{"paper":{"id":"site-5001","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":null,"variant":null,"exam_pdf":null,"key_pdf":null,"question_count":12,"source_label":"Matematyka · Zbiory zadań","subject_label":"Matematyka","category_label":"Zbiory zadań"},"questions":[{"id":"site-5001/zad/5000","paper_id":"site-5001","number":"5000","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":null,"text":"Na początku roku akademickiego mężczyźni stanowili 40% wszystkich studentów. Na koniec roku liczba wszystkich studentów zmalała o 10% i wówczas okazało się, że mężczyźni stanowią 33(1/3)% wszystkich studentów. O ile procent zmieniła się liczba mężczyzn na koniec roku w stosunku do liczby mężczyzn na początku roku?","answer":null,"answer_text":null,"solution":null,"image":"img/site/5001/zad-5000.svg","solution_image":"img/site/5001/rozw-5000.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-5001/zad/5002","paper_id":"site-5001","number":"5002","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":null,"text":"Funkcja f jest funkcją kwadratową. Zbiorem wszystkich rozwiązań nierówności f(x)<0 jest przedział (1,5). Rozwiąż nierówność -f(x+3)<0.","answer":null,"answer_text":null,"solution":null,"image":"img/site/5001/zad-5002.svg","solution_image":"img/site/5001/rozw-5002.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-5001/zad/5003","paper_id":"site-5001","number":"5003","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":null,"text":"Wartość wyrażenia ∛4 ⋅ ∛(-16) / -8 jest równa A. 2^(1/3), B. 2^(1/2), C. 2^(-1), D. 2^(-2).","answer":null,"answer_text":null,"solution":null,"image":"img/site/5001/zad-5003.svg","solution_image":"img/site/5001/rozw-5003.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-5001/zad/5004","paper_id":"site-5001","number":"5004","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":null,"text":"Odwrotnością liczby 2√2(1/8)^(-(4/3)) jest liczba A. -2^(11/2), B. -2^(-(11/2)), C. 2^(-(11/2)), D. 2^(11/2).","answer":null,"answer_text":null,"solution":null,"image":"img/site/5001/zad-5004.svg","solution_image":"img/site/5001/rozw-5004.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-5001/zad/5005","paper_id":"site-5001","number":"5005","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":null,"text":"Liczba ∛(4^(-1))⋅2^(1/4)⋅16^(1/3) jest równa A. 2^(1/6), B. 2^(1/4), C. 2^(1/3), D. 2^(11/12).","answer":null,"answer_text":null,"solution":null,"image":"img/site/5001/zad-5005.svg","solution_image":"img/site/5001/rozw-5005.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-5001/zad/5006","paper_id":"site-5001","number":"5006","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":null,"text":"Dane są liczby a=log3, b=log2. Wyznacz logarytm dziesiętny z liczby 72 za pomocą a i b.","answer":null,"answer_text":null,"solution":null,"image":"img/site/5001/zad-5006.svg","solution_image":"img/site/5001/rozw-5006.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-5001/zad/5007","paper_id":"site-5001","number":"5007","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":null,"text":"Liczba o 2 większa od liczby log_5 4 jest równa A. log_5 6, B. log_5 8, C. log_5 29, D. log_5 100.","answer":null,"answer_text":null,"solution":null,"image":"img/site/5001/zad-5007.svg","solution_image":"img/site/5001/rozw-5007.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-5001/zad/5008","paper_id":"site-5001","number":"5008","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":null,"text":"Na lokacie złożono 1000 zł przy rocznej stopie procentowej p% (procent składany). Odsetki naliczane są co kwartał. Po upływie roku wielkość kapitału na lokacie będzie równa A. 1000(1+4p/100), B. 1000(1+p/100)^4, C. 1000(1+p/400), D. 1000(1+p/400)^4.","answer":null,"answer_text":null,"solution":null,"image":"img/site/5001/zad-5008.svg","solution_image":"img/site/5001/rozw-5008.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-5001/zad/5009","paper_id":"site-5001","number":"5009","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":null,"text":"Dany jest trójkąt o bokach długości a, b, c. Stosunek a : b : c jest równy 3 : 5 : 7. Które zdanie jest fałszywe? A. Liczba c jest o 12,5^ mniejsza od liczby a+b. B. Liczba a stanowi 20% liczby a+b+c. C. Liczba a stanowi 25% liczby b+c. D. Liczba b to 60% liczby c.","answer":null,"answer_text":null,"solution":null,"image":"img/site/5001/zad-5009.svg","solution_image":"img/site/5001/rozw-5009.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-5001/zad/5010","paper_id":"site-5001","number":"5010","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":null,"text":"Nominalna stopa oprocentowania lokaty wynosi 3% w stosunku rocznym (bez uwzględnienia podatku). Odsetki kapitalizowane są na koniec każdego kolejnego okresu czteromiesięcznego. Oblicz, jaką kwotę wpłacono na tę lokatę, jeśli na koniec ośmiu miesięcy oszczędzania na rachunku lokaty było o 916,56 zł więcej niż przy jej otwarciu.","answer":null,"answer_text":null,"solution":null,"image":"img/site/5001/zad-5010.svg","solution_image":"img/site/5001/rozw-5010.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-5001/zad/5011","paper_id":"site-5001","number":"5011","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":null,"text":"W pewnej szkole przez trzy kolejne lata zmieniała się liczba uczniów. W pierwszym roku liczba uczniów zmalała i na koniec roku była o 10% mniejsza niż na początku. W drugim roku wzrosła i ukończyło go 20% więcej uczniów niż pierwszy. O ile procent, w stosunku do liczby uczniów kończących drugi rok, zmniejszyła się ich liczba w następnym roku, jeśli na koniec trzeciego roku było tyle samo uczniów co na początku pierwszego? Wynik zaokrąglij do 0,1%.","answer":null,"answer_text":null,"solution":null,"image":"img/site/5001/zad-5011.svg","solution_image":"img/site/5001/rozw-5011.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-5001/zad/5012","paper_id":"site-5001","number":"5012","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":null,"text":"Dane są liczby a = 3⋅log_3 2 - log_3 16; b = 2⋅log_3 6 - log_3 18. Wykaż, że a+b=0.","answer":null,"answer_text":null,"solution":null,"image":"img/site/5001/zad-5012.svg","solution_image":"img/site/5001/rozw-5012.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań","subject_label":"Matematyka","category_label":"Zbiory zadań"}]}