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@pufinek
Created March 14, 2018 20:53
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{
"test": {
"title": "S02T03",
"slug": "S02T03",
"description": "Přípravný test k státní maturitě.",
"successfulLimit": 33,
"tasks": [
{
"slug": "S02T03U01",
"title": "S02T03U01",
"question":
"Na jakou hodnotu vzroste jistina 10 000 Kč po jednom roce, při roční úrokové sazbě 7%, jestliže banka vybírá daň 15% z úroků ročně?",
"maxPoints": 1,
"type": "options",
"categories": ["59eba1833ed54d1200c8d3f1"],
"options": [
{ "name": "opt1", "problem": "##595##Kč" },
{ "name": "opt2", "problem": "##10~595##Kč" },
{ "name": "opt3", "problem": "##10~715##Kč" },
{ "name": "opt4", "problem": "##715##Kč" },
{ "name": "opt5", "problem": "jiná hodnota " }
],
"correctAnswer": ["opt2"],
"solutions": [{}]
},
{
"slug": "S02T03U02",
"title": "S02T03U02",
"question":
"Vypočítejte, v kterém intervalu je výsledek? $${{[(-{1\\over3})+{1\\over6}]:(-{5\\over6})}\\over{-(-{3 \\over 2})^2 - 0.3 \\cdot {30 \\over 12}}}=$$",
"maxPoints": 1,
"type": "options",
"categories": ["59eba1833ed54d1200c8d3f1"],
"options": [
{
"name": "opt1",
"problem": "##\\lt-{1\\over7};{1\\over7}##"
},
{
"name": "opt2",
"problem": "##\\lt-{1\\over20};-{1\\over7}##"
},
{
"name": "opt3",
"problem": "##\\lt{1\\over7};{1\\over20}##"
},
{
"name": "opt4",
"problem": "##\\lt-\\infty;-{1\\over20}##"
},
{ "name": "opt5", "problem": "##\\lt{1\\over20};\\infty##" }
],
"correctAnswer": ["opt!!"],
"solutions": [{}]
},
{
"slug": "S02T03U03",
"title": "S02T03U03",
"taskText":
"Zboží bylo nejprve zlevněno o 15% a později z této nové ceny o dalších 10%. Cena po obou zlevnění je 1 600 Kč.",
"question": "Jaká byla původní cena před prvním zlevnění?",
"maxPoints": 1,
"type": "options",
"categories": ["59eba1833ed54d1200c8d3f1"],
"options": [
{ "name": "opt1", "problem": "##2~156##" },
{ "name": "opt2", "problem": "##2~232##" },
{ "name": "opt3", "problem": "##2~092##" },
{ "name": "opt4", "problem": "##2~186##" },
{ "name": "opt5", "problem": "##2~065##" }
],
"correctAnswer": ["opt3"],
"solutions": [{}]
},
{
"slug": "S020T03U04",
"title": "S02T03U04",
"taskText": "Sedm dělníků postaví dům za 330 dní.",
"question":
"Jaký je nejmenší možný počet dělníků, aby stavba trvala méně než 140 dnů?",
"maxPoints": 1,
"type": "options",
"categories": ["59eba1833ed54d1200c8d3f1"],
"options": [
{ "name": "opt1", "problem": "##18##" },
{ "name": "opt2", "problem": "##15##" },
{ "name": "opt3", "problem": "##16##" },
{ "name": "opt4", "problem": "##17##" },
{ "name": "opt5", "problem": "jiný počet" }
],
"correctAnswer": ["opt4"],
"solutions": [{}]
},
{
"slug": "S02T03U05",
"title": "S02T03U05",
"taskText":
"Součet druhých mocnin tří za sebou jdoucích celých je o 25 menší, než trojnásobek druhé mocniny největšího z těchto tří čísel. ",
"question": "Které číslo je z této řady nejmenší?",
"maxPoints": 2,
"type": "options",
"categories": ["59eba1833ed54d1200c8d3f1"],
"options": [
{ "name": "opt1", "problem": "##8##" },
{ "name": "opt2", "problem": "##9##" },
{ "name": "opt3", "problem": "##4##" },
{ "name": "opt4", "problem": "##2##" },
