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March 19, 2018 21:34
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| { | |
| "test": { | |
| "title": "S02T16", | |
| "slug": "S02T16", | |
| "description": "Přípravný test k státní maturitě.", | |
| "successfulLimit": 33, | |
| "tasks": [ | |
| { | |
| "slug": "S02T16U01", | |
| "title": "S02T16U01", | |
| "taskText": "&&\\images\\tasks\\S02T16\\S02T16P01.jpg&&", | |
| "question": | |
| "Jaký je obsah celého obrazce, víme-li, že je složen ze stejných čtverců a trojúhelníků? Jeden čtverec má obsah ##4m^2## a jeden trojúhelník tvoří ##1\\over{18}## obsahu útvaru.", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a8a0654bf5e07c5af6d5fba"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##48m^2##" }, | |
| { "name": "opt2", "problem": "##36m^2##" }, | |
| { "name": "opt3", "problem": "##60m^2##" }, | |
| { "name": "opt4", "problem": "##96m^2##" }, | |
| { "name": "opt5", "problem": "jiná hodnota " } | |
| ], | |
| "correctAnswer": ["opt1"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T16U02", | |
| "title": "S02T16U02", | |
| "taskText": | |
| "Mějte množiny ##A=\\{-1;0;1;2;4;5;7\\}~B=\\{0;1;2;4;5;6;7;11;12\\}~C=\\{2;4;5;6;12\\}##", | |
| "question": | |
| "Který z Veronnových diagramů zobrazuje tyto množiny? ", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a89fdfbbf5e07c5af6d5f9b"], | |
| "options": [ | |
| { | |
| "name": "opt1", | |
| "problem": "&&\\images\\tasks\\S02T16\\S02T16P02C.jpg&&" | |
| }, | |
| { | |
| "name": "opt2", | |
| "problem": "&&\\images\\tasks\\S02T16\\S02T16P02B.jpg&&" | |
| }, | |
| { | |
| "name": "opt3", | |
| "problem": "&&\\images\\tasks\\S02T16\\S02T16P02A.jpg&&" | |
| }, | |
| { | |
| "name": "opt4", | |
| "problem": "&&\\images\\tasks\\S02T16\\S02T16P02D.jpg&&" | |
| }, | |
| { "name": "opt5", "problem": "žádný z uvedených " } | |
| ], | |
| "correctAnswer": ["opt3"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T16U03", | |
| "title": "S02T16U03", | |
| "question": | |
| "Vypočítejte: $${{4\\over5}-1-{1\\over2}}\\over{1-{1\\over10}-{1\\over5}}=$$", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a89fddbbf5e07c5af6d5f99"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##-7\\over10##" }, | |
| { "name": "opt2", "problem": "##7\\over10##" }, | |
| { "name": "opt3", "problem": "##1##" }, | |
| { "name": "opt4", "problem": "##-10\\over7##" }, | |
| { "name": "opt5", "problem": "##-1##" } | |
| ], | |
| "correctAnswer": ["opt5"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T16U04", | |
| "title": "S02T16U04", | |
| "question": | |
| "Zjednodušte : ##{{{2\\overa}-{1\\over{a-1}}}\\over{{1\\over{a-1}}-{1\\overa}}}=##", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a89fe4dbf5e07c5af6d5fa0"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##2a-1##" }, | |
| { "name": "opt2", "problem": "##2a+2##" }, | |
| { "name": "opt3", "problem": "##a-2##" }, | |
| { "name": "opt4", "problem": "##a-1##" }, | |
| { "name": "opt5", "problem": "##2a+1##" } | |
| ], | |
| "correctAnswer": ["opt3"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T16U05", | |
| "title": "S02T16U05", | |
| "question": | |
| "Řešte pro ##x\\in\\mathbb{N}##: $${{{(5x-4)^2}-{(4x-3)}^2}\\over(3x-5)^2}~~~~\\lt1$$", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "categories": ["5a8a04c3bf5e07c5af6d5faa"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##K=\\{1;2\\}##" }, | |
| { "name": "opt2", "problem": "##K=\\{1;2;3\\}##" }, | |
| { "name": "opt3", "problem": "##K=\\{2\\}##" }, | |
| { "name": "opt4", "problem": "##K=\\{1\\}##" }, | |
| { "name": "opt5", "problem": "##K=\\{2;3\\}##" } | |
| ], | |
| "correctAnswer": ["opt4"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T16U06", | |
| "title": "S02T16U06", | |
| "question": | |
| "V oboru ##\\mathbb{R}## řešte: $${3\\overx}+1={1\\over{2x}}$$", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a8a046cbf5e07c5af6d5fa5"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##K=\\{-{5\\over2}\\}##" }, | |
| { "name": "opt2", "problem": "##K=\\{-{4\\over3}\\}##" }, | |
| { "name": "opt3", "problem": "##K=\\{-{2\\over5}\\}##" }, | |
| { "name": "opt4", "problem": "##K=\\{-{3\\over4}\\}##" }, | |
| { "name": "opt5", "problem": "jiná hodnota " } | |
| ], | |
| "correctAnswer": ["opt1"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T16U07", | |
| "title": "S02T16U07", | |
| "taskText": | |
| "Je dána přímka ##p:~~x=2+3t;~y=1-t;~~t\\in\\mathbb{R}##.", | |
| "question": | |
| "Která z uvedených obecných rovnic je rovnicí přímky ##p##? ", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a8a0688bf5e07c5af6d5fbd"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##3x-y-5=0##" }, | |
| { "name": "opt2", "problem": "##2x-y+7=0##" }, | |
| { "name": "opt3", "problem": "##x+3y+5=0##" }, | |
| { "name": "opt4", "problem": "##x+3y-5=0##" }, | |
| { "name": "opt5", "problem": "##3x-y+7=0##" } | |
| ], | |
| "correctAnswer": ["opt4"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T16U08", | |
| "title": "S02T16U08", | |
| "taskText": | |
| "V trojúhelníku ABC je dáno: ##A[-1;2] C[2;6] \\vec{CB}=\\vec{a}=(3;-3)##", | |
| "question": "Určete souřadnice středu S strany AB.", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "categories": ["5a8a0680bf5e07c5af6d5fbc"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##[2,5;1,5]##" }, | |
| { "name": "opt2", "problem": "##[2+2,5]##" }, | |
| { "name": "opt3", "problem": "##[1;2]##" }, | |
| { "name": "opt4", "problem": "##[1,5;2,5]##" }, | |
| { "name": "opt5", "problem": "jiný bod" } | |
| ], | |
| "correctAnswer": ["opt2"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T16U09", | |
| "title": "S02T16U09", | |
| "taskText": | |
| "V grafu jsou zaznaménány známky z matematiky třídy 2B. &&\\images\\tasks\\S02T16\\S02T16P09.jpg&&", | |
| "question": "Jaká byla průměrná známka?", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a8a06eebf5e07c5af6d5fbf"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##1##" }, | |
| { "name": "opt2", "problem": "##2##" }, | |
| { "name": "opt3", "problem": "##4##" }, | |
| { "name": "opt4", "problem": "##3##" }, | |
| { "name": "opt5", "problem": "jiná hodnota " } | |
| ], | |
| "correctAnswer": ["opt2"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T16U10", | |
| "title": "S02T16U10", | |
| "taskText": | |
| "V aritmetické posloupnosti je první člen ##a_1=12;s_{32}=-608##", | |
| "question": "Určete desátý člen posloupnosti.", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a8a05f3bf5e07c5af6d5fb5"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##-4##" }, | |
| { "name": "opt2", "problem": "##-6##" }, | |
| { "name": "opt3", "problem": "##-10##" }, | |
| { "name": "opt4", "problem": "##-8##" }, | |
| { "name": "opt5", "problem": "##-7##" } | |
| ], | |
| "correctAnswer": ["opt2"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T16U11", | |
| "title": "S02T16U11", | |
| "question": | |
| "Určete první člen geometrické posloupnostikde ##a_3=8;~a_6=64##.", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a8a05c6bf5e07c5af6d5fb3"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##4##" }, | |
| { "name": "opt2", "problem": "##2##" }, | |
| { "name": "opt3", "problem": "##3##" }, | |
| { "name": "opt4", "problem": "##1##" }, | |
| { "name": "opt5", "problem": "##5##" } | |
| ], | |
| "correctAnswer": ["opt2"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T16U12", | |
| "title": "S02T16U12", | |
| "question": "##4^x-3\\cdot2^x-4=0##", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "categories": ["5a8a0581bf5e07c5af6d5fb0"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##K=\\{2;1\\}##" }, | |
| { "name": "opt2", "problem": "##K=\\{0;-1\\}##" }, | |
| { "name": "opt3", "problem": "##K=\\{2;-1\\}##" }, | |
| { "name": "opt4", "problem": "##K=\\{2;\\}##" }, | |
| { "name": "opt5", "problem": "K=\\{-1\\}##" } | |
| ], | |
| "correctAnswer": ["opt4"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T16U13", | |
| "title": "S02T16U13", | |
| "question": "Řešte nerovnici: ##4^{x-2}\\gt128##", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a8a04c3bf5e07c5af6d5faa"], | |
| "options": [ | |
| { | |
| "name": "opt1", | |
| "problem": "##K=(-\\infty;{11\\over2})##" | |
| }, | |
| { "name": "opt2", "problem": "##K=({5\\over2};\\infty)##" }, | |
| { | |
| "name": "opt3", | |
| "problem": "##K=(-\\infty;{5\\over2})##" | |
| }, | |
| { | |
| "name": "opt4", | |
| "problem": "##K=({11\\over2};\\infty)##" | |
| }, | |
