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. tenglamaning ildizlari yig‘indisini toping. A) -6 B) -2 C) 6 D) 10 2 / 25 2. Tenglamani yeching: A) πk; π−arcctg4+πk; k∈Z B) arccos0,8+2πk; k∈Z C) π −arcctg4+πk; k∈Z D) πk; −arcctg4+πk; