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pufinek/S02T02

Last active March 14, 2018 20:36
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S02T02
{
"test": {
"title": "S02T02",
"slug": "S02T02",
"description": "Přípravný test k státní maturitě.",
"successfulLimit": 33,
"tasks": [
{
"slug": "S02T02U01",
"title": "S02T02U01",
"taskText":
"Vypočítejte: Jedna celá jedna setina + nula celá sedmdesát sedm tisícin - šest set sedmdesát osm celých tři sta třicet šest sto tisícin + osm set pět celých osm set pět desetitisícin.",
"question": "Ve kterém intervalu se nachází výsledek?",
"maxPoints": 1,
"type": "options",
"categories": ["5a89fd0ebf5e07c5af6d5f95"],
"options": [
{ "name": "opt1", "problem": "##\\langle-100;100)##" },
{ "name": "opt2", "problem": "##\\langle100;250)##" },
{ "name": "opt3", "problem": "##\\langle250;350)##" },
{ "name": "opt4", "problem": "##\\langle-250;-100)##" },
{ "name": "opt5", "problem": "není v žádném intervalu " }
],
"correctAnswer": ["opt2"],
"solutions": [{}]
},
{
"slug": "S02T02U02",
"title": "S02T02U02",
"question":
"Na číselné ose určete pozici hodnoty ##0.4##. &&\\images\\tasks\\S02T02\\S02T02P02.jpg&&",
"maxPoints": 1,
"type": "options",
"categories": ["5a89fd0ebf5e07c5af6d5f95"],
"options": [
{ "name": "opt1", "problem": "##A.B##" },
{ "name": "opt2", "problem": "##B.D##" },
{ "name": "opt3", "problem": "##C.A##" },
{ "name": "opt4", "problem": "##D.C##" },
{ "name": "opt5", "problem": "##E.E##" }
],
"correctAnswer": ["opt5"],
"solutions": [{}]
},
{
"slug": "S02T02U03",
"title": "S02T02U03",
"question":
"Upravte:$$a^2-b^2-\\{3ab-2b^2-[a^2+2ab-(b^2-ab)]\\}=$$",
"maxPoints": 1,
"type": "options",
"categories": ["5a89fd0ebf5e07c5af6d5f95"],
"options": [
{ "name": "opt1", "problem": "##0##" },
{ "name": "opt2", "problem": "##2a^2##" },
{ "name": "opt3", "problem": "##-2b(b+3a)##" },
{ "name": "opt4", "problem": "##-2b(2b+a)##" },
{ "name": "opt5", "problem": "jiná hodnota " }
],
"correctAnswer": ["opt2"],
"solutions": [{}]
},
{
"slug": "S02T02U04",
"title": "S02T02U04",
"question":
"Upravte: $$\\left({a\\over{a+b}}+{b\\over {a-b}}+1 \\right):\\left({a\\over{a-b}}-{b\\over {a+b}}+1 \\right) =$$",
"maxPoints": 2,
"type": "options",
"categories": ["5a89fd0ebf5e07c5af6d5f95"],
"options": [
{ "name": "opt1", "problem": "##b+1##" },
{ "name": "opt2", "problem": "##a\\over{a^2-b^2}##" },
{ "name": "opt3", "problem": "##b\\over{a^2-b^2}##" },
{ "name": "opt4", "problem": "##a+1##" },
{ "name": "opt5", "problem": "jiná hodnota" }
],
"correctAnswer": ["opt5"],
"solutions": [{}]
},
{
"slug": "S02T02U05",
"title": "S02T02U05",
"question": "Vypočítejte $$(z^2+7z+12):(4+z)=$$",
"maxPoints": 1,
"type": "options",
"categories": ["5a89fd0ebf5e07c5af6d5f95"],
"options": [
{ "name": "opt1", "problem": "##z+2##" },
{ "name": "opt2", "problem": "##z+3##" },
