestliže za 1 minutu natře ##{3\\over4}{m^2}##?",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "1h 16 minut" },
{ "name": "opt2", "problem": "1h 20 minut" },
{ "name": "opt3", "problem": "1h 22 minut" },
{ "name": "opt4", "problem": "1h 18 minut" },
{ "name": "opt5", "problem": "jiná hodnota" }
],
"correctAnswer": ["opt2"],
"solutions": [{}]
},
{
"slug": "S02T19U04",
"title": "S02T19U04",
"taskText": "4cm na mapě představují 80km ve skutečnosti.",
"question": "Jaké je měřítko mapy?",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##1:4~000~000##" },
{ "name": "opt2", "problem": "##1:200~000##" },
{ "name": "opt3", "problem": "##1:400~000##" },
{ "name": "opt4", "problem": "##1:2~000~000##" },
{ "name": "opt5", "problem": "jiné měřítko" }
],
"correctAnswer": ["opt4"],
"solutions": [{}]
},
{
"slug": "S02T19U05",
"title": "S02T19U05",
"taskText":
"Metr látky byl zlevněn o 42Kč, takže 4m látky za novou cenu byly o 20Kč levnější, než 3m látky za starou cenu.",
"question": "Jaká by byla cena 2m látky zastarou cenu?",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##274##Kč" },
{ "name": "opt2", "problem": "##296##Kč" },
{ "name": "opt3", "problem": "##376##Kč" },
{ "name": "opt4", "problem": "##188##Kč" },
{ "name": "opt5", "problem": "jiná hodnota" }
],
"correctAnswer": ["opt2"],
"solutions": [{}]
},
{
"slug": "S02T19U06",
"title": "S02T19U06",
"taskText":
"U stolu sedí 9 stolovníků, každý z nich pije buď pivo nebo víno. Číšník o nich říká:'Aspoň čtyři pijí pivo'.",
"question": "Pokud číšník nemá pravdu, pak určitě",
"maxPoints": 2,
"type": "options",
"options": [
{
"name": "opt1",
"problem": "nejvýše tři stolovníci pijí pivo"
},
{
"name": "opt2",
"problem": "aspoň pět stolovníků pije pivo"
},
{
"name": "opt3",
"problem": "šest stolovníků pije víno a tři pivo"
},
{
"name": "opt4",
"problem": "nejvýše pět stolovníků pije víno"
},
{
"name": "opt5",
"problem": "žádná z možností není správná"
}
],
"correctAnswer": ["opt1"],
"solutions": [{}]
},
{
"slug": "S02T19U07",
"title": "S02T19U07",
"question":
"Kolika způsoby lze ze 6 chlapců a 11 dívek vytvořit pětici tak, aby v každé pětici byly dvě dívky a tři chlapci?",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##1~100##" },
{ "name": "opt2", "problem": "##230##" },
{ "name": "opt3", "problem": "##75##" },
{ "name": "opt4", "problem": "##26~400##" },
{ "name": "opt5", "problem": "##13~200##" }
],
"correctAnswer": ["opt1"],
"solutions": [{}]
},
{
"slug": "S02T19U08",
"title": "S02T19U08",
"taskText": "Je dána funkce ##y=2x-x^2.## ",
"question": "Určete její obor hodnot.",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##(-\\infty;-1\\rangle##" },
{ "name": "opt2", "problem": "##\\langle1;\\infty)##" },
{ "name": "opt3", "problem": "##\\langle2;\\infty)##" },
{ "name": "opt4", "problem": "##(-\\infty;1\\rangle##" },
{ "name": "opt5", "problem": "jiný interval" }
],
"correctAnswer": ["opt4"],
"solutions": [{}]
},
{
"slug": "S02T19U09",
"title": "S02T19U09",
"question":
"Upravte výraz pro ##n\\in{N};n\\geqq2.## $$V={{n!}\\over{(n-2)}}+{{n!}\\over{(n-1)!}}-{{(n-1)!}\\over{(n-2)!}}$$",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##V=n-1##" },
{ "name": "opt2", "problem": "jiná hodnota" },
{ "name": "opt3", "problem": "##V=n##" },
{ "name": "opt4", "problem": "##V=1##" },
{ "name": "opt5", "problem": "##V=1-n##" }
],
"correctAnswer": ["opt2"],
"solutions": [{}]
},
{
"slug": "S02T19U10",
"title": "S02T19U10",
"taskText":
"Množina všech bodů ##[x;y]##, pro které platí zároveň ##xy\\leq0;x^2+y^2=4## je na obrázku:",
"maxPoints": 2,
"type": "options",
"options": [
{
"name": "opt1",
"problem": "&&\\images\\tasks\\S02T19\\S02T19P10C.jpg&&"
},
{
"name": "opt2",
"problem": "&&\\images\\tasks\\S02T19\\S02T19P10B.jpg&&"
},
{
"name": "opt3",
"problem": "&&\\images\\tasks\\S02T19\\S02T19P10A.jpg&&"
},
{
"name": "opt4",
"problem": "&&\\images\\tasks\\S02T19\\S02T19P10D.jpg&&"
