{"paper":{"id":"site-2860","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","variant":null,"exam_pdf":null,"key_pdf":null,"question_count":11,"source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},"questions":[{"id":"site-2860/zad/2861","paper_id":"site-2860","number":"2861","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Diagram przedstawia wyniki ankiety, w której ankietowani odpowiedzieli na pytanie, jakie napoje piją między posiłkami. Ankietowani wybierali tylko jeden z czterech rodzajów napojów.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2860/zad-2861.svg","solution_image":"img/site/2860/rozw-2861.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 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2860/zad/2862","paper_id":"site-2860","number":"2862","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Dany jest ciąg (a_n) określony wzorem a_n = (-1)^n{2-n / n^2} dla n=1,2,3... Oblicz a_2, a_4 i a_5.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2860/zad-2862.svg","solution_image":"img/site/2860/rozw-2862.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 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2860/zad/2863","paper_id":"site-2860","number":"2863","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Przedstaw 4^(-1) - 3 * (2/3)^(-2) / 5 - (1/2)^(-1) w postaci nieskracalnego ułamka zwykłego. Przekształcanie i upraszczanie potęg.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2860/zad-2863.svg","solution_image":"img/site/2860/rozw-2863.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 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2860/zad/2864","paper_id":"site-2860","number":"2864","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Podaj miejsca zerowe funkcji określonych dla wszystkich liczb rzeczywistych x: f(x)=x(x+2), g(x)=(x-5)(x+2), h(x)=(5-2x)(2x+1)","answer":null,"answer_text":null,"solution":null,"image":"img/site/2860/zad-2864.svg","solution_image":"img/site/2860/rozw-2864.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 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2860/zad/2872","paper_id":"site-2860","number":"2872","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Na osi liczbowej zaznaczono przedział A złożony z tych liczb rzeczywistych, których odległość od punktu 1 jest niewiększa od 4,5. Przedział A przesunięto wzdłuż osi o 2 jednostki w kierunku dodatnim, otrzymując przedział B. Wyznacz wszystkie liczby całkowite, które należą jednocześnie do A i B.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2860/zad-2872.svg","solution_image":"img/site/2860/rozw-2872.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 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2860/zad/2873","paper_id":"site-2860","number":"2873","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Rozwiąż równanie x+x^3 = 1+x^2 - przykładowe zadanie z poziomu podstawowego informatora maturalnego","answer":null,"answer_text":null,"solution":null,"image":"img/site/2860/zad-2873.svg","solution_image":"img/site/2860/rozw-2873.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 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2860/zad/2874","paper_id":"site-2860","number":"2874","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Oblicz największą i najmniejszą wartość funkcji f(x)=2x^2-4x+11 w przedziale A=<0,4>.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2860/zad-2874.svg","solution_image":"img/site/2860/rozw-2874.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 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2860/zad/2876","paper_id":"site-2860","number":"2876","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Pan Kowalski planując wyjazd na wakacje letnie w następnym roku postanowił założyć lokatę, wpłacając do banku 2000 zł na okres jednego roku. Ma do wyboru trzy rodzaje lokat: lokata A -- oprocentowanie w stosunku rocznym 5 %, kapitalizacja odsetek po roku, lokata B -- oprocentowanie w stosunku rocznym 4.8 %, kapitalizacja odsetek co pół roku, lokata C -- oprocentowanie w stosunku rocznym 4,6 %, kapitalizacja odsetek co kwartał. Oceń, wykonując odpowiednie obliczenia, która lokata jest najkorzystniejsza dla Pana Kowalskiego.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2860/zad-2876.svg","solution_image":"img/site/2860/rozw-2876.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 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2860/zad/2879","paper_id":"site-2860","number":"2879","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Ostrokątny trójkąt równoramienny ABC o podstawie AB jest wpisany w okrąg o środku S, przy czym kąt SAB ma miarę 40. Oblicz miarę kąta CAB.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2860/zad-2879.svg","solution_image":"img/site/2860/rozw-2879.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 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2860/zad/2883","paper_id":"site-2860","number":"2883","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"O zdarzeniach losowych A i B wiemy że: P(A)=1/2, P(B)=2/3, P(AuB)=4/5. Oblicz: a) P(AnB) b) P(A\\B)}","answer":null,"answer_text":null,"solution":null,"image":"img/site/2860/zad-2883.svg","solution_image":"img/site/2860/rozw-2883.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 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2860/zad/2884","paper_id":"site-2860","number":"2884","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Na podstawie fragmentu wykresu funkcji kwadratowej f(x) wskaż, które zdanie jest prawdziwe. a) Miejscami zerowymi funkcji są liczby: -2 oraz 4. b) Funkcja jest rosnąca w przedziale (-2,4). c) Funkcja przyjmuje wartości większe od zera dla x<1. d) Zbiorem wartości funkcji jest przedział (-oo,9)","answer":null,"answer_text":null,"solution":null,"image":"img/site/2860/zad-2884.svg","solution_image":"img/site/2860/rozw-2884.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 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"}]}