{"paper":{"id":"site-2671","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","variant":null,"exam_pdf":null,"key_pdf":null,"question_count":9,"source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},"questions":[{"id":"site-2671/zad/3154","paper_id":"site-2671","number":"3154","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Punkty A=(1,-2), C=(4,2) są dwoma wierzchołkami trójkąta równobocznego ABC. Wysokość tego trójkąta jest równa A. 5 pierwiastków z 3 / 2 B. 5 pierwiastków z 3 / 3 C. 5 pierwiastków 3 / 6 D. 5 pierwiastków z 3 / 9","answer":null,"answer_text":null,"solution":null,"image":"img/site/2671/zad-3154.svg","solution_image":"img/site/2671/rozw-3154.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-2671/zad/4348","paper_id":"site-2671","number":"4348","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Punkty A = (-6 - 2 * pierwiastek z 2, 4 - 2 * pierwiastek z 2), B = (2 + 4 * pierwiastek z 2, -6 * pierwiastek z 2), C = (2 + 6 * pierwiastek z 2, 6 - 2 * pierwiastek z 2) są kolejnymiwierzchołkami równoległoboku ABCD. Przekątne tego równoległoboku przecinają się w punkcie A. S = (-1 + 4 * pierwiastek z 2, 5 - 5 * pierwiastek z 2), S = (-2 + pierwiastek z 2, 2 - 4 * pierwiastek z 2), C. S = (2 + 5 * pierwiastek z 2, 3 - 4 * pierwiastek z 2), D. S = (-2 + 2 * pierwiastek z 2, 5 - 2 * pierwiastek z 2).","answer":null,"answer_text":null,"solution":null,"image":"img/site/2671/zad-4348.svg","solution_image":"img/site/2671/rozw-4348.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-2671/zad/5481","paper_id":"site-2671","number":"5481","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Rozwiązanie zadania. Końcami odcinka PR są punkty P=(4,7) i R=(-2,-3). Odległość punktu T=(3,-1) od środka odcinka PR jest równa A. √3 B. √13 C. √17 D. 6√2","answer":null,"answer_text":null,"solution":null,"image":"img/site/2671/zad-5481.svg","solution_image":"img/site/2671/rozw-5481.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-2671/zad/5774","paper_id":"site-2671","number":"5774","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Rozwiązanie zadania. Punkt S=(4,8) jest środkiem odcinka PQ, którego koniec P leży na osi Oy, a koniec Q - na osi Ox. Wynika stąd, że A. P=(0,16) i Q=(8,0) B. P=(0,8) i Q=(16,0) C. P=(0,4) i Q=(4,0) D. P=(0,8) i Q=(8,0).","answer":null,"answer_text":null,"solution":null,"image":"img/site/2671/zad-5774.svg","solution_image":"img/site/2671/rozw-5774.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-2671/zad/5782","paper_id":"site-2671","number":"5782","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Rozwiązanie zadania. Dane są punkty A=(4,1), B=(1,3), C=(4,-1). Pole trójkąta ABC jest równe A. 3 B. 6 C. 8 D. 16","answer":null,"answer_text":null,"solution":null,"image":"img/site/2671/zad-5782.svg","solution_image":"img/site/2671/rozw-5782.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-2671/zad/6666","paper_id":"site-2671","number":"6666","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"W kartezjańskim układzie współrzędnych (x,y) dany jest kwadrat AB. Wierzchołki A=(-2,1) i C=(4,5) są końcami przekątnej tego kwadratu. Długość przekątnej kwadratu ABCD jest równa A. 10 B. 2√13 C. 2√10 D. 8","answer":null,"answer_text":null,"solution":null,"image":"img/site/2671/zad-6666.svg","solution_image":"img/site/2671/rozw-6666.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-2671/zad/7236","paper_id":"site-2671","number":"7236","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Punkty E=(7,1) i F=(9,7) to środki boków, odpowiednio AB i BC kwadratu ABCD. Przekątna tego kwadratu ma długość A. 4√5 B. 10 C. 4√10 D. 20","answer":null,"answer_text":null,"solution":null,"image":"img/site/2671/zad-7236.svg","solution_image":"img/site/2671/rozw-7236.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-2671/zad/8161","paper_id":"site-2671","number":"8161","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"W kartezjańskim układzie współrzędnych (x,y) punkty A=(0,-6), B=(4,2) oraz C=(0,4) są wierzchołkami trójkąta prostokątnego. Tangens kąta ostrego CAB jest równy A. 1/2 B. 2 C. √5/5 D. 2√5/5","answer":null,"answer_text":null,"solution":null,"image":"img/site/2671/zad-8161.svg","solution_image":"img/site/2671/rozw-8161.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-2671/zad/8162","paper_id":"site-2671","number":"8162","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"W kartezjańskim układzie współrzędnych (x,y) dany jest okrąg O o środku w punkcie S=(-8,-6). Odcinek AB , gdzie A=(4,-15) i B=(-20,y_B), jest średnicą okręgu O. Współrzędna y_B punktu B jest równa A. 3 B. 8 C. (-1/2) D. (-9/2)","answer":null,"answer_text":null,"solution":null,"image":"img/site/2671/zad-8162.svg","solution_image":"img/site/2671/rozw-8162.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"}]}