{"paper":{"id":"site-2906","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":null,"variant":null,"exam_pdf":null,"key_pdf":null,"question_count":10,"source_label":"Matematyka · Zbiory zadań","subject_label":"Matematyka","category_label":"Zbiory zadań"},"questions":[{"id":"site-2906/zad/2904","paper_id":"site-2906","number":"2904","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":null,"text":"Dany jest prostokąt o bokach a i b. Zmniejszamy długość boku a o 10% oraz zwiększamy długość boku b o 20%. a) O ile procent zwiększy się pole tego prostokąta? b) Wyznacz długość boku b, dla której nowy prostokąt będzie miał taki sam obwód jak prostokąt wyjściowy, jeśli wiadomo, że bok a ma długość 30cm","answer":null,"answer_text":null,"solution":null,"image":"img/site/2906/zad-2904.svg","solution_image":"img/site/2906/rozw-2904.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-2906/zad/2909","paper_id":"site-2906","number":"2909","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":null,"text":"Dla każdej liczby rzeczywistej b równanie y={1/2}x^2-bx+2 opisuje pewną parabolę. Wyznacz wszystkie wartości parametru b, dla których wierzchołek paraboli leży nad osią Ox.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2906/zad-2909.svg","solution_image":"img/site/2906/rozw-2909.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-2906/zad/2911","paper_id":"site-2906","number":"2911","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":null,"text":"Punkt B=(-1,9) należy do okręgu stycznego do osi Ox w punkcie A=(2,0). Wyznacz równanie tego okręgu.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2906/zad-2911.svg","solution_image":"img/site/2906/rozw-2911.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-2906/zad/2916","paper_id":"site-2906","number":"2916","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":null,"text":"Strzelając do tarczy pewien strzelec uzyskuje co najmniej 9 punktów z prawdopodobieństwem 0,5, a co najwyżej 9 punktów z prawdopodobieństwem 0,7. Oblicz prawdopodobieństwo, że ten strzelec uzyska dokładnie 9 punktów.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2906/zad-2916.svg","solution_image":"img/site/2906/rozw-2916.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-2906/zad/2955","paper_id":"site-2906","number":"2955","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":null,"text":"Podaj przykład liczb całkowitych dodatnich a i b, spełniających nierówność 5/7 < a/b < 6/7.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2906/zad-2955.svg","solution_image":"img/site/2906/rozw-2955.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-2906/zad/2956","paper_id":"site-2906","number":"2956","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":null,"text":"Stosując wzory skróconego mnożenia rozłóż na czynniki wyrażenie 1-a^2+2ab-b^2.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2906/zad-2956.svg","solution_image":"img/site/2906/rozw-2956.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-2906/zad/3009","paper_id":"site-2906","number":"3009","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":null,"text":"Liczby dodatnie a, b, c spełniają warunek: log_4 c = log_3 b = log_2 a = 2. Oblicz pierwiastek z abc.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2906/zad-3009.svg","solution_image":"img/site/2906/rozw-3009.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-2906/zad/3026","paper_id":"site-2906","number":"3026","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":null,"text":"Ile punktów wspólnych ma okrąg o równaniu x^2+(y-3)^2=6 z prostą o równaniu 3x+y-15=0?","answer":null,"answer_text":null,"solution":null,"image":"img/site/2906/zad-3026.svg","solution_image":"img/site/2906/rozw-3026.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-2906/zad/3027","paper_id":"site-2906","number":"3027","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":null,"text":"Zbiorem wartości funkcji kwadratowej g jest przedział (-oo,5), a zbiorem rozwiązań nierówności g(x)>0 jest przedział (2,8). Wyznacz wzór funkcji g.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2906/zad-3027.svg","solution_image":"img/site/2906/rozw-3027.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-2906/zad/3030","paper_id":"site-2906","number":"3030","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":null,"text":"Dany jest trójkąt prostokątny ABC o przeciwprostokątnej AB, taki że sin kat BAC = 0.3 i |AC|=7. Oblicz pole koła opisanego na tym trójkącie.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2906/zad-3030.svg","solution_image":"img/site/2906/rozw-3030.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"}]}