{"paper":{"id":"site-4403","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"podstawowa","variant":null,"exam_pdf":null,"key_pdf":null,"question_count":32,"source_label":"Matematyka · Zbiory zadań · 2015 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},"questions":[{"id":"site-4403/zad/4405","paper_id":"site-4403","number":"4405","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"podstawowa","text":"Rozwiąż nierówność 2x^2 - 4x > (x+3)(x-2).","answer":null,"answer_text":null,"solution":null,"image":"img/site/4403/zad-4405.svg","solution_image":"img/site/4403/rozw-4405.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 · 2015 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4403/zad/4406","paper_id":"site-4403","number":"4406","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"podstawowa","text":"Wysokość graniastosłupa prawidłowego czworokątnego wynosi 16. Przekątna graniastosłupa tworzy kąt alfa z płaszczyzną podstawy i cos alfa = 3/5. Oblicz pole powierzchni całkowitej tego graniastosłupa.","answer":null,"answer_text":null,"solution":null,"image":"img/site/4403/zad-4406.svg","solution_image":"img/site/4403/rozw-4406.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 · 2015 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4403/zad/4407","paper_id":"site-4403","number":"4407","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"podstawowa","text":"Dany jest kwadrat ABC. Przekątne AC i BD przecinają się w punkcie E. Punkty K i M są środkami odcinków - odpowiednio - AE i EC. Punkty L i N leżą na przekątnej BD tak, że |BL| = 1/3 * |BE| i |DN| = 1/3 * |DE| (zobacz rysunek). Wykaż, że stosunek pola czworokąta KLMN do pola kwadratu ABCD jest równy 1 : 3.","answer":null,"answer_text":null,"solution":null,"image":"img/site/4403/zad-4407.svg","solution_image":"img/site/4403/rozw-4407.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 · 2015 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4403/zad/4408","paper_id":"site-4403","number":"4408","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"podstawowa","text":"Oblicz najmniejszą i największą wartość funkcji kwadratowej f(x) = x^2 - 6x +3 w przedziale <0,4>.","answer":null,"answer_text":null,"solution":null,"image":"img/site/4403/zad-4408.svg","solution_image":"img/site/4403/rozw-4408.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 · 2015 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4403/zad/4409","paper_id":"site-4403","number":"4409","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"podstawowa","text":"W układzie współrzędnych są dane punkty A = (-43,-12), B = (50,19). Prosta AB przecina oś Ox w punkcie P. Oblicz pierwszą współrzędną punktu P.","answer":null,"answer_text":null,"solution":null,"image":"img/site/4403/zad-4409.svg","solution_image":"img/site/4403/rozw-4409.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 · 2015 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4403/zad/4410","paper_id":"site-4403","number":"4410","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"podstawowa","text":"Wśród 115 osób przeprowadzono badania ankietowe, związane z zakupami w pewnym kiosku. W poniższej tabeli przedstawiono informacje o tym, ile osób kupiło bilety tramwajowe ulgowe oraz ile osób kupiło bilety tramwajowe normalne. Rodzaj kupionych biletów: ulgowe, normalne. Liczba osób: 76, 41. Uwaga! 27 osób spośród ankietowanych kupiło oba rodzaje biletów. Oblicz prawdopodobieństwo zdarzenia polegającego na tym, że osoba losowo wybrana spośród ankietowanych nie kupiła żadnego biletu. Wynik przedstaw w formie nieskracalnego ułamka.","answer":null,"answer_text":null,"solution":null,"image":"img/site/4403/zad-4410.svg","solution_image":"img/site/4403/rozw-4410.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 · 2015 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4403/zad/4411","paper_id":"site-4403","number":"4411","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"podstawowa","text":"W nieskończonym ciągu arytmetycznym a_n, określonym dla n >= 1 , suma jedenastu początkowych wyrazów tego ciągu jest równa 187. Średnia arytmetyczna pierwszego, trzeciego i dziewiątego wyrazu tego ciągu, jest równa 12. Wyrazy a_1, a_3, a_k ciągu a_n, w podanej kolejności, tworzą nowy ciąg - trzywyrazowy ciąg geometryczny (b_n). Oblicz k.","answer":null,"answer_text":null,"solution":null,"image":"img/site/4403/zad-4411.svg","solution_image":"img/site/4403/rozw-4411.