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 73 Ko'rishlar 1 izoh SaqlashSaqlanganOlib tashlandi 0 1 12345678910111213141516171819202122232425 Vaqtingiz tugadi! 11-sinf Matematika olimpiada №3 2021-2022 o'quv yilida viloyat bosqichida tushgan savollar 1 / 25 1. ABC uchburchakka aylana tashqi chizilgan. Uchburchakning AM medianasi aylana bilan K nuqtada kesishguncha davom ettirilgan. Agar AM=18,MK=8,BK=10 bo‘lsa, AC tomonini toping. A) 14 B) 12 C) 15 D) 16 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) 45 D) 27 3 / 25 3. 100 dan kichik musbat butun sonlar orasida 2 ga ham, 3 ga ham, 7 ga ham bo‘linmaydigan nechta son mavjud? A) 27 B) 26 C) 29 D) 28 4 / 25 4. Aylananing ОА, ОВ, ОС radiuslari o‘tkazilgan. Agar bo‘lsa, АОВ burchakni toping. A) 120° B) 90° C) 30° D) 60° 5 / 25 5. Soddalashtiring: A) 3cosx B) 3cos2x C) cosx D) 3sin2x 6 / 25 6. Tenglama nechta yechimga ega? Bunda, x ∈ (1; 47) A) 14 B) 15 C) 12 D) 16 7 / 25 7. (?²+ 4? + 8)² + 3?³ + 14?² + 24? = 0 tenglamaning ildizlari yig’indisini toping. A) -11 B) -7 C) -6 D) -5 8 / 25 8. ABC uchburchakning AC tomonida shunday D nuqta olinganki, bunda ∠ABC=∠BDC, 5AB=4BD. Agar BC=10 bo‘lsa, ACni toping. A) 12 B) 10 C) 8 D) 6 9 / 25 9. Funksiyaning eng kichik qiymatini toping. ?(?) = (2? + 6)5 − 4(2? + 6)4, bunda |? + 3| ≤ 2. A) -2⁹ B) -4⁵ C) -2¹¹ D) -4⁴ 10 / 25 10. Hisoblang: 1 + 2 ∙ 2 + 3 ∙ 22 + 4 ∙ 23+. … + 100 ∙ 299 A) D B) B C) C D) A 11 / 25 11. Hisoblang: (1 − tg5°)(1 − tg20°)2 + 2(2tg20° + tg5°) A) 2 B) 1 C) 4 D) 3 12 / 25 12. 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) 260/17 C) 120/17 D) 20/3 13 / 25 13. bo‘lsa, ?² + ?² ni toping. A) 65/21 B) 20.2 C) 20 D) 61/20 14 / 25 14. Aylanaga АВС uchburchak ichki chizilgan. Uchburchakning СС1medianasining davomi aylanani ? nuqtada kesib o‘tadi. ni toping. A) √5 B) 2 C) 1 D) 4 15 / 25 15. 80 ni qanday musbat butun songa bo‘lganda, hosil bo‘ladigan qoldiq bo‘linmaning 25%iga teng bo‘ladi? A) 10 B) 21 C) 19 D) 11 16 / 25 16. Tenglamalar sistemasi nechta yechimga ega? A) 8 B) 6 C) 10 D) 12 17 / 25 17. To‘g‘ri burchakli uchburchakka ichki va tashqi chizilgan aylana radiuslari nisbati 2 : 5 bo‘lsa, uchburchakning katta o‘tkir burchagining kosinusini toping. A) 0.8 B) 0.5 C) 0.2 D) 0.6 18 / 25 18. 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) 3 B) 5 C) 4 D) 6 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. АВС uchburchak ∠C=60° burchagining bissektrisasi 5√3 ga teng. Agar АС : ВС = 5 :2 bo‘lsa, ВС ni toping. A) B B) D C) A D) C 21 / 25 21. Sektor perimetri 28 sm ga teng, uning yuzi esa 49 sm2. Sektor yoyining uzunligini toping. A) 14 sm B) 7 sm C) 12 sm D) 18 sm 22 / 25 22. Hisoblang: A) 95/243 B) 85/104 C) 172/249 D) 81/109 23 / 25 23. Quyidagi sonlar orasidan musbat sonni aniqlang. A) A B) C C) D D) B 24 / 25 24. Agar a = √5 + 1 va b = √5 − 1 bo‘lsa, 2a² − ab − a² ifodaning qiymatini toping. A) 3√5 + 6 B) √5 + 6 C) 6√5 + 2 D) 6√5 + 1 25 / 25 25. Agar ?(?) = ?2021 + 3?2020 + 3?2019 − ?2018 + 1 bo‘lsa, ni toping. A) 3 B) 1 C) 0 D) 2 0% Testni qayta ishga tushiring Author: InfoMaster Foydali bo'lsa mamnunmiz