{ "name": "opt3", "problem": "##z-2##" },
{ "name": "opt4", "problem": "##3-z##" },
{ "name": "opt5", "problem": "##z-1##" }
],
"correctAnswer": ["opt2"],
"solutions": [{}]
},
{
"slug": "S02T02U06",
"title": "S02T02U06",
"taskText":
"V obdélníku ABCD je dáno:|AB|=63mm, |AD|=25mm. Body E a F rozdělují stranu CD na třetiny. ",
"question":
"Vypočítejte velikost vnitřních úhlů trojúhelníku AEF. &&\\images\\tasks\\S02T02\\S02T02P06.jpg&& ",
"maxPoints": 2,
"type": "options",
"categories": ["5a89fd0ebf5e07c5af6d5f95"],
"options": [
{
"name": "opt1",
"problem": "##\\alpha=19°,~\\beta=130°,~\\gamma=31°##"
},
{
"name": "opt2",
"problem": "##\\alpha=25°,~\\beta=130°,~\\gamma=25°##"
},
{
"name": "opt3",
"problem": "##\\alpha=25°,~\\beta=105°,~\\gamma=50°##"
},
{
"name": "opt4",
"problem": "##\\alpha=22°,~\\beta=130°,~\\gamma=28°##"
},
{ "name": "opt5", "problem": "jiné hodnoty " }
],
"correctAnswer": ["opt1"],
"solutions": [{}]
},
{
"slug": "S02T02U07",
"title": "S02T02U07",
"taskText":
"Máme dva čtverce. Druhý má stranu o ##1cm## delší a obsah o ##17cm^2## větší než první čtverec.",
"question": "Vypočítejte délku strany prvního čtverce.",
"maxPoints": 1,
"type": "options",
"categories": ["5a89fd0ebf5e07c5af6d5f95"],
"options": [
{ "name": "opt1", "problem": "jiná hodnota" },
{ "name": "opt2", "problem": "##8dm##" },
{ "name": "opt3", "problem": "##7dm##" },
{ "name": "opt4", "problem": "##9dm##" },
{ "name": "opt5", "problem": "##10dm##" }
],
"correctAnswer": ["opt2"],
"solutions": [{}]
},
{
"slug": "S02T02U08",
"title": "S02T02U08",
"taskText":
"Čtvrtkruh na obrázku má poloměr 7cm. &&\\images\\tasks\\S02T02\\S02T02P08.jpg&& ",
"question": "Vypočítejte obsah vybarvené části.",
"maxPoints": 2,
"type": "options",
"categories": ["5a89fd0ebf5e07c5af6d5f95"],
"options": [
{
"name": "opt1",
"problem": "##{{49(\\pi-2)}\\over8}~cm^2##"
},
{
"name": "opt2",
"problem": "##{{49(\\pi-1)}\\over8}~cm^2##"
},
{
"name": "opt3",
"problem": "##{{49(\\pi-2)}\\over4}~cm^2##"
},
{
"name": "opt4",
"problem": "##{{49(\\pi-1)}\\over4}~cm^2##"
},
{ "name": "opt5", "problem": "jiná hodnota " }
],
"correctAnswer": ["opt1"],
"solutions": [{}]
},
{
"slug": "S02T02U09",
"title": "S02T02U09",
"question":
"Vypočítejte neznámou x. $$\\log_3(2x+1)-\\log_3(x-1)=1$$",
"maxPoints": 1,
"type": "options",
"categories": ["5a89fd0ebf5e07c5af6d5f95"],
"options": [
{ "name": "opt1", "problem": "##x=2##" },
{ "name": "opt2", "problem": "##x=4##" },
{ "name": "opt3", "problem": "##x=3##" },
{ "name": "opt4", "problem": "##x=7##" },
{ "name": "opt5", "problem": "jiná hodnota " }
],
"correctAnswer": ["opt2"],
"solutions": [{}]
},
{
"slug": "S02T02U10",
"title": "S02T02U10",
"taskText":
"Při statistickém šetření byly zjištěny tyto údaje (hmotnost v kg):75;90;84;55;63;70;85;100;65;70;90;92;71;70;52;70;90;70;65;100",
"question": "Zjistěte modus a medián.",