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 · 2015 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4403/zad/4413","paper_id":"site-4403","number":"4413","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"podstawowa","text":"Wskaż rysunek, na którym przedstawiono przedział, będący zbiorem wszystkich rozwiązań nierówności -4 < x-1 < 4.","answer":null,"answer_text":null,"solution":null,"image":"img/site/4403/zad-4413.svg","solution_image":"img/site/4403/rozw-4413.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 · 2015 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4403/zad/4414","paper_id":"site-4403","number":"4414","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"podstawowa","text":"Dane są liczby a = - 1/27, b = log_(1/4) 64, c = log_(1/3) 27. Iloczyn abc jest równy A. -9, B. - 1/3 C. 1/3, D. 3","answer":null,"answer_text":null,"solution":null,"image":"img/site/4403/zad-4414.svg","solution_image":"img/site/4403/rozw-4414.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 · 2015 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4403/zad/4415","paper_id":"site-4403","number":"4415","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"podstawowa","text":"Kwotę 1000 zł ulokowano w banku na roczną lokatę oprocentowaną w wysokości 4% w stosunku rocznym. Po zakończeniu lokaty od naliczonych odsetek odprowadzany jest podatek w wysokości 19 %. Maksymalna kwota, jaką po upływie roku będzie można wypłacić z banku, jest równa A. 1000 * (1 - (81/100) * (4/100), B. 1000 * (1 + (19/100) * (4/100)), C. 1000 * (1 + (81/100) * (4/100), D. 1000 * (1 - (19/100) * (4/100)).","answer":null,"answer_text":null,"solution":null,"image":"img/site/4403/zad-4415.svg","solution_image":"img/site/4403/rozw-4415.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 · 2015 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4403/zad/4416","paper_id":"site-4403","number":"4416","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"podstawowa","text":"Równość m / (5 - √5) = (5 + √5) / 5 zachodzi dla A. m = 5, B. m = 4, C. m = 1 D. m = -5.","answer":null,"answer_text":null,"solution":null,"image":"img/site/4403/zad-4416.svg","solution_image":"img/site/4403/rozw-4416.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 · 2015 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4403/zad/4417","paper_id":"site-4403","number":"4417","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"podstawowa","text":"Układ równań { x-y=3; 2x+0,5y=4 } opisuje w układzie współrzędnych na płaszczyźnie A. zbiór pusty, B. dokładnie jeden punkt, C. dokładnie dwa różne punkty, D. zbiór nieskończony.","answer":null,"answer_text":null,"solution":null,"image":"img/site/4403/zad-4417.svg","solution_image":"img/site/4403/rozw-4417.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 · 2015 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4403/zad/4418","paper_id":"site-4403","number":"4418","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"podstawowa","text":"Suma wszystkich pierwiastków równania (x+3)(x+7)(x-11) = 0 jest równa A. -1, B. 21, C. 1, D. -21.","answer":null,"answer_text":null,"solution":null,"image":"img/site/4403/zad-4418.svg","solution_image":"img/site/4403/rozw-4418.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 · 2015 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4403/zad/4419","paper_id":"site-4403","number":"4419","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"podstawowa","text":"Równanie x-1 / x+1 = x-1 A. ma dokładnie jedno rozwiązanie: x=1, B. ma dokładnie jedno rozwiązanie: x=0, C. ma dokładnie jedno rozwiązanie: x=-1, D. ma dokładnie dwa rozwiązania: x=0, x=1.","answer":null,"answer_text":null,"solution":null,"image":"img/site/4403/zad-4419.svg","solution_image":"img/site/4403/rozw-4419.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 · 2015 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4403/zad/4420","paper_id":"site-4403","number":"4420","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"podstawowa","text":"Na rysunku przedstawiono wykres funkcji f. Zbiorem wartości funkcji jest A. (-2,2), B. <-2,2), C. <-2,2>, D. (-2,2>.","answer":null,"answer_text":null,"solution":null,"image":"img/site/4403/zad-4420.svg","solution_image":"img/site/4403/rozw-4420.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 · 2015 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4403/zad/4421","paper_id":"site-4403","number":"4421","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"podstawowa","text":"Na wykresie funkcji liniowej określonej wzorem f(x) = (m-1)x+3 leży punkt S = (5,-2). Zatem A. m=-1, B. m=0, C. m=1, D. m=1.","answer":null,"answer_text":null,"solution":null,"image":"img/site/4403/zad-4421.svg","solution_image":"img/site/4403/rozw-4421.