S02T06

{
  "test": {
    "title": "S02T06",
    "slug": "S02T06",
    "description": "Příprava k maturitě.",
    "successfulLimit": 44,
    "cermat":false,
    "tasks": [
      {
        "slug": "S02T06U01",
        "title": "S02T06U01",
        "taskText": "Svíce uhoří za 12minut o 2centimetry.",
        "question": "Jak vysoká musí být svíce, aby hořela 1 hodinu a 36 minut?",
        "maxPoints": 2,
        "type": "options",
        
        "options": [
          { "name": "opt1", "problem": "####" },
          { "name": "opt2", "problem": "####" },
          { "name": "opt3", "problem": "16 cm" },
          { "name": "opt4", "problem": "####" },
          { "name": "opt5", "problem": "jiný " }
        ],
        "correctAnswer": ["opt3"],
        "solutions": []
      },
      {
        "slug": "S02T06U02",
        "title": "S02T06U02",
        "taskText":
          "Obdélník má obvod 56cm a jednu stranu o 20cm delší než druhou.",
        "question": " Jaký je jeho obsah?.",
        "maxPoints": 2,
        "type": "options",
        
        "options": [
          { "name": "opt1", "problem": "##195dm^3##" },
          { "name": "opt2", "problem": "####" },
          { "name": "opt3", "problem": "####" },
          { "name": "opt4", "problem": "####" },
          { "name": "opt5", "problem": "jiný " }
        ],
        "correctAnswer": ["opt1"],
        "solutions": []
      },
      {
        "slug": "S02T06U03",
        "title": "S02T06U03",
        "question":
          " Vypočítej: $${2a-c\\over4c}-{3a^2-2bc\\over6ac}~~~~-{3a\\over~b}~~+{5a-b\\over2b}~-{4b+a\\over8b}=$$.",
        "maxPoints": 2,
        "type": "options",
        
        "options": [
          { "name": "opt1", "problem": "##{8b^2-30ab-15a^2}\\over24ab##" },
          { "name": "opt2", "problem": "####" },
          { "name": "opt3", "problem": "####" },
          { "name": "opt4", "problem": "####" },
          { "name": "opt5", "problem": "jiný " }
        ],
        "correctAnswer": ["opt1"],
        "solutions": []
      },
      {
        "slug": "S02T06U04",
        "title": "S02T06U04",
        "taskText":
          "200 krabic bylo narovnáno ve třech řadách. V první řadě bylo o 13 více než ve druhé řadě. Ve druhé řadě bylo o jednu pětinu více než ve třetí řadě.",
        "question": "Kolik krabic bylo v druhé řadě ?",
        "maxPoints": 2,
        "type": "options",
        
        "options": [
          { "name": "opt1", "problem": "####" },
          { "name": "opt2", "problem": "####" },
          { "name": "opt3", "problem": "####" },
          { "name": "opt4", "problem": "##66##" },
          { "name": "opt5", "problem": "jiný " }
        ],
        "correctAnswer": ["opt4"],
        "solutions": []
      },
      {
        "slug": "S02T06U05",
        "title": "S02T06U05",
        "question":
          "Součet délek všech stěnových, tělesových uhlopříček v krychli s hranou délky 1 cm je :",
        "maxPoints": 2,
        "type": "options",
        
        "options": [
          { "name": "opt1", "problem": "####" },
          { "name": "opt2", "problem": "####" },
          { "name": "opt3", "problem": "####" },
          { "name": "opt4", "problem": "##4\\cdot\\sqrt{3}(\\sqrt{6}+1)##" },
          { "name": "opt5", "problem": "jiný " }
        ],
        "correctAnswer": ["opt4"],
        "solutions": []
      },
      {
        "slug": "S02T06U06",
        "title": "S02T06U06",
        "question":
          "Řešte nerovnici : ##{{2-3x}\\over{(x+1)(1-x)}}~~~~~~~~{\\lt}0##.",
        "maxPoints": 2,
        "type": "options",
        
