{"paper":{"id":"site-2664","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","variant":null,"exam_pdf":null,"key_pdf":null,"question_count":10,"source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},"questions":[{"id":"site-2664/zad/2923","paper_id":"site-2664","number":"2923","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Długość ramienia BC trapezu prostokątnego jest dwa razy większa od różnicy długości jego podstaw. Kąt ABC ma miarę.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2664/zad-2923.svg","solution_image":"img/site/2664/rozw-2923.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-2664/zad/3152","paper_id":"site-2664","number":"3152","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Drut o długości 27 m pocięto na trzy części, których stosunek długości jest równy 2:3:4. Jaką długość ma najkrótsza z tych części?","answer":null,"answer_text":null,"solution":null,"image":"img/site/2664/zad-3152.svg","solution_image":"img/site/2664/rozw-3152.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-2664/zad/3296","paper_id":"site-2664","number":"3296","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Pole prostokąta jest równe 40. Stosunek długości jego boków jest równy 2:5. Dłuższy bok tego prostokąta jest równy A. 10, B. 8, C. 7, D. 6","answer":null,"answer_text":null,"solution":null,"image":"img/site/2664/zad-3296.svg","solution_image":"img/site/2664/rozw-3296.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-2664/zad/4351","paper_id":"site-2664","number":"4351","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Dany jest trójkąt równoramienny, w którym ramię o długości 20 tworzy z podstawą kąt 67,5 stopni. Pole tego trójkąta jest równe A. 100 * pierwiastków z 3, B. 100 * pierwiastków z 2, C. 200 * pierwiastków z 3, D. 200 * pierwiastków z 2.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2664/zad-4351.svg","solution_image":"img/site/2664/rozw-4351.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-2664/zad/5322","paper_id":"site-2664","number":"5322","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Pole prostokąta ABCD jest równe 90. Na bokach AB i CD wybrano - odpowiednio - punkty P i R, takie, że |AP|/|PB| = |CR|/|RD| = 3/2 (zobacz rysunek). Pole czworokąta APCR jest równe A. 36; B. 40; C. 54; D. 60.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2664/zad-5322.svg","solution_image":"img/site/2664/rozw-5322.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-2664/zad/5486","paper_id":"site-2664","number":"5486","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Rozwiązanie zadania. W trapezie równoramiennym ABCD podstawy AB i CD mają długości równe odpowiednio a i b (przy czym a>b). Miara kąta ostrego trapezu jest równa 30°. Wtedy wysokość tego trapezu jest równa A. a-b/2⋅√3 B. a-b/6⋅√3 C. a+b/2 D. a+b/4.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2664/zad-5486.svg","solution_image":"img/site/2664/rozw-5486.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-2664/zad/5775","paper_id":"site-2664","number":"5775","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Rozwiązanie zadania. Przyprostokątna AC trójkąta prostokątnego ABC ma długość 6, a wysokość CD dzieli go na dwa takie trójkąty ADC i CDB, że pole trójkąta ADC jest 4 razy większe od pola trójkąta CDB (zobacz rysunek). Przyprostokątna BC trójkąta prostokątnego ABC jest równa A. 1,5 B. 2 C. 2,5 D. 3","answer":null,"answer_text":null,"solution":null,"image":"img/site/2664/zad-5775.svg","solution_image":"img/site/2664/rozw-5775.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-2664/zad/6662","paper_id":"site-2664","number":"6662","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Dany jest trójkąt ABC, w którym AB=6, BC=5, |AC|=10. Oceń prawdziwość poniższych stwierdzeń. Wybierz P, jeśli stwierdzenie jest prawdziwe, albo F - jeśli jest fałszywe.Cosinus kąta ABC jest równy (-0,65). P F. Trójkąt ABC jest rozwartokątny. P F.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2664/zad-6662.svg","solution_image":"img/site/2664/rozw-6662.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-2664/zad/6900","paper_id":"site-2664","number":"6900","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Dane są trójkąt równoramienny ABC, w którym |AC|=|BC| i |∠ACB|=45°, oraz kwadrat DEFG o polu równym 1. Wierzchołki E i F kwadratu leżą na ramieniu BC danego trójkąta, wierzchołek G leży na ramieniu AC, a wierzchołek D leży na podstawie AB trójkąta (zobacz rysunek). [rysunek] Oceń prawdziwość poniższych stwierdzeń. Wybierz P, jeśli stwierdzenie jest prawdziwe, albo F - jeśli jest fałszywe. |∠AGD|=45° P F |AG|-|BE|=2-√2 P F","answer":null,"answer_text":null,"solution":null,"image":"img/site/2664/zad-6900.svg","solution_image":"img/site/2664/rozw-6900.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-2664/zad/8158","paper_id":"site-2664","number":"8158","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"W prostokątnym trójkącie równoramiennym przeciwprostokątna ma długość 8. Obwód tego trójkąta jest równy A. 4√2+2 B. 4√2+4 & C. 8√2+1 D. 8√2+2","answer":null,"answer_text":null,"solution":null,"image":"img/site/2664/zad-8158.svg","solution_image":"img/site/2664/rozw-8158.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"}]}