| { | |
| "name": "opt5", | |
| "problem": "##K=({5\\over2};{11\\over2})##" | |
| } | |
| ], | |
| "correctAnswer": ["opt4"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T16U14", | |
| "title": "S02T16U14", | |
| "question": "##\\log_{1\\over5}125+\\log_216-\\log100=##", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a8a0581bf5e07c5af6d5fb0"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##-1##" }, | |
| { "name": "opt2", "problem": "##8##" }, | |
| { "name": "opt3", "problem": "##5##" }, | |
| { "name": "opt4", "problem": "##3##" }, | |
| { "name": "opt5", "problem": "jiná hodnota" } | |
| ], | |
| "correctAnswer": ["opt1"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T16U15", | |
| "title": "S02T16U15", | |
| "question": | |
| "Zapište zlomkem, jaká část obrázku je vybarvena. &&\\images\\tasks\\S02T16\\S02T16P15.jpg&&", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a89fd44bf5e07c5af6d5f97"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##1\\over3##" }, | |
| { "name": "opt2", "problem": "jiná hodnota" }, | |
| { "name": "opt3", "problem": "##2\\over9##" }, | |
| { "name": "opt4", "problem": "##3\\over4##" }, | |
| { "name": "opt5", "problem": "##4\\over7##" } | |
| ], | |
| "correctAnswer": ["opt2"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T16U16", | |
| "title": "S02T16U16", | |
| "taskText": | |
| "Při bouřce se borovice vysoká 14,4m zlomila tak, že se koruna dotýká země ve vzdálenosti 4,8m od paty kolmého kmene stromu.", | |
| "question": "V jaké výšce se borovice zlomila?", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a8a061ebf5e07c5af6d5fb7"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##4,3m##" }, | |
| { "name": "opt2", "problem": "##3,8m##" }, | |
| { "name": "opt3", "problem": "##8,2m##" }, | |
| { "name": "opt4", "problem": "##6,4m##" }, | |
| { "name": "opt5", "problem": "jiná hodnota" } | |
| ], | |
| "correctAnswer": ["opt4"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T16U17", | |
| "title": "S02T16U17", | |
| "taskText": | |
| "Klára přečte denně 15 stránek knihy. Romana začala číst o pět dní později, ale přečte o 25 stránek denně víc než Klára.", | |
| "question": | |
| "Jak dlouho musí Romana číst, aby byla na stejné stránce jako Klára?", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a8a0442bf5e07c5af6d5fa4"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##8##dní" }, | |
| { "name": "opt2", "problem": "##6##dní" }, | |
| { "name": "opt3", "problem": "##3##dní" }, | |
| { "name": "opt4", "problem": "##5##dní" }, | |
| { "name": "opt5", "problem": "jiná hodnota" } | |
| ], | |
| "correctAnswer": ["opt3"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T16U18", | |
| "title": "S02T16U18", | |
| "question": | |
| "Vypočítejte délku červené křivky, která je vyznačena na obrázku. &&\\images\\tasks\\S02T16\\S02T16P18.jpg&&", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "categories": ["5a8a063cbf5e07c5af6d5fb9"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##13,85##cm" }, | |
| { "name": "opt2", "problem": "##21,75##cm" }, | |
| { "name": "opt3", "problem": "##15,54##cm" }, | |
| { "name": "opt4", "problem": "##18,63##cm" }, | |
| { "name": "opt5", "problem": "jiná hodnota" } | |
| ], | |
| "correctAnswer": ["opt1"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T16U19", | |
| "title": "S02T16U19", | |
| "question": | |
| "Jsou dány množiny:$$A=\\{x\\in\\mathbb{R};x\\geqq3\\}$$;$$B=\\{x\\in\\mathbb{Z};|x|\\leqq4\\}$$;$$C={x\\in\\mathbb{N};2\\leqq{x}\\leqq3\\}$$", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a89fdfbbf5e07c5af6d5f9b"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##K=\\{3;4\\}##" }, | |
| { "name": "opt2", "problem": "##K=\\{2;3\\}##" }, | |
| { "name": "opt3", "problem": "##K=\\{3\\}##" }, | |
| { "name": "opt4", "problem": "##K=\\{2;3;4\\}##" }, | |
| { "name": "opt5", "problem": "jiná hodnota" } | |
| ], | |
| "correctAnswer": ["opt3"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T16U20", | |
| "title": "S02T16U20", | |
| "taskText": | |
| "Délky stran trojúhelníku jsou v poměru 2:5:7. Jeho obvod je 42 cm.", | |
| "question": "Určete délky stran trojúhelníku.", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "categories": ["5a89fd44bf5e07c5af6d5f97"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##10cm,~14cm,~18cm##" }, | |