        "options": [
          { "name": "opt1", "problem": "####" },
          {
            "name": "opt2",
            "problem": "##K=(-1;{2\\over3})\\cup(1;\\infty)##"
          },
          { "name": "opt3", "problem": "####" },
          { "name": "opt4", "problem": "####" },
          { "name": "opt5", "problem": "jiný " }
        ],
        "correctAnswer": ["opt2"],
        "solutions": []
      },
      {
        "slug": "S02T06U07",
        "title": "S02T06U07",
        "question": "Vyřešte :##{\\sqrt{3-x}}+{\\sqrt{3+x}}={\\sqrt2x}##",
        "maxPoints": 2,
        "type": "options",
        
        "options": [
          { "name": "opt1", "problem": "####" },
          { "name": "opt2", "problem": "####" },
          { "name": "opt3", "problem": "####" },
          { "name": "opt4", "problem": "##K=\\{3\\}##" },
          { "name": "opt5", "problem": "jiný " }
        ],
        "correctAnswer": ["opt4"],
        "solutions": []
      },
      {
        "slug": "S02T06U08",
        "title": "S02T06U08",
        "taskText":
          "Student dostal test, který obsahuje 5 otázek. Ke každé otázce vybírá právě jednu odpověď.",
        "question":
          "Jaká je pravděpodobnost, že student zodpoví více než 60% otázek správně, volí-li odpovědi zcela náhodně ? .",
        "maxPoints": 2,
        "type": "options",
        
        "options": [
          { "name": "opt1", "problem": "##18,8%##" },
          { "name": "opt2", "problem": "####" },
          { "name": "opt3", "problem": "####" },
          { "name": "opt4", "problem": "####" },
          { "name": "opt5", "problem": "jiný " }
        ],
        "correctAnswer": ["opt1"],
        "solutions": []
      },
      {
        "slug": "S02T06U09",
        "title": "S02T06U09",
        "taskText":
          "V lichoběžníku ABCD znáte délky stran a=30cm, b=15cm, c=20cm, d=12cm.",
        "question": "Určete velikost největšího vnitřního úhlu.",
        "maxPoints": 2,
        "type": "options",
        
        "options": [
          { "name": "opt1", "problem": "##94°32´##" },
          { "name": "opt2", "problem": "##85°28´##" },
          { "name": "opt3", "problem": "##103°15´##" },
          { "name": "opt4", "problem": "##137°07´##" },
          { "name": "opt5", "problem": "jiný " }
        ],
        "correctAnswer": ["opt5"],
        "solutions": []
      },
      {
        "slug": "S02T06U10",
        "title": "S02T06U10",
        "question": "Čtvrtina kterého čísla je o 5 větší 40?.",
        "maxPoints": 2,
        "type": "options",
        
        "options": [
          { "name": "opt1", "problem": "####" },
          { "name": "opt2", "problem": "##180##" },
          { "name": "opt3", "problem": "####" },
          { "name": "opt4", "problem": "####" },
          { "name": "opt5", "problem": "jiný " }
        ],
        "correctAnswer": ["opt2"],
        "solutions": []
      },
      {
        "slug": "S02T06U11",
        "title": "S02T06U11",
        "taskText": "",
        "question": "Rozhodněte o následujících tvrzeních, zda jsou pravdivá (ANO) či nepravdivá (NE).",
        "maxPoints": 3,
        "type": "yes-no",
        "partPoints":[3, 2, 1, 0],
        "options": [
          {
              "name": "opt1",
              "problem": " ##\\text{Pro každá dvě reálná čísla a, b platí: } (a-b) \\cdot (a-b) = a^2 - b^2##"
          },
          {
              "name": "opt2",
              "problem": "##\\text{Pro každé reálné číslo } x \\text{ platí: } (x-7)^2  = x^{2}-14x-49##"
          },
          { "name": "opt3", "problem": "##\\text{Pro každá reálné číslo } x~(x \\neq \\pm 1) \\text{ platí: } \\\\ {{x} \\over {x+1}}-{{x} \\over {x-1}}={{2x} \\over {1-x^2}}##" },
          { "name": "opt4", "problem": "##\\text{Pro každé reálné } x \\neq 3 \\text{platí:} \\\\ {{x^{2} + 3} \\over {x-3}}=x+3+ {{12} \\over {x-3}}##" }
      ],
      "correctAnswer": [
          { "name": "opt1", "correct": false },
          { "name": "opt2", "correct": false },
          { "name": "opt3", "correct": true },
          { "name": "opt4", "correct": true }
      ],
        "solutions": []
      },
      {
        "slug": "S02T06U12",
        "title": "S02T06U12",
        "question":
          "Zjednodušte : $$\\left({\\sqrt(3) + \\sqrt(11) \\over \\sqrt3 - \\sqrt(11)}~~~~~ +{\\sqrt(11)-\\sqrt(3) \\over \\sqrt (11)+\\sqrt 3}~~~~~\\right) =$$.",
        "maxPoints": 2,
        "type": "options",
        