{ "name": "opt5", "problem": "jiná hodnota " }
],
"correctAnswer": ["opt3"],
"solutions": [{}]
},
{
"slug": "S02T03U06",
"title": "S02T03U06",
"question":
"Vypočítejte velikost úhlu ##\\phi##, jestliže ##\\alpha=84°##a ##\\beta=145°##. &&\\images\\tasks\\S02T03\\S02T03U06.jpg&&",
"maxPoints": 2,
"type": "options",
"categories": ["59eba1833ed54d1200c8d3f1"],
"options": [
{ "name": "opt1", "problem": "##56°##" },
{ "name": "opt2", "problem": "##35°##" },
{ "name": "opt3", "problem": "##61°##" },
{ "name": "opt4", "problem": "##53°##" },
{ "name": "opt5", "problem": "jiná hodnota " }
],
"correctAnswer": ["opt3"],
"solutions": [{}]
},
{
"slug": "S02T03U07",
"title": "S02T03U07",
"taskText":
"Ze zápalek máme sestavenou následující řadu obrazců. &&\\images\\tasks\\S02T03\\S02T03U07.jpg&&",
"question":
"Kolik zápalek budeme potřebovat na sestavení desátého obrazce?",
"maxPoints": 1,
"type": "options",
"categories": ["59eba1833ed54d1200c8d3f1"],
"options": [
{ "name": "opt1", "problem": "##39##" },
{ "name": "opt2", "problem": "##35##" },
{ "name": "opt3", "problem": "##42##" },
{ "name": "opt4", "problem": "##33##" },
{ "name": "opt5", "problem": "jiná hodnota" }
],
"correctAnswer": ["opt4"],
"solutions": [{}]
},
{
"slug": "S02T03U08",
"title": "S02T03U08",
"taskText":
"Ve čtvercové síti je nakreslen pětiúhelník. &&\\images\\tasks\\S02T03\\S02T03U08.jpg&&",
"question": "Jak dlouhá je tato lomená čára?",
"maxPoints": 2,
"type": "options",
"categories": ["59eba1833ed54d1200c8d3f1"],
"options": [
{
"name": "opt1",
"problem": "##6+\\sqrt{5}(3\\cdot\\sqrt2+1)##"
},
{ "name": "opt2", "problem": "##8+\\sqrt{5}(\\sqrt2+3)##" },
{ "name": "opt3", "problem": "##8+\\sqrt{2}(\\sqrt5+3)##" },
{
"name": "opt4",
"problem": "##6+\\sqrt{10}+3\\cdot\\sqrt2##"
},
{ "name": "opt5", "problem": "##6+\\sqrt{2}(\\sqrt5+2)##" }
],
"correctAnswer": ["opt3"],
"solutions": [{}]
},
{
"slug": "S02T03U09",
"title": "S02T03U09",
"question":
"##{{2x+1}\\over{x+3}}-{5\\overx}={15\\over{x^2+3x}}{+2}##",
"maxPoints": 2,
"type": "options",
"categories": ["59eba1833ed54d1200c8d3f1"],
"options": [
{ "name": "opt1", "problem": "##K=0##" },
{ "name": "opt2", "problem": "##K=-3##" },
{ "name": "opt3", "problem": "##K={1\\over3}##" },
{ "name": "opt4", "problem": "##K=-{1\\over3}##" },
{ "name": "opt5", "problem": "##K=3##" }
],
"correctAnswer": ["opt1"],
"solutions": [{}]
},
{
"slug": "S02T03U10",
"title": "S02T03U10",
"question":
"Určete součet prvních 20-ti členů aritmetické posloupnosti ve které je ##a_8=-2,~a_{10}=0##",
"maxPoints": 1,
"type": "options",
"categories": ["59eba1833ed54d1200c8d3f1"],
"options": [
{ "name": "opt1", "problem": "##0##" },
{ "name": "opt2", "problem": "##22##" },
{ "name": "opt3", "problem": "##20##" },
{ "name": "opt4", "problem": "##10##" },
{ "name": "opt5", "problem": "jiná hodnota " }
],
"correctAnswer": ["opt4"],
"solutions": [{}]
},
{
"slug": "S02T03U11",
"title": "S02T03U11",
"question":
"Určete délku strany ##s## &&\\images\\tasks\\S02T03\\S02T03U11.jpg&&",
"maxPoints": 2,
"type": "options",
"categories": ["59eba1833ed54d1200c8d3f1"],
"options": [
{ "name": "opt1", "problem": "##4##cm" },
{ "name": "opt2", "problem": "##5##cm" },