| { "name": "opt2", "problem": "##8cm,~16cm,~18cm##" }, | |
| { "name": "opt3", "problem": "##6cm,~15cm,~21cm##" }, | |
| { "name": "opt4", "problem": "##4cm,~12cm,~26cm##" }, | |
| { "name": "opt5", "problem": "jiná hodnota" } | |
| ], | |
| "correctAnswer": ["opt3"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T16U21", | |
| "title": "S02T16U21", | |
| "question": | |
| "Jak se změní objem krychle o hraně ##m##, protáhneme-li její hranu o 3 cm?", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a8a065cbf5e07c5af6d5fbb"], | |
| "options": [ | |
| { | |
| "name": "opt1", | |
| "problem": "##Zvětší se o 6m^2+18m+27##" | |
| }, | |
| { | |
| "name": "opt2", | |
| "problem": "##Zvětší se o 9m^2+27m+27##" | |
| }, | |
| { "name": "opt3", "problem": "##Zvětší se o 12m##" }, | |
| { "name": "opt4", "problem": "##Zvětší se o 36m##" }, | |
| { "name": "opt5", "problem": "##Zvětší se o 16m^2+12m##" } | |
| ], | |
| "correctAnswer": ["opt2"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T16U22", | |
| "title": "S02T16U22", | |
| "taskText": | |
| "V nádrži tvaru válce s vnitřním průměrem 6m je 942hl vody. Voda sahá do 2/3 hloubky nádrže.", | |
| "question": "Vypočítejte hloubku nádrže.", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "categories": ["5a8a065cbf5e07c5af6d5fbb"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##55dm##" }, | |
| { "name": "opt2", "problem": "##40dm##" }, | |
| { "name": "opt3", "problem": "##45dm##" }, | |
| { "name": "opt4", "problem": "##50dm##" }, | |
| { "name": "opt5", "problem": "jiná hodnota" } | |
| ], | |
| "correctAnswer": ["op4"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T16U23", | |
| "title": "S02T16U23", | |
| "question": | |
| "Z výrazu ##t=\\sqrt{{2s}\\overg}## vyjádřete proměnnou ##g##.", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a8a0430bf5e07c5af6d5fa3"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##t=\\sqrt{{2s}\\overg}##" }, | |
| { "name": "opt2", "problem": "##g={t\\over{2s}}##" }, | |
| { "name": "opt3", "problem": "##g={2s\\over{t}}##" }, | |
| { "name": "opt4", "problem": "##g={t\\over{4s^2}}##" }, | |
| { "name": "opt5", "problem": "jiný výraz" } | |
| ], | |
| "correctAnswer": ["opt1"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T16U24", | |
| "title": "S02T16U24", | |
| "question": | |
| "Kolika způsoby můžeme posadit do jedné řady 12 návštěvníků kina, pokud každý ze šesti manželských párů chce sedět vedle sebe?", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "categories": ["59eba2813ed54d1200c8d3f8"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##6\\cdot6!##" }, | |
| { "name": "opt2", "problem": "##12!\\over2##" }, | |
| { "name": "opt3", "problem": "##12!\\over6##" }, | |
| { "name": "opt4", "problem": "##2\\cdot6!##" }, | |
| { "name": "opt5", "problem": "##6!##" } | |
| ], | |
| "correctAnswer": ["opt4"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T16U25", | |
| "title": "S02T16U25", | |
| "question": | |
| "Jaká je pravděpodobnost, že při hodu mincí 5x po sobě padne hlava?", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "categories": ["5a8a06e4bf5e07c5af6d5fbe"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##0,125##" }, | |
| { "name": "opt2", "problem": "##0,067##" }, | |
| { "name": "opt3", "problem": "##0,031##" }, | |
| { "name": "opt4", "problem": "##0,106##" }, | |
| { "name": "opt5", "problem": "jiná hodnota" } | |
| ], | |
| "correctAnswer": ["opt3"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T16U26", | |
| "title": "S02T16U26", | |
| "question": | |
| "Určete definiční obor funkce $$y={\\sqrt{2x+10}\\over{16-x^2}}$$", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "categories": ["5a8a0495bf5e07c5af6d5fa7"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##(-4;4)##" }, | |
| { "name": "opt2", "problem": "žádný z uvedených" }, | |
| { "name": "opt3", "problem": "##(-5;-4)\\cup(-4;4)##" }, | |
| { "name": "opt4", "problem": "##(-5;-4)\\cup(-4;5)##" }, | |
| { "name": "opt5", "problem": "##(-4;5)##" } | |
| ], | |
| "correctAnswer": ["opt2"], | |
| "solutions": [{}] | |
| } | |
| ] | |
| } | |
| } |
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