11-sinf Matematika olimpiada №3 Oktabr 4, 2022Oktabr 4, 2022 da chop etilgan InfoMaster tomonidan 11-sinf Matematika olimpiada №3 ga fikr bildirilmagan. 0 12345678910111213141516171819202122232425 Vaqtingiz tugadi! 11-sinf Matematika olimpiada №3 2021-2022 o'quv yilida viloyat bosqichida tushgan savollar 1 / 25 1. tenglama nechta natural yechimga ega? A) 4 B) 1 C) 2 D) 3 2 / 25 2. Tengsizlikni yeching. A) (2/3;2) B) (5/3;2) C) (1/2;∞) D) (4/3;3) 3 / 25 3. Soddalashtiring: A) 2 B) cosα C) 1 D) 2sinα 4 / 25 4. Hisoblang: (1 − tg5°)(1 − tg20°)2 + 2(2tg20° + tg5°) A) 2 B) 3 C) 4 D) 1 5 / 25 5. Aylananing ОА, ОВ, ОС radiuslari o‘tkazilgan. Agar bo‘lsa, АОВ burchakni toping. A) 120° B) 90° C) 30° D) 60° 6 / 25 6. Aylanaga АВС uchburchak ichki chizilgan. Uchburchakning СС1medianasining davomi aylanani ? nuqtada kesib o‘tadi. ni toping. A) 4 B) √5 C) 2 D) 1 7 / 25 7. Quyidagi sonlar orasidan musbat sonni aniqlang. A) D B) A C) B D) C 8 / 25 8. Agar a = √5 + 1 va b = √5 − 1 bo‘lsa, 2a² − ab − a² ifodaning qiymatini toping. A) 6√5 + 1 B) 6√5 + 2 C) 3√5 + 6 D) √5 + 6 9 / 25 9. Agar ?(?) = ?2021 + 3?2020 + 3?2019 − ?2018 + 1 bo‘lsa, ni toping. A) 1 B) 2 C) 0 D) 3 10 / 25 10. (?²+ 4? + 8)² + 3?³ + 14?² + 24? = 0 tenglamaning ildizlari yig’indisini toping. A) -6 B) -5 C) -11 D) -7 11 / 25 11. Funksiyaning eng kichik qiymatini toping. ?(?) = (2? + 6)5 − 4(2? + 6)4, bunda |? + 3| ≤ 2. A) -2⁹ B) -4⁵ C) -2¹¹ D) -4⁴ 12 / 25 12. Tenglama nechta yechimga ega? Bunda, x ∈ (1; 47) A) 12 B) 15 C) 16 D) 14 13 / 25 13. 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 14 / 25 14. 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) 0.6 C) 0.5 D) 0.8 15 / 25 15. Hisoblang: 1 + 2 ∙ 2 + 3 ∙ 22 + 4 ∙ 23+. … + 100 ∙ 299 A) D B) B C) A D) C 16 / 25 16. 80 ni qanday musbat butun songa bo‘lganda, hosil bo‘ladigan qoldiq bo‘linmaning 25%iga teng bo‘ladi? A) 21 B) 11 C) 19 D) 10 17 / 25 17. 100 dan kichik musbat butun sonlar orasida 2 ga ham, 3 ga ham, 7 ga ham bo‘linmaydigan nechta son mavjud? A) 27 B) 28 C) 29 D) 26 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) 3 B) 177/48 C) 211/47 D) 175/48 19 / 25 19. Uchburchakning tomonlari 10, 24 va 26. Aylananing markazi uchburchakning katta tomonida yotadi va ikki kichik tomonlari bu aylanaga urinadi. Aylana radiusini toping. A) 120/17 B) 260/17 C) 20/3 D) 60/7 20 / 25 20. bo‘lsa, ?² + ?² ni toping. A) 61/20 B) 20.2 C) 20 D) 65/21 21 / 25 21. Sektor perimetri 28 sm ga teng, uning yuzi esa 49 sm2. Sektor yoyining uzunligini toping. A) 12 sm B) 7 sm C) 14 sm D) 18 sm 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) 1.4 B) 4/3 C) √5/2 D) √6/2 23 / 25 23. 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 24 / 25 24. Tenglamalar sistemasi nechta yechimga ega? A) 6 B) 12 C) 8 D) 10 25 / 25 25. Agar ? + 4/√?= 17 bo‘lsa, ? + 4√? ni toping. A) 4 B) 3 C) 2 D) 1 0% Testni qayta ishga tushiring Author: InfoMaster Matematika olimpiada