{"paper":{"id":"site-2642","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-2642/zad/3282","paper_id":"site-2642","number":"3282","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Potęga {y/x}^5 (gdzie x i y są różne od zera) jest równa A. -5 * x/y B. (x/y)^{-5} C. y^5/x D. -(x/y)^5","answer":null,"answer_text":null,"solution":null,"image":"img/site/2642/zad-3282.svg","solution_image":"img/site/2642/rozw-3282.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-2642/zad/4321","paper_id":"site-2642","number":"4321","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Wyrażenie (3x+1+y)^2 jest równe A. 3x^2+y^2+1, B. 9x^2+6x+y^2+1, C. 3x^2+y^2+6xy+6x+1, D. 9x^2+y^2+6xy+6x+2y+1","answer":null,"answer_text":null,"solution":null,"image":"img/site/2642/zad-4321.svg","solution_image":"img/site/2642/rozw-4321.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-2642/zad/5301","paper_id":"site-2642","number":"5301","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Wartość wyrażenia x^2-6x+9 dla x=√3+3 jest równa A. 1; B. 3; C. 1+2√3; D. 1-2√3.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2642/zad-5301.svg","solution_image":"img/site/2642/rozw-5301.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-2642/zad/5464","paper_id":"site-2642","number":"5464","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Rozwiązanie zadania. Liczba (√6 - √2)^2 - 2√3 jest równa A. 8-6√3 B. 8-2√3 C. 4-2√3 D. 8-4√3.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2642/zad-5464.svg","solution_image":"img/site/2642/rozw-5464.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-2642/zad/5761","paper_id":"site-2642","number":"5761","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Rozwiązanie zadania. Liczba (√5 + 2√3)² jest równa A. 11 B. 17 C. 17+14√15 D. 17+2√15","answer":null,"answer_text":null,"solution":null,"image":"img/site/2642/zad-5761.svg","solution_image":"img/site/2642/rozw-5761.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-2642/zad/6647","paper_id":"site-2642","number":"6647","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Dla każdej liczby rzeczywistej a wartość wyrażenia (3+4a)^2-(3-4a)² jest równa A. 32a² B. 0 C. 48a D. 8a^2","answer":null,"answer_text":null,"solution":null,"image":"img/site/2642/zad-6647.svg","solution_image":"img/site/2642/rozw-6647.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-2642/zad/6699","paper_id":"site-2642","number":"6699","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Dana jest liczba x=(a√3-√2)^2, gdzie a należy do zbioru \\R liczb rzeczywistych. W rozwiązaniu zadania uwzględnij fakt, że liczby √3 oraz √2⋅√3 są niewymierne. Dokończ zdanie. Zaznacz dwie odpowiedzi, tak aby dla każdej z nich dokończenie zdania było prawdziwe. Liczba x jest wymierna dla A. a=5 B. a=-√3+√2 C. a=(√2-√3)^2+0,3 D. a=6 E. a=-2√6+12,5 F. a=(√2-√3)^2-2√6 G. a=-√6.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2642/zad-6699.svg","solution_image":"img/site/2642/rozw-6699.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-2642/zad/7240","paper_id":"site-2642","number":"7240","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Wyrażenie 16-(3x+1)² jest równe A. (3-3x)⋅(5+3x) B. (15-3x)² C. (5-3x)⋅(5+3x) D. 15-9x^2","answer":null,"answer_text":null,"solution":null,"image":"img/site/2642/zad-7240.svg","solution_image":"img/site/2642/rozw-7240.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-2642/zad/8140","paper_id":"site-2642","number":"8140","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Liczba (π+1)² - (π-1)² jest równa A. 0 B. 2 C. 4π D. 4π+2","answer":null,"answer_text":null,"solution":null,"image":"img/site/2642/zad-8140.svg","solution_image":"img/site/2642/rozw-8140.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"}]}