"maxPoints": 2,
"type": "options",
"categories": ["5a89fd0ebf5e07c5af6d5f95"],
"options": [
{ "name": "opt1", "problem": "modus=70; medián=70,5" },
{ "name": "opt2", "problem": "modus=71; medián=70" },
{ "name": "opt3", "problem": "modus=70,5; medián=70" },
{ "name": "opt4", "problem": "modus=70; medián=71" },
{ "name": "opt5", "problem": "modus=medián=70" }
],
"correctAnswer": ["opt1"],
"solutions": [{}]
},
{
"slug": "S02T02U11",
"title": "S02T02U11",
"question":
"Pro které hodnoty ##x\\in\\mathbb{R}## má tato rovnice řešení? $${x-10\\choose{x-12}}=10$$",
"maxPoints": 1,
"type": "options",
"categories": ["5a89fd0ebf5e07c5af6d5f95"],
"options": [
{ "name": "opt1", "problem": "##6##" },
{ "name": "opt2", "problem": "##15##" },
{ "name": "opt3", "problem": "jiná hodnota" },
{ "name": "opt4", "problem": "##8##" },
{ "name": "opt5", "problem": "##13## " }
],
"correctAnswer": ["opt3"],
"solutions": [{}]
},
{
"slug": "S02T02U12",
"title": "S02T02U12",
"taskText":
"Vybarvený obrazec v centimetrové čtvercové síti má obsah ##784cm^2.## ",
"question": "Určete jeho obvod.",
"maxPoints": 1,
"type": "options",
"categories": ["5a89fd0ebf5e07c5af6d5f95"],
"options": [
{ "name": "opt1", "problem": "##120cm##" },
{ "name": "opt2", "problem": "##160cm##" },
{ "name": "opt3", "problem": "##140cm##" },
{ "name": "opt4", "problem": "##180cm##" },
{ "name": "opt5", "problem": "jiná hodnota " }
],
"correctAnswer": ["opt3"],
"solutions": [{}]
},
{
"slug": "S02T02U13",
"title": "S02T02U13",
"question": "##4^x+2^{x+1}=24## Kolik je x?",
"maxPoints": 1,
"type": "options",
"categories": ["5a89fd0ebf5e07c5af6d5f95"],
"options": [
{ "name": "opt1", "problem": "##x=2##" },
{ "name": "opt2", "problem": "##x=1##" },
{ "name": "opt3", "problem": "##x=4##" },
{ "name": "opt4", "problem": "##x=0##" },
{ "name": "opt5", "problem": "jiná hodnota " }
],
"correctAnswer": ["opt1"],
"solutions": [{}]
},
{
"slug": "S02T02U14",
"title": "S02T02U14",
"taskText":
"V soustavě Oxy jsou dány body ##A[-2;5],B[1;-7],C[3;2]## tvořící trojúhelník.",
"question":
"Určete velikost úhlu ##\\alpha##. Výsledek zapište jako prosté číslo.",
"maxPoints": 2,
"type": "write",
"categories": ["5a89fd0ebf5e07c5af6d5f95"],
"correctAnswer": ["45"],
"solutions": [{}]
},
{
"slug": "S02T02U15",
"title": "S02T02U15",
"taskText":
"V soustavě Oxy jsou dány body ##A[-2;5],B[1;-7],C[3;2]## tvořící trojúhelník.",
"maxPoints": 2,
"question":
"Určete obvod trojúhelníku ##ABC##. Výsledek zaokrouhlete na desítky.",
"type": "write",
"categories": ["5a89fd0ebf5e07c5af6d5f95"],
"correctAnswer": ["30"],
"solutions": [{}]
},
{
"slug": "S02T02U16",
"title": "S02T02U16",
"taskText":
"V osudí je 5 modrých a 8 žlutých koulí. Provedeme náhodný tah 4 koulí.",
"question":
"Jaká je pravděpodobnost? Přiřaďte správnou odpověď.",
"maxPoints": 3,
"partPoints": [0, 1, 2, 3],
"type": "pairs",