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 · 2015 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4403/zad/4422","paper_id":"site-4403","number":"4422","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"podstawowa","text":"Funkcja liniowa f określona wzorem f(x) = 2x+b ma takie samo miejsce zerowe, jakie ma funkcja liniowa g(x) = -3x+4. Stąd wynika, że A. b=4, B. b=-3/2, C. b=-8/3, D. b=4/3.","answer":null,"answer_text":null,"solution":null,"image":"img/site/4403/zad-4422.svg","solution_image":"img/site/4403/rozw-4422.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 · 2015 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4403/zad/4423","paper_id":"site-4403","number":"4423","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"podstawowa","text":"Funkcja kwadratowa określona jest wzorem f(x) = x^2+x+c. Jeżeli f(3)=4, to A. f(1)=-6, B. f(1)=0, C. f(1)=6, D. f(1)=18.","answer":null,"answer_text":null,"solution":null,"image":"img/site/4403/zad-4423.svg","solution_image":"img/site/4403/rozw-4423.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 · 2015 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4403/zad/4424","paper_id":"site-4403","number":"4424","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"podstawowa","text":"Ile liczb całkowitych x spełnia nierówność 2/7 < x/14 < 4/3. A. 14, B. 15, C. 16, D. 17.","answer":null,"answer_text":null,"solution":null,"image":"img/site/4403/zad-4424.svg","solution_image":"img/site/4403/rozw-4424.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 · 2015 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4403/zad/4425","paper_id":"site-4403","number":"4425","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"podstawowa","text":"W rosnącym ciągu geometrycznym (a_n), określonym dla n>=1 , spełniony jest warunek a_4=3a_1. Iloraz q tego ciągu jest równy A. q=1/3, B. q=1/(pierwiastek 3 stopnia z 3), C. pierwiastek 3 stopnia z 3, D. q=3.","answer":null,"answer_text":null,"solution":null,"image":"img/site/4403/zad-4425.svg","solution_image":"img/site/4403/rozw-4425.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 · 2015 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4403/zad/4426","paper_id":"site-4403","number":"4426","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"podstawowa","text":"Tangens kąta alpha zaznaczonego na rysunku jest równy A. -(pierwiastek z 3/3), B. -4/5, C. -1, D. -5/4. P = (-4,5).","answer":null,"answer_text":null,"solution":null,"image":"img/site/4403/zad-4426.svg","solution_image":"img/site/4403/rozw-4426.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 · 2015 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4403/zad/4429","paper_id":"site-4403","number":"4429","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"podstawowa","text":"Jeżeli 0 stopni < alfa < 90 stopni oraz tg alfa = 2 * sin alfa to A. cos alfa = 1/2, B. cos alfa = pierwiastek z 2 / 2, C. cos alfa = pierwiastek z 3 / 2, D. cos alfa = 1.","answer":null,"answer_text":null,"solution":null,"image":"img/site/4403/zad-4429.svg","solution_image":"img/site/4403/rozw-4429.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 · 2015 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4403/zad/4430","paper_id":"site-4403","number":"4430","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"podstawowa","text":"Miara kąta wpisanego w okrąg jest o 20 stopni mniejsza od miary kąta środkowego opartego na tym samym łuku. Wynika stąd, że miara kąta wpisanego jest równa A. 5 stopni, B. 10 stopni, C. 20 stopni, D. 30 stopni.","answer":null,"answer_text":null,"solution":null,"image":"img/site/4403/zad-4430.svg","solution_image":"img/site/4403/rozw-4430.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 · 2015 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4403/zad/4431","paper_id":"site-4403","number":"4431","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"podstawowa","text":"Pole rombu o obwodzie 8 jest równe 1. Kąt ostry tego rombu ma miarę alfa. Wtedy A. 14 stopni < alfa < 15 stopni, B. 29 stopni < alfa < 30, C. 60 stopni < alfa < 61 stopni, D. 75 stopni < alfa < 76 stopni.","answer":null,"answer_text":null,"solution":null,"image":"img/site/4403/zad-4431.svg","solution_image":"img/site/4403/rozw-4431.