},
{
"name": "opt5",
"problem": "&&\\images\\tasks\\S02T19\\S02T19P10E.jpg&&"
}
],
"correctAnswer": ["opt3"],
"solutions": [{}]
},
{
"slug": "S02T19U11",
"title": "S02T19U11",
"question":
"Pro posloupnost ##(a_n)_{n=1}^\\infty=2;3;5;8;12;17;...## platí vzorec:",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##a_{n+1}=2a_{n+1}-n-1##" },
{ "name": "opt2", "problem": "##a_{n+1}=2a_n-n+1##" },
{ "name": "opt3", "problem": "##a_{n+1}=a_n+n##" },
{ "name": "opt4", "problem": "##a_{n+1}=a_n+n-1##" },
{ "name": "opt5", "problem": "##a_{n+1}=2a_n-n##" }
],
"correctAnswer": ["opt3"],
"solutions": [{}]
},
{
"slug": "S02T19U12",
"title": "S02T19U12",
"question":
"Pravděpodobnost, že při hodu dvěma kostkami padne součet sedm, je:",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##1\\over9##" },
{ "name": "opt2", "problem": "##1\\over18##" },
{ "name": "opt3", "problem": "##1\\over6##" },
{ "name": "opt4", "problem": "##1\\over3##" },
{ "name": "opt5", "problem": "##1\\over36##" }
],
"correctAnswer": ["opt3"],
"solutions": [{}]
},
{
"slug": "S02T19U13",
"title": "S02T19U13",
"taskText":
"Poměr mezi plochami obývacího pokoje, dětského pokoje a ložnice je 5:2:3. Obývací pokoj a ložnice zabírají dohromady ##57,6m^2##.",
"question": "Kolik ##m^2## zbývá na dětský pokoj?",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##14,4m^2##" },
{ "name": "opt2", "problem": "##24,7m^2##" },
{ "name": "opt3", "problem": "##18,4m^2##" },
{ "name": "opt4", "problem": "##11,5m^2##" },
{ "name": "opt5", "problem": "##23m^2##" }
],
"correctAnswer": ["opt1"],
"solutions": [{}]
},
{
"slug": "S02T19U14",
"title": "S02T19U14",
"question":
"Průměrný věk čtyř lidí je 33let. Průměrný věk tří z nich je 28let. Čtvrtý z nich je stár:",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "15 let" },
{ "name": "opt2", "problem": "20 let" },
{ "name": "opt3", "problem": "28 let" },
{ "name": "opt4", "problem": "48 let" },
{ "name": "opt5", "problem": "jiná hodnota" }
],
"correctAnswer": ["opt4"],
"solutions": [{}]
},
{
"slug": "S02T19U15",
"title": "S02T19U15",
"question":
"V rovnoramenném trojúhelníku ABC se základnou AB o délce 4cm a ramenech o délkách 8cm má výška na základnu délku",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##4\\sqrt{5}##" },
{ "name": "opt2", "problem": "##2\\sqrt{17}##" },
{ "name": "opt3", "problem": "##4\\sqrt{3}##" },
{ "name": "opt4", "problem": "##2\\sqrt{15}##" },
{ "name": "opt5", "problem": "##2\\sqrt{10}##" }
],
"correctAnswer": ["opt4"],
"solutions": [{}]
},
{
"slug": "S02T19U16",
"title": "S02T19U16",
"taskText":
"Nad stranou AB rovnostranného trojúhelníku ABC je sestrojena půlkružnice s poloměrem ##r##. Průsečíky této půlkružnice se stranami BC a AC trojúhelníku ABC jsou body D, E. &&\\images\\tasks\\S02T19\\S02T19P16.jpg&&",
"question": "Vzdálenost bodů D, E je : ",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##r##" },
{ "name": "opt2", "problem": "##{2\\over3}r##" },
{ "name": "opt3", "problem": "##{1\\over2}r\\sqrt{3}##" },
{ "name": "opt4", "problem": "##{4\\over5}r##" },
{ "name": "opt5", "problem": "##r\\sqrt{2}##" }
],
"correctAnswer": ["opt1"],
"solutions": [{}]
},
{
"slug": "S02T19U17",
"title": "S02T19U17",
"question": "Číslo ##8{2\\over3}## je rovno ",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##16##" },
{ "name": "opt2", "problem": "##4\\sqrt[3]{2}##" },
{ "name": "opt3", "problem": "##2sqrt[3]{4}##" },
{ "name": "opt4", "problem": "##4##" },
{ "name": "opt5", "problem": "##\\sqrt[3]{16}##" }
],
"correctAnswer": ["opt4"],
"solutions": [{}]
},
{
"slug": "S02T19U18",
"title": "S02T19U18",
"question":
"Pro všechna reálná čísla ##a\\neq\\pm1## je výraz ##{1\\over{a-1}}-{1\\over{a+1}}## roven",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##0##" },
{ "name": "opt2", "problem": "##{2\\over{a^2-1}}##" },
{ "name": "opt3", "problem": "##{{a^2-1}\\over2}##" },