        "options": [
          { "name": "opt1", "problem": "####" },
          { "name": "opt2", "problem": "##-{{\\sqrt(33)}\\over2}##" },
          { "name": "opt3", "problem": "####" },
          { "name": "opt4", "problem": "####" },
          { "name": "opt5", "problem": "jiný " }
        ],
        "correctAnswer": ["opt2"],
        "solutions": []
      },
      {
        "slug": "S02T06U13",
        "title": "S02T06U13",
        "taskText": "Šest dělníků zhotoví za 4 směny 900 výrobků.",
        "question": "Kolik výrobků zhotoví osm dělníků za 5 směn?.",
        "maxPoints": 2,
        "type": "options",
        
        "options": [
          { "name": "opt1", "problem": "####" },
          { "name": "opt2", "problem": "3000" },
          { "name": "opt3", "problem": "####" },
          { "name": "opt4", "problem": "####" },
          { "name": "opt5", "problem": "jiný " }
        ],
        "correctAnswer": ["opt2"],
        "solutions": []
      },
      {
        "slug": "S02T06U14",
        "title": "S02T06U14",
        "taskText":
          "Na počátku roku 1994 jsme vložili 15 000 Kč na vkladní knížku s roční úrokovou mírou 6%(úrokové období je 1 rok). Úroky nebudou nikdy vybírány. Úroky jsou úročeny a připočteny vždy ke konci roku.",
        "question":
          "Jak velká částka bude na vkladní knížce na počátku roku 2003?.",
        "maxPoints": 2,
        "type": "options",
        
        "options": [
          { "name": "opt1", "problem": "##25~342##" },
          { "name": "opt2", "problem": "####" },
          { "name": "opt3", "problem": "####" },
          { "name": "opt4", "problem": "####" },
          { "name": "opt5", "problem": "jiný " }
        ],
        "correctAnswer": ["opt1"],
        "solutions": []
      },
      {
        "slug": "S02T06U15",
        "title": "S02T06U15",
        "question":
          " Přiřaďte definiční obory k funkcím: $$(-\\infty;-2\\rangle\\cup\\langle2;\\infty)$$.",
        "maxPoints": 4,
        "partPoints": [0, 0, 1, 2, 4],
        "type": "pairs",
        
        "options": [
          { "name": "opt1", "problem": "##y=\\sqrt{x^2-4}##", "part": "opt" },
          {
            "name": "opt2",
            "problem": "##y=\\sqrt{{x-2}\\over{x+2}}##",
            "part": "opt"
          },
          { "name": "opt3", "problem": "##y=|x|-4##", "part": "opt" },
          {
            "name": "opt4",
            "problem": "##y={{x-3}\\over{x-2}}##",
            "part": "opt"
          },
          {
            "name": "ans1",
            "problem": "##x\\in(-\\infty;2)\\cup(2;\\infty)##",
            "part": "ans"
          },
          { "name": "ans2", "problem": "##x\\in\\mathbb{R}##", "part": "ans" },
          {
            "name": "ans3",
            "problem": "##x\\in(-\\infty;-2\\rangle\\cup\\langle2;\\infty)##",
            "part": "ans"
          },
          {
            "name": "ans4",
            "problem": "##x\\in(-\\infty;-2)\\cup\\langle2;\\infty)##",
            "part": "ans"
          }
        ],
        "correctAnswer": [
          { "name": "opt1", "correct": "ans3" },
          { "name": "opt2", "correct": "ans4" },
          { "name": "opt3", "correct": "ans2" },
          { "name": "opt4", "correct": "ans1" }
        ],
        "solutions": []
      },
      {
        "slug": "S02T06U16",
        "title": "S02T06U16",
        "question":
          "Určete rozměry obdélníku se stranami ##a;~b;~a\\lt b##, jehož obvod je 34cm a délka úhlopříčky je 13cm.",
        "maxPoints": 2,
        "type": "options",
        
