Uy » Online olimpiada » Matematika olimpiada » 11-sinf Matematika olimpiada №3 Matematika olimpiadaViloyat 2021-2022 o'quv yili 11-sinf Matematika olimpiada №3 InfoMaster Avgust 19, 2024 97 Ko'rishlar 1 izoh SaqlashSaqlanganOlib tashlandi 0 0 12345678910111213141516171819202122232425 Vaqtingiz tugadi! 11-sinf Matematika olimpiada №3 2021-2022 o'quv yilida viloyat bosqichida tushgan savollar 1 / 25 1. tenglamaning ildizlari yig‘indisini toping. A) -6 B) 10 C) 6 D) -2 2 / 25 2. a+b=−1 a+c=6 va b+c=1 bo`lsa, a² (3b+3c+2a)+b² (3a+3c+2b)+c² (3a+3b+2c) ning son qiymatini toping. A) 216 B) 100 C) 27 D) 45 3 / 25 3. АВС uchburchak ∠C=60° burchagining bissektrisasi 5√3 ga teng. Agar АС : ВС = 5 :2 bo‘lsa, ВС ni toping. A) A B) B C) C D) D 4 / 25 4. Soddalashtiring: A) 3sin2x B) cosx C) 3cosx D) 3cos2x 5 / 25 5. 80 ni qanday musbat butun songa bo‘lganda, hosil bo‘ladigan qoldiq bo‘linmaning 25%iga teng bo‘ladi? A) 19 B) 21 C) 10 D) 11 6 / 25 6. bo‘lsa, ?² + ?² ni toping. A) 20.2 B) 65/21 C) 61/20 D) 20 7 / 25 7. Hisoblang: 1 + 2 ∙ 2 + 3 ∙ 22 + 4 ∙ 23+. … + 100 ∙ 299 A) D B) C C) B D) A 8 / 25 8. 100 dan kichik musbat butun sonlar orasida 2 ga ham, 3 ga ham, 7 ga ham bo‘linmaydigan nechta son mavjud? A) 29 B) 28 C) 26 D) 27 9 / 25 9. (?²+ 4? + 8)² + 3?³ + 14?² + 24? = 0 tenglamaning ildizlari yig’indisini toping. A) -11 B) -5 C) -7 D) -6 10 / 25 10. 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) 433 B) 443 C) 423 D) 444 11 / 25 11. Quyidagi sonlar orasidan musbat sonni aniqlang. A) C B) A C) B D) D 12 / 25 12. To‘g‘ri burchakli uchburchakka ichki va tashqi chizilgan aylana radiuslari nisbati 2 : 5 bo‘lsa, uchburchakning katta o‘tkir burchagining kosinusini toping. A) 0.2 B) 0.5 C) 0.8 D) 0.6 13 / 25 13. Uchburchakning tomonlari 10, 24 va 26. Aylananing markazi uchburchakning katta tomonida yotadi va ikki kichik tomonlari bu aylanaga urinadi. Aylana radiusini toping. A) 60/7 B) 20/3 C) 260/17 D) 120/17 14 / 25 14. 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) 211/47 B) 177/48 C) 3 D) 175/48 15 / 25 15. Soddalashtiring: A) IV B) III C) I D) II 16 / 25 16. Hisoblang: A) 85/104 B) 95/243 C) 172/249 D) 81/109 17 / 25 17. Hisoblang: A) 2 B) 1.5 C) 1 D) 0 18 / 25 18. Aylanaga АВС uchburchak ichki chizilgan. Uchburchakning СС1medianasining davomi aylanani ? nuqtada kesib o‘tadi. ni toping. A) √5 B) 1 C) 4 D) 2 19 / 25 19. 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 20 / 25 20. 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) 3 C) 4 D) 6 21 / 25 21. Hisoblang: (1 − tg5°)(1 − tg20°)2 + 2(2tg20° + tg5°) A) 1 B) 2 C) 3 D) 4 22 / 25 22. Sektor perimetri 28 sm ga teng, uning yuzi esa 49 sm2. Sektor yoyining uzunligini toping. A) 18 sm B) 7 sm C) 14 sm D) 12 sm 23 / 25 23. ABC uchburchakning AC tomonida shunday D nuqta olinganki, bunda ∠ABC=∠BDC, 5AB=4BD. Agar BC=10 bo‘lsa, ACni toping. A) 10 B) 12 C) 8 D) 6 24 / 25 24. Tenglamalar sistemasi nechta yechimga ega? A) 10 B) 8 C) 6 D) 12 25 / 25 25. Tenglama nechta yechimga ega? Bunda, x ∈ (1; 47) A) 15 B) 16 C) 12 D) 14 0% Testni qayta ishga tushiring Author: InfoMaster Foydali bo'lsa mamnunmiz
