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 103 Ko'rishlar 1 izoh SaqlashSaqlanganOlib tashlandi 0 0 Savollar 12345678910111213141516171819202122232425 Vaqtingiz tugadi! Tomonidan yaratilgan InfoMaster 11-sinf Matematika olimpiada №3 2021-2022 o'quv yilida viloyat bosqichida tushgan savollar 1 / 25 1. ko‘phadning barcha koeffitsientlari va ozod hadining yig‘indisini toping. A) 125 B) -247 C) 245 D) -238 2 / 25 2. Tenglamani yeching: A) πk; π−arcctg4+πk; k∈Z B) arccos0,8+2πk; k∈Z C) πk; −arcctg4+πk; k∈Z D) π −arcctg4+πk; k∈Z 3 / 25 3. Aylananing ОА, ОВ, ОС radiuslari o‘tkazilgan. Agar bo‘lsa, АОВ burchakni toping. A) 90° B) 120° C) 60° D) 30° 4 / 25 4. Agar ? + 4/√?= 17 bo‘lsa, ? + 4√? ni toping. A) 2 B) 3 C) 4 D) 1 5 / 25 5. Soddalashtiring: A) 1 B) 2 C) 2sinα D) cosα 6 / 25 6. To‘g‘ri burchakli uchburchakka ichki va tashqi chizilgan aylana radiuslari nisbati 2 : 5 bo‘lsa, uchburchakning katta o‘tkir burchagining kosinusini toping. A) 0.6 B) 0.8 C) 0.5 D) 0.2 7 / 25 7. Soddalashtiring: A) 3cos2x B) cosx C) 3cosx D) 3sin2x 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) 28 B) 29 C) 26 D) 27 9 / 25 9. 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) 6 D) 4 10 / 25 10. Hisoblang: A) 2 B) 1.5 C) 1 D) 0 11 / 25 11. Hisoblang: (1 − tg5°)(1 − tg20°)2 + 2(2tg20° + tg5°) A) 3 B) 1 C) 2 D) 4 12 / 25 12. 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 13 / 25 13. Sektor perimetri 28 sm ga teng, uning yuzi esa 49 sm2. Sektor yoyining uzunligini toping. A) 7 sm B) 12 sm C) 14 sm D) 18 sm 14 / 25 14. (?²+ 4? + 8)² + 3?³ + 14?² + 24? = 0 tenglamaning ildizlari yig’indisini toping. A) -6 B) -5 C) -11 D) -7 15 / 25 15. ABC uchburchakning AC tomonida shunday D nuqta olinganki, bunda ∠ABC=∠BDC, 5AB=4BD. Agar BC=10 bo‘lsa, ACni toping. A) 8 B) 6 C) 10 D) 12 16 / 25 16. Aylanaga АВС uchburchak ichki chizilgan. Uchburchakning СС1medianasining davomi aylanani ? nuqtada kesib o‘tadi. ni toping. A) 4 B) 1 C) 2 D) √5 17 / 25 17. Uchburchakning tomonlari 10, 24 va 26. Aylananing markazi uchburchakning katta tomonida yotadi va ikki kichik tomonlari bu aylanaga urinadi. Aylana radiusini toping. A) 260/17 B) 120/17 C) 20/3 D) 60/7 18 / 25 18. Agar ?(?) = ?2021 + 3?2020 + 3?2019 − ?2018 + 1 bo‘lsa, ni toping. A) 1 B) 2 C) 0 D) 3 19 / 25 19. Soddalashtiring: A) II B) I C) III D) IV 20 / 25 20. 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) √5/2 B) 1.4 C) 4/3 D) √6/2 21 / 25 21. Agar a = √5 + 1 va b = √5 − 1 bo‘lsa, 2a² − ab − a² ifodaning qiymatini toping. A) 6√5 + 2 B) 6√5 + 1 C) 3√5 + 6 D) √5 + 6 22 / 25 22. 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) 423 C) 444 D) 443 23 / 25 23. Tenglamalar sistemasi nechta yechimga ega? A) 8 B) 6 C) 10 D) 12 24 / 25 24. Quyidagi sonlar orasidan musbat sonni aniqlang. A) B B) C C) D D) A 25 / 25 25. Hisoblang: A) 95/243 B) 85/104 C) 172/249 D) 81/109 0% Testni qayta ishga tushiring Author: InfoMaster Foydali bo'lsa mamnunmiz