{ "name": "opt3", "problem": "##5,5##cm" },
{ "name": "opt4", "problem": "##4,4##cm" },
{ "name": "opt5", "problem": "jiná hodnota " }
],
"correctAnswer": ["opt1"],
"solutions": [{}]
},
{
"slug": "S02T03U12",
"title": "S02T03U12",
"taskText":
"Obdélník má obvod 82m, délka jeho uhlopříčky je 29m.",
"question": "O kolik centimetrů je delší strana delší?",
"maxPoints": 2,
"type": "options",
"categories": ["59eba1833ed54d1200c8d3f1"],
"options": [
{ "name": "opt1", "problem": "##1##cm" },
{ "name": "opt2", "problem": "##4##cm" },
{ "name": "opt3", "problem": "##21##cm" },
{ "name": "opt4", "problem": "##6##cm" },
{ "name": "opt5", "problem": "jiná hodnota " }
],
"correctAnswer": ["opt1"],
"solutions": [{}]
},
{
"slug": "S02T03U13",
"title": "S02T03U13",
"question": "##{{{(x-3)!+(x-1)!}}\\over{(x-2)!}}=3##",
"maxPoints": 1,
"type": "options",
"categories": ["59eba1833ed54d1200c8d3f1"],
"options": [
{ "name": "opt1", "problem": "##K=-1;3##" },
{ "name": "opt2", "problem": "##K=-1##" },
{ "name": "opt3", "problem": "##K=0##" },
{ "name": "opt4", "problem": "##K=3##" },
{ "name": "opt5", "problem": "jiná hodnota " }
],
"correctAnswer": ["opt4"],
"solutions": [{}]
},
{
"slug": "S02T03U14",
"title": "S02T03U14",
"taskText": "Na přímce je znázorněno 10 různých bodů.",
"question": "Kolik různých přímek tyto body určují?",
"maxPoints": 1,
"type": "options",
"categories": ["59eba1833ed54d1200c8d3f1"],
"options": [
{ "name": "opt1", "problem": "##25##přímek" },
{ "name": "opt2", "problem": "##60##přímek" },
{ "name": "opt3", "problem": "##120##přímek" },
{ "name": "opt4", "problem": "##45##přímek" },
{ "name": "opt5", "problem": "jiný počet " }
],
"correctAnswer": ["opt4"],
"solutions": [{}]
},
{
"slug": "S02T03U15",
"title": "S02T03U15",
"taskText": "Silniční válec má průměr 80cm a délku 1,5m.",
"question":
"Určete obsah plochy, kterou uválcuje za 1 hodinu, otočí-li se kolem své osy jednou za 15 sekund.",
"maxPoints": 2,
"type": "options",
"categories": ["59eba1833ed54d1200c8d3f1"],
"options": [
{ "name": "opt1", "problem": "##933m^2##" },
{ "name": "opt2", "problem": "##1002m^2##" },
{ "name": "opt3", "problem": "##856m^2##" },
{ "name": "opt4", "problem": "##905m^2##" },
{ "name": "opt5", "problem": "jiná hodnota " }
],
"correctAnswer": ["opt4"],
"solutions": [{}]
},
{
"slug": "S02T03U16",
"title": "S02T03U16",
"question":
"K jednotlivým rovnicím přiřaďte množinu jejích řešení.",
"maxPoints": 3,
"partPoints": [0, 1, 2, 4],
"type": "pairs",
"categories": ["59eba1833ed54d1200c8d3f1"],
"options": [
{
"name": "opt1",
"problem": "##{{\\log(x)}\\over{\\log(3x-5)}}=1##",
"part": "opt"
},
{
"name": "opt2",
"problem": "##\\log_5(x)=2##",
"part": "opt"
},
{
"name": "opt3",
"problem": "##\\log_5\\sqrt{1\\over{125}}=x##",
"part": "opt"
},
{ "name": "ans1", "problem": "##25##", "part": "ans" },
{
"name": "ans2",
"problem": "##x={5\\over2}##",
"part": "ans"
},
{ "name": "ans3", "problem": "##x=5##", "part": "ans" },
{
"name": "ans4",
"problem": "##2\\over5##",
"part": "ans"
},
{
"name": "ans5",
"problem": "##-{3\\over2}##",
"part": "ans"
}
],
"correctAnswer": [
{ "name": "opt1", "correct": "ans2" },
{ "name": "opt2", "correct": "ans1" },