{ "name": "opt4", "problem": "##{2\\over{(a-1)^2}}##" },
{ "name": "opt5", "problem": "žádná z uvedených možností" }
],
"correctAnswer": ["opt2"],
"solutions": [{}]
},
{
"slug": "S02T19U19",
"title": "S02T19U19",
"taskText":
"Na plánu jsou břehy řeky zakresleny jako přímky o rovnicích ##p_1:y=x;~p_2:y=x+3##.",
"question":
"Jaká je délka mostu kolmého k oběma břehům? &&\\images\\tasks\\S02T19\\S02T19P19.jpg&&",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##2\\sqrt{3}##" },
{ "name": "opt2", "problem": "##{3\\over2}\\sqrt{3}##" },
{ "name": "opt3", "problem": "##{3\\over2}\\sqrt{2}##" },
{ "name": "opt4", "problem": "##3\\sqrt{2}##" },
{ "name": "opt5", "problem": "##\\sqrt{3}##" }
],
"correctAnswer": ["opt3"],
"solutions": [{}]
},
{
"slug": "S02T19U20",
"title": "S02T19U20",
"question": "Směrový vektor přímky ##p:x+3y+8=0## je",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##(3;1)##" },
{ "name": "opt2", "problem": "##(-3;1)##" },
{ "name": "opt3", "problem": "##(-1;3)##" },
{ "name": "opt4", "problem": "##(1;3)##" },
{ "name": "opt5", "problem": "##(1;-3)##" }
],
"correctAnswer": ["opt2"],
"solutions": [{}]
},
{
"slug": "S02T19U21",
"title": "S02T19U21",
"taskText":
"V aritmetické posloupnosti ##(a_n)## platí ##a_1=1;a_1+a_2=4##.",
"question":
"Součet prvních čtrnácti členů této posloupnosti je :",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##198##" },
{ "name": "opt2", "problem": "##196##" },
{ "name": "opt3", "problem": "##192##" },
{ "name": "opt4", "problem": "##194##" },
{ "name": "opt5", "problem": "##200##" }
],
"correctAnswer": ["opt2"],
"solutions": [{}]
},
{
"slug": "S02T19U22",
"title": "S02T19U22",
"question": "Výraz ##(\\sqrt{2}+1)^4## je roven",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##12\\sqrt{2}+17##" },
{ "name": "opt2", "problem": "##14\\sqrt{2}+17##" },
{ "name": "opt3", "problem": "##11\\sqrt{2}+17##" },
{ "name": "opt4", "problem": "##13\\sqrt{2}+17##" },
{ "name": "opt5", "problem": "##15\\sqrt{2}+17##" }
],
"correctAnswer": ["opt1"],
"solutions": [{}]
},
{
"slug": "S02T19U23",
"title": "S02T19U23",
"taskText":
"Krychle o straně 15cm má být provrtána tak, aby objem otvoru byl 40% objemu krychle.",
"question": "Vypočítejte průměr otvoru.",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##10,7~cm##" },
{ "name": "opt2", "problem": "##9,8~cm##" },
{ "name": "opt3", "problem": "##6,9~cm##" },
{ "name": "opt4", "problem": "##11,2~cm##" },
{ "name": "opt5", "problem": "jiná hodnota" }
],
"correctAnswer": ["opt1"],
"solutions": [{}]
},
{
"slug": "S02T19U24",
"title": "S02T19U24",
"question":
"K funkci ##f## určete předpis pro funkci inverzní; ##f:y=2-3x## ",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##y={2over3}-{xover3}##" },
{ "name": "opt2", "problem": "##y={1over3}-{xover3}##" },
{ "name": "opt3", "problem": "##y={1over2}-{xover2}##" },
{ "name": "opt4", "problem": "##y={3over2}-{xover2}##" },
{ "name": "opt5", "problem": "##y={1over3}-{xover2}##" }
],
"correctAnswer": ["opt1"],
"solutions": [{}]
},
{
"slug": "S02T19U25",
"title": "S02T19U25",
"taskText":
"Tabulka uvádí roční příjmy 30 podnikatelů s rozdělěním četností. &&\\images\\tasks\\S02T19\\S02T19P25.png&&",
"question":
"Vypočítejte průměrný roční příjem podnikatelů.",
"maxPoints": 2,
"type": "options",
"options": [
{ "name": "opt1", "problem": "##387~757##" },
{ "name": "opt2", "problem": "##312~254##" },
{ "name": "opt3", "problem": "##424~224##" },
{ "name": "opt4", "problem": "##338~333##" },
{ "name": "opt5", "problem": "jiná hodnota" }
],
"correctAnswer": ["opt4"],
"solutions": [{}]
},
{
"slug": "S02T19U26",
"title": "S02T19U26",
"question":
"Určete neznámou ##a## tak, aby ##\\vec{u}T\\vec{v};\\vec{u}(4;-1);\\vec{v}(-1;a)##",
"maxPoints": 1,
"type": "write",
"correctAnswer": ["-4"],
"solutions": [{}]
}
]
}
}
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