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 · 2015 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4403/zad/4432","paper_id":"site-4403","number":"4432","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"podstawowa","text":"Prosta l o równaniu y = m^2x+3 jest równoległa do prostej k o równaniu y=(4m-4)x-3. Zatem A. m = 2, B. m = -2, C. m = -2 - 2√2, D. m = 2 + 2√2.","answer":null,"answer_text":null,"solution":null,"image":"img/site/4403/zad-4432.svg","solution_image":"img/site/4403/rozw-4432.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 · 2015 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4403/zad/4433","paper_id":"site-4403","number":"4433","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"podstawowa","text":"Proste o równaniach: y =2mx - m^2 -1 oraz y = 4m^2 + m^2 +1 są prostopadłe dla A. m = -{1\\o2}, B. m = 1/2, C. m = 1, D. m = 2.","answer":null,"answer_text":null,"solution":null,"image":"img/site/4403/zad-4433.svg","solution_image":"img/site/4403/rozw-4433.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 · 2015 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4403/zad/4434","paper_id":"site-4403","number":"4434","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"podstawowa","text":"Dane są punkty M = (-2,1) i N = (-1,3). Punkt K jest środkiem odcinka MN. Obrazem punktu K w symetrii względem początku układu współrzędnych jest punkt A. K' = (2,-3/2), B. K' = (2,3/2), C. K' = (3/2,2), D. K' = (3/2, -2).","answer":null,"answer_text":null,"solution":null,"image":"img/site/4403/zad-4434.svg","solution_image":"img/site/4403/rozw-4434.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 · 2015 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4403/zad/4435","paper_id":"site-4403","number":"4435","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"podstawowa","text":"W graniastosłupie prawidłowym czworokątnym EFGHIJKL wierzchołki E, G, L połączono odcinkami (tak jak na rysunku). Wskaż kąt między wysokością OL trójkąta EGL i płaszczyzną podstawy tego graniastosłupa. A. kat HOL, B. kat OGL, C. kat HLO, D.kat OHL.","answer":null,"answer_text":null,"solution":null,"image":"img/site/4403/zad-4435.svg","solution_image":"img/site/4403/rozw-4435.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 · 2015 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4403/zad/4436","paper_id":"site-4403","number":"4436","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"podstawowa","text":"Przekrojem osiowym stożka jest trójkąt równoboczny o boku długości 6. Objętość tego stożka jest równa A. 27 * pi * pierwiastek z 3, B. 9 * pi * pierwiastek z 3, C. 18 * pi, D. 6 * pi.","answer":null,"answer_text":null,"solution":null,"image":"img/site/4403/zad-4436.svg","solution_image":"img/site/4403/rozw-4436.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 · 2015 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4403/zad/4437","paper_id":"site-4403","number":"4437","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"podstawowa","text":"Każda krawędź graniastosłupa prawidłowego trójkątnego ma długość równą 8. Pole powierzchni całkowitej tego graniastosłupa jest równe A. 8^2/3 * (((pierwiastek z 3) / 2) + 4), B. 8^2 * pierwiastek z 3, C. (8^2 * pierwiastek z 6) / 3, D. 8^2(((pierwiastek z 3) / 2) + 3).","answer":null,"answer_text":null,"solution":null,"image":"img/site/4403/zad-4437.svg","solution_image":"img/site/4403/rozw-4437.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 · 2015 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4403/zad/4439","paper_id":"site-4403","number":"4439","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"podstawowa","text":"W każdym z trzech pojemników znajduje się para kul, z których jedna jest czerwona, a druga - niebieska. Z każdego pojemnika losujemy jedną kulę. Niech p oznacza prawdopodobieństwo zdarzenia polegającego na tym, że dokładnie dwie z trzech wylosowanych kul będą czerwone. Wtedy A. p = 1/4, B. p = 3/8, C. p = 1/2, D. p = 2/3.","answer":null,"answer_text":null,"solution":null,"image":"img/site/4403/zad-4439.svg","solution_image":"img/site/4403/rozw-4439.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 · 2015 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4403/zad/4440","paper_id":"site-4403","number":"4440","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"podstawowa","text":"Jeżeli do licznika i do mianownika nieskracalnego dodatniego ułamka dodamy połowę jego licznika, to otrzymamy 4/7, a jeżeli do licznika i do mianownika dodamy 1, to otrzymamy 1/2. Wyznacz ten ułamek.","answer":null,"answer_text":null,"solution":null,"image":"img/site/4403/zad-4440.svg","solution_image":"img/site/4403/rozw-4440.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 · 2015 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"}]}