{ "name": "opt3", "correct": "ans5" }
],
"solutions": [{}]
},
{
"slug": "S02T03U17",
"title": "S02T03U17",
"question":
"Určete číslo ##p## tak, aby bod C ležel na přímce AB. A[-2;-1], B[1;3], C[2p-1;p-3]",
"maxPoints": 2,
"type": "options",
"categories": ["59eba1833ed54d1200c8d3f1"],
"options": [
{ "name": "opt1", "problem": "##p=-1##" },
{ "name": "opt2", "problem": "##p=-2##" },
{ "name": "opt3", "problem": "##p=2##" },
{ "name": "opt4", "problem": "##p=3##" },
{ "name": "opt5", "problem": "##p=-3##" }
],
"correctAnswer": ["opt2"],
"solutions": [{}]
},
{
"slug": "S02T03U18",
"title": "S02T03U18",
"question":
"Určete odchylku přímek ##p,q## je-li ##q:2x+y-1=0;~p:x=1+t;~y=2+3t;~t\\in\\mathbb{R}##",
"maxPoints": 2,
"type": "options",
"categories": ["59eba1833ed54d1200c8d3f1"],
"options": [
{ "name": "opt1", "problem": "##\\pi\\over2##" },
{ "name": "opt2", "problem": "##\\pi##" },
{ "name": "opt3", "problem": "##\\pi\\over3##" },
{ "name": "opt4", "problem": "##\\pi\\over4##" },
{ "name": "opt5", "problem": "##3\\pi\\over2##" }
],
"correctAnswer": ["opt4"],
"solutions": [{}]
},
{
"slug": "S02T03U19",
"title": "S02T03U19",
"question":
"Určete, zda je zobrazená množina bodů grafem funkce.",
"maxPoints": 3,
"partPoints": [0, 0, 2, 3, 3],
"type": "yes-no",
"categories": ["59eba1833ed54d1200c8d3f1"],
"options": [
{
"name": "opt1",
"problem":
"&&\\images\\tasks\\S02T03\\S02T03U019_A.jpg&&"
},
{
"name": "opt2",
"problem":
"&&\\images\\tasks\\S02T03\\S02T03U019_B.jpg&&"
},
{
"name": "opt3",
"problem":
"&&\\images\\tasks\\S02T03\\S02T03U019_C.jpg&&"
},
{
"name": "opt4",
"problem":
"&&\\images\\tasks\\S02T03\\S02T03U019_D.jpg&&"
}
],
"correctAnswer": [
{ "name": "opt1", "correct": true },
{ "name": "opt2", "correct": false },
{ "name": "opt3", "correct": true },
{ "name": "opt4", "correct": true }
],
"solutions": [{}]
},
{
"slug": "S02T03U20",
"title": "S02T03U20",
"question": "Přiřaďte správný definiční obor k funkcím:",
"maxPoints": 4,
"partPoints": [0, 0, 1, 2, 4],
"type": "pairs",
"categories": ["59eba1833ed54d1200c8d3f1"],
"options": [
{
"name": "opt1",
"problem": "##x^2+3x-1##",
"part": "opt"
},
{
"name": "opt2",
"problem": "##\\sqrt{{x+2}\\over{{4x-6}}}##",
"part": "opt"
},
{
"name": "opt3",
"problem": "##\\log(x-2)##",
"part": "opt"
},
{
"name": "opt4",
"problem": "##\\sqrt{x+2}##",
"part": "opt"
},
{
"name": "ans1",
"problem": "##x\\in(2;\\infty)##",
"part": "ans"
},
{
"name": "ans2",
"problem": "##x\\in\\langle-2;\\infty)##",
"part": "ans"
},
{
"name": "ans3",
"problem": "##x\\in(-\\infty;-2\\rangle##",
"part": "ans"
},
{
"name": "ans4",
"problem":
"##x\\in(-\\infty,-2\\rangle\\cup({3\\over2},\\infty)##",
"part": "ans"
},
{
"name": "ans5",
"problem": "##x\\in\\mathbb{R}##",
"part": "ans"
}
],
"correctAnswer": [
{ "name": "opt1", "correct": "ans5" },
{ "name": "opt2", "correct": "ans4" },
{ "name": "opt3", "correct": "ans1" },
{ "name": "opt4", "correct": "ans2" }
],
"solutions": [{}]
},
{
"slug": "S02T03U21",
"title": "S02T03U21",
"taskText":
"Jsou dány dvě funkce ##f(x)=3x+1## a ##g(x)=x^2+3x+2##",
"question": "Vypočítejte ##f(g(1))##",
"maxPoints": 1,
"type": "options",