"categories": ["5a89fd0ebf5e07c5af6d5f95"],
"options": [
{
"name": "opt1",
"problem": "vytáhneme 2 modré a 2 žluté koule",
"part": "opt"
},
{
"name": "opt2",
"problem": "vytáhneme všechny koule stejné barvy",
"part": "opt"
},
{
"name": "opt3",
"problem": "vytáhneme aspoň 3 žluté koule?",
"part": "opt"
},
{
"name": "ans1",
"problem": "##70\\over143##",
"part": "ans"
},
{
"name": "ans2",
"problem": "##56\\over143##",
"part": "ans"
},
{
"name": "ans3",
"problem": "##70\\over75##",
"part": "ans"
},
{
"name": "ans4",
"problem": "##15\\over143##",
"part": "ans"
},
{ "name": "ans5", "problem": "jiná možnost", "part": "ans" }
],
"correctAnswer": [
{ "name": "opt1", "correct": "ans2" },
{ "name": "opt2", "correct": "ans4" },
{ "name": "opt3", "correct": "ans1" }
],
"solutions": [{}]
},
{
"slug": "S02T02U17",
"title": "S02T02U17",
"taskText":
"Kuželovitá nádoba s průměrem 60cm a stranou 50cm je zcela naplněna vodou. Vodu nalijeme do válcové nádoby o poloměru 30cm a výšce 20cm.",
"question":
"Kolik litrů vody je třeba dolít, aby tato nádoba byla zcela naplněna?",
"maxPoints": 2,
"type": "options",
"categories": ["5a89fd0ebf5e07c5af6d5f95"],
"options": [
{ "name": "opt1", "problem": "méně než 19 l" },
{ "name": "opt2", "problem": "21 l" },
{ "name": "opt3", "problem": "20 l" },
{ "name": "opt4", "problem": "19 l" },
{ "name": "opt5", "problem": "více než 21 l " }
],
"correctAnswer": ["opt4"],
"solutions": [{}]
},
{
"slug": "S02T02U18",
"title": "S02T02U18",
"question":
"Kolik prvních členů aritmetické posloupnosti dává součet 250, je-li ##a_3=5;~d=1##?",
"maxPoints": 1,
"type": "options",
"categories": ["5a89fd0ebf5e07c5af6d5f95"],
"options": [
{ "name": "opt1", "problem": "##21## členů" },
{ "name": "opt2", "problem": "##19## členů" },
{ "name": "opt3", "problem": "##22## členů" },
{ "name": "opt4", "problem": "##20## členů" },
{ "name": "opt5", "problem": "##23## členů" }
],
"correctAnswer": ["opt4"],
"solutions": [{}]
},
{
"slug": "S02T02U19",
"title": "S02T02U19",
"taskText":
"Z kasáren vyjela kolona aut jedoucí průměrnou rychlostí 28km\\hod. do výcvikového prostoru a za 1 hodinu 15 minut vyjelo za kolonou vojenské terénní vozidlo. Toto vozidlo jelo průměrnou rychlostí 63km\\hod. a přijelo do výcvikového prostoru současně s kolonou.",
"question":
"Určete vzdálenost vojenského výcvikového prostoru od kasáren. Výslednou vzdálenost zaokrouhlete na celé km.",
"maxPoints": 2,
"type": "options",
"categories": ["5a89fd0ebf5e07c5af6d5f95"],
"options": [
{ "name": "opt1", "problem": "##\\langle64;68)##" },
{ "name": "opt2", "problem": "více než 72 km" },
{ "name": "opt3", "problem": "##\\langle68;72)##" },
{ "name": "opt4", "problem": "##\\langle60;64)##" },
{ "name": "opt5", "problem": "méně než 60 km" }
],
"correctAnswer": ["opt4"],
"solutions": [{}]
}
]
}
}
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