        "options": [
          { "name": "opt1", "problem": "##5;12##" },
          { "name": "opt2", "problem": "####" },
          { "name": "opt3", "problem": "####" },
          { "name": "opt4", "problem": "####" },
          { "name": "opt5", "problem": "jiný " }
        ],
        "correctAnswer": ["opt1"],
        "solutions": []
      },
      {
        "slug": "S02T06U17",
        "title": "S02T06U17",
        "question":
          "Určete vzdálenost bodu M od přímky p, je-li ##M[2;-1]p:3x+4y-12=0##.",
        "maxPoints": 2,
        "type": "options",
        
        "options": [
          { "name": "opt1", "problem": "####" },
          { "name": "opt2", "problem": "####" },
          { "name": "opt3", "problem": "####" },
          { "name": "opt4", "problem": "##2##" },
          { "name": "opt5", "problem": "jiný " }
        ],
        "correctAnswer": ["opt4"],
        "solutions": []
      },
      {
        "slug": "S02T06U18",
        "title": "S02T06U18",
        "question": "Vypočítej: $$3^x+3^{x+2}={10\\over3}$$.",
        "maxPoints": 2,
        "type": "options",
        
        "options": [
          { "name": "opt1", "problem": "####" },
          { "name": "opt2", "problem": "##x=-1##" },
          { "name": "opt3", "problem": "####" },
          { "name": "opt4", "problem": "####" },
          { "name": "opt5", "problem": "jiný " }
        ],
        "correctAnswer": ["opt2"],
        "solutions": []
      },
      {
        "slug": "S02T06U19",
        "title": "S02T06U19",
        "question":
          "Vyjádřete neznámou ##R_z## výrazu: $$S=\\pi(\\mathbb{R}^2-r^2)$$.",
        "maxPoints": 2,
        "type": "options",
        
        "options": [
          { "name": "opt1", "problem": "####" },
          { "name": "opt2", "problem": "####" },
          { "name": "opt3", "problem": "####" },
          {
            "name": "opt4",
            "problem": "##\\mathbb{R}=\\sqrt{S\\over\\pi}+r^2##"
          },
          { "name": "opt5", "problem": "jiný " }
        ],
        "correctAnswer": ["opt4"],
        "solutions": []
      },
      {
        "slug": "S02T06U20",
        "title": "S02T06U20",
        "question":
          "Určete ##S_8##, jestliže jsou první 3 členy geometrické posloupnosti dány graficky: &&\\images\\tasks\\S02T06\\S02T06P20.jpg&&",
        "maxPoints": 2,
        "type": "options",
        
        "options": [
          { "name": "opt1", "problem": "####" },
          { "name": "opt2", "problem": "####" },
          {
            "name": "opt3",
            "problem": "##(S_8=-{255\\over32};q={1\\over2})##"
          },
          { "name": "opt4", "problem": "####" },
          { "name": "opt5", "problem": "jiný " }
        ],
        "correctAnswer": ["opt3"],
        "solutions": []
      },
      {
        "slug": "S02T06U21",
        "title": "S02T06U21",
        "taskText": "V aritmetrické posloupnosti je dáno ##a_1=2;d=3##.",
        "question":
          "Určete součet všech členů posloupnosti od desáteho po dvacátý člen včetně.",
        "maxPoints": 2,
        "type": "options",
        
