11-sinf Matematika olimpiada №3 Oktabr 4, 2022Avgust 19, 2024 da chop etilgan InfoMaster tomonidan 11-sinf Matematika olimpiada №3 ga 1 fikr bildirilgan 0 12345678910111213141516171819202122232425 Vaqtingiz tugadi! Tomonidan yaratilgan InfoMaster 11-sinf Matematika olimpiada №3 2021-2022 o'quv yilida viloyat bosqichida tushgan savollar 1 / 25 1. Agar va bo‘lsa, ni toping. A) 39 B) 11 C) 25 D) 31 2 / 25 2. ABCD tetraedrning D uchidagi barcha yassi burchaklari to`g`ri. Shu tetraedrda kub shunday ichki chizilganki, kubning bitta uchi D nuqtada, unga qarama−qarshi uchi esa ABC yoqda yotibdi. Agar DA=5, DB=6 va DC=10 bo`lsa, kub qirrasining uzunligini toping. A) 2√2 B) 2 C) 25/12 D) 15/7 3 / 25 3. Hisoblang: A) 81/109 B) 95/243 C) 172/249 D) 85/104 4 / 25 4. АВCDE beshburchak berilgan, М, N, Р va Q nuqtalar —АВ, ВС, CD va DE tomonlarning o‘rtalari. Agar U va V — МP? va NQ ning o‘rtasi bo‘lsa, АЕ: UV nisbatni toping. A) 5 B) 4 C) 6 D) 3 5 / 25 5. Sektor perimetri 28 sm ga teng, uning yuzi esa 49 sm2. Sektor yoyining uzunligini toping. A) 18 sm B) 12 sm C) 7 sm D) 14 sm 6 / 25 6. Hisoblang: 1 + 2 ∙ 2 + 3 ∙ 22 + 4 ∙ 23+. … + 100 ∙ 299 A) A B) B C) C D) D 7 / 25 7. 100 dan kichik musbat butun sonlar orasida 2 ga ham, 3 ga ham, 7 ga ham bo‘linmaydigan nechta son mavjud? A) 28 B) 27 C) 29 D) 26 8 / 25 8. Soddalashtiring: A) 2 B) 2sinα C) 1 D) cosα 9 / 25 9. Funksiyaning eng kichik qiymatini toping. ?(?) = (2? + 6)5 − 4(2? + 6)4, bunda |? + 3| ≤ 2. A) -2¹¹ B) -2⁹ C) -4⁴ D) -4⁵ 10 / 25 10. Hisoblang: (1 − tg5°)(1 − tg20°)2 + 2(2tg20° + tg5°) A) 3 B) 4 C) 2 D) 1 11 / 25 11. Aylanaga АВС uchburchak ichki chizilgan. Uchburchakning СС1medianasining davomi aylanani ? nuqtada kesib o‘tadi. ni toping. A) 1 B) 2 C) √5 D) 4 12 / 25 12. Tenglama nechta yechimga ega? Bunda, x ∈ (1; 47) A) 12 B) 14 C) 16 D) 15 13 / 25 13. Quyidagi sonlar orasidan musbat sonni aniqlang. A) D B) C C) B D) A 14 / 25 14. Agar ? + 4/√?= 17 bo‘lsa, ? + 4√? ni toping. A) 4 B) 1 C) 3 D) 2 15 / 25 15. Hisoblang: A) 1 B) 2 C) 1.5 D) 0 16 / 25 16. To‘g‘ri burchakli uchburchakka ichki va tashqi chizilgan aylana radiuslari nisbati 2 : 5 bo‘lsa, uchburchakning katta o‘tkir burchagining kosinusini toping. A) 0.5 B) 0.6 C) 0.8 D) 0.2 17 / 25 17. Tenglamalar sistemasi nechta yechimga ega? A) 12 B) 10 C) 8 D) 6 18 / 25 18. Teng yonli АВС uchburchakda: АВ = ВС = 25 sm va АС = 14 sm. ВС tomonga AD balandlikning D asosida urinuvchi va АС tomon o‘rtasidan o‘tuvchi aylana radiusini toping. A) 177/48 B) 211/47 C) 175/48 D) 3 19 / 25 19. Agar a = √5 + 1 va b = √5 − 1 bo‘lsa, 2a² − ab − a² ifodaning qiymatini toping. A) √5 + 6 B) 3√5 + 6 C) 6√5 + 1 D) 6√5 + 2 20 / 25 20. bo‘lsa, ?² + ?² ni toping. A) 65/21 B) 20 C) 61/20 D) 20.2 21 / 25 21. (?²+ 4? + 8)² + 3?³ + 14?² + 24? = 0 tenglamaning ildizlari yig’indisini toping. A) -7 B) -6 C) -11 D) -5 22 / 25 22. To‘g‘ri burchakli uchburchak o‘tkir burchaklari yarimlarining tangenslari ko‘paytmasi 1/6 ga teng bo‘lsa, uchburchak o‘tkir burchaklarining kosinuslari yig‘indisini toping. A) 4/3 B) √5/2 C) 1.4 D) √6/2 23 / 25 23. Soddalashtiring: A) cosx B) 3cosx C) 3sin2x D) 3cos2x 24 / 25 24. АВС uchburchak ∠C=60° burchagining bissektrisasi 5√3 ga teng. Agar АС : ВС = 5 :2 bo‘lsa, ВС ni toping. A) A B) D C) B D) C 25 / 25 25. Berilgan natural son 400 dan katta va 500 dan kichik. Uning raqamlari yig‘indisi 9 va u berilgan sonning raqamlari teskari tartibda yozilgan sonning 47/36 qismiga teng. Berilgan sonni toping. A) 444 B) 423 C) 443 D) 433 0% Testni qayta ishga tushiring tomonidan Wordpress Quiz plugin Matematika olimpiada, Viloyat 2021-2022 o'quv yili