"categories": ["59eba1833ed54d1200c8d3f1"],
"options": [
{ "name": "opt1", "problem": "##17##" },
{ "name": "opt2", "problem": "##15##" },
{ "name": "opt3", "problem": "##23##" },
{ "name": "opt4", "problem": "##19##" },
{ "name": "opt5", "problem": "##25##" }
],
"correctAnswer": ["opt4"],
"solutions": [{}]
},
{
"slug": "S02T03U22",
"title": "S02T03U22",
"taskText": "Ve třídě 1A se vyučuje 11 různých předmětů.",
"question":
"Kolika způsoby lze sestavit rozvrh na jeden den, vyučuje-li se tento den 6 různých předmětů.",
"maxPoints": 1,
"type": "options",
"categories": ["59eba1833ed54d1200c8d3f1"],
"options": [
{ "name": "opt1", "problem": "##11!\\over5!##" },
{ "name": "opt2", "problem": "##{11\\choose5}##" },
{ "name": "opt3", "problem": "##{11\\choose6}##" },
{ "name": "opt4", "problem": "##11!\\over6!##" },
{ "name": "opt5", "problem": "##11!-5!##" }
],
"correctAnswer": ["opt1"],
"solutions": [{}]
},
{
"slug": "S02T03U23",
"title": "S02T03U23",
"taskText":
"Řešte nerovnici s neznámou ##n\\in\\mathbb{N}## $${n!\\over{n-2}}+24\\geq10n$$.",
"maxPoints": 2,
"type": "options",
"categories": ["59eba1833ed54d1200c8d3f1"],
"options": [
{
"name": "opt1",
"problem": "##n\\in\\mathbb{N}-\\langle3;8\\rangle##"
},
{
"name": "opt2",
"problem": "##n\\in\\langle8,\\infty)\\cup\\{2;3\\}##"
},
{ "name": "opt3", "problem": "##\\{0;1;2;3\\}##" },
{
"name": "opt4",
"problem": "##n\\in\\langle3;8\\rangle##"
},
{ "name": "opt5", "problem": "jiná množina" }
],
"correctAnswer": ["opt2"],
"solutions": [{}]
},
{
"slug": "S02T03U24",
"title": "S02T03U24",
"question":
"Kolikrát je pravděpodobnější, že padnou na kostkách všechna čísla stejná při hodu dvěma kostkama než při hodu třema?",
"maxPoints": 2,
"type": "options",
"categories": ["59eba1833ed54d1200c8d3f1"],
"options": [
{ "name": "opt1", "problem": "##4x##" },
{ "name": "opt2", "problem": "##2x##" },
{ "name": "opt3", "problem": "##8x##" },
{ "name": "opt4", "problem": "##6x##" },
{ "name": "opt5", "problem": "##3x##" }
],
"correctAnswer": ["opt4"],
"solutions": [{}]
},
{
"slug": "S02T03U25",
"title": "S02T03U25",
"question":
"Vypočtěte výšku komolého rotačního kužele, je-li dán jeho objem ##V=516~cm^3## a poloměr podstavy ##r_1=9,4~cm##. ",
"maxPoints": 2,
"type": "options",
"categories": ["59eba1833ed54d1200c8d3f1"],
"options": [
{ "name": "opt1", "problem": "##5,9##" },
{ "name": "opt2", "problem": "##3,5##" },
{ "name": "opt3", "problem": "##6,3##" },
{ "name": "opt4", "problem": "##4,4##" },
{ "name": "opt5", "problem": "jiná hodnota " }
],
"correctAnswer": ["opt4"],
"solutions": [{}]
},
{
"slug": "S02T03U26",
"title": "S02T03U26",
"question":
"Určete rozlohu obdélníkového pozemku, který je na plánku s měřítkem 1:500 nakreslen s rozměry 0,83dm a 0,2dm.",
"maxPoints": 1,
"type": "options",
"categories": ["59eba1833ed54d1200c8d3f1"],
"options": [
{ "name": "opt1", "problem": "##415m^2##" },
{ "name": "opt2", "problem": "##41,5m^2##" },
{ "name": "opt3", "problem": "##66,4m^2##" },
{ "name": "opt4", "problem": "##664m^2##" },
{ "name": "opt5", "problem": "jiná hodnota " }
],
"correctAnswer": ["opt1"],
"solutions": [{}]
}
]
}
}
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