        "options": [
          { "name": "opt1", "problem": "##484##" },
          { "name": "opt2", "problem": "####" },
          { "name": "opt3", "problem": "####" },
          { "name": "opt4", "problem": "####" },
          { "name": "opt5", "problem": "jiný " }
        ],
        "correctAnswer": ["opt1"],
        "solutions": []
      },
      {
        "slug": "S02T06U22",
        "title": "S02T06U22",
        "taskText":
          "Ze tří kovových koulí s poloměry ##r_3,~r_4,~r_5## byla zhotovena jediná koule.",
        "question": "Jaký je její poloměr?.",
        "maxPoints": 2,
        "type": "options",
        
        "options": [
          { "name": "opt1", "problem": "####" },
          { "name": "opt2", "problem": "####" },
          { "name": "opt3", "problem": "####" },
          { "name": "opt4", "problem": "##[r=6cm];V_0={4\\over3}{\\pi}r^3##" },
          { "name": "opt5", "problem": "jiný " }
        ],
        "correctAnswer": ["opt4"],
        "solutions": []
      },
      {
        "slug": "S02T06U23",
        "title": "S02T06U23",
        "taskText":
          "Hranol s čtvercovou podstavou o hraně ##a## má výšku ##v##. Objem hranolu je ##V##.",
        "question":
          "Vyjádřete velikost hrany ##a## v závislosti na objemu ##V## a výšce ##v##.",
        "maxPoints": 2,
        "type": "options",
        
        "options": [
          { "name": "opt1", "problem": "##a=v\\cdot~V##" },
          { "name": "opt2", "problem": "##a=\\sqrt{V\\over~v}##" },
          { "name": "opt3", "problem": "##a=\\sqrt{v\\over~V}##" },
          { "name": "opt4", "problem": "##a={v\\over~V}##" },
          { "name": "opt5", "problem": "##a={V\\over~v}##" }
        ],
        "correctAnswer": ["opt2"],
        "solutions": []
      },
      {
        "slug": "S02T06U24",
        "title": "S02T06U24",
        "question": "Který z grafů A-D je zobrazením funkce ##f:y=x^2-4x+3##.",
        "maxPoints": 2,
        "type": "options",
        
        "options": [
          { "name": "opt1", "problem": "&&\\images\\tasks\\S02T06\\S02T06P24_b.jpg&&" },
          { "name": "opt2", "problem": "&&\\images\\tasks\\S02T06\\S02T06P24_a.jpg&&" },
          { "name": "opt3", "problem": "&&\\images\\tasks\\S02T06\\S02T06P24_c.jpg&&" },
          { "name": "opt4", "problem": "&&\\images\\tasks\\S02T06\\S02T06P24_d.jpg&&" },
          { "name": "opt5", "problem": "jiný " }
        ],
        "correctAnswer": ["opt2"],
        "solutions": []
      },
      {
        "slug": "S02T06U25",
        "title": "S02T06U25",
        "taskText":
          "Všechny 3 obrázky znázorňují totéž těleso sestavené z kostek při pohledu zepředu, shora a zleva. ",
        "question":
          "Z kolika kostek se skládá toto těleso? &&\\images\\tasks\\S02T06\\S02T06P25.jpg&&",
        "maxPoints": 2,
        "type": "options",
        
        "options": [
          { "name": "opt1", "problem": "##10##" },
          { "name": "opt2", "problem": "##11##" },
          { "name": "opt3", "problem": "##12##" },
          { "name": "opt4", "problem": "##13##" },
          { "name": "opt5", "problem": "##14##" }
        ],
        "correctAnswer": ["opt5"],
        "solutions": []
      },
      {
        "slug": "S02T06U26",
        "title": "S02T06U26",
        "question":
          "Vypočtěte : ##A=log_55^{log_24}-log_2{2\\over 0,5}-log_2 0,125##.",
        "maxPoints": 2,
        "type": "options",
        
        "options": [
          { "name": "opt1", "problem": "####" },
          { "name": "opt2", "problem": "####" },
          { "name": "opt3", "problem": "##A=3##" },
          { "name": "opt4", "problem": "####" },
          { "name": "opt5", "problem": "jiný " }
        ],
        "correctAnswer": ["opt3"],
        "solutions": []
      }
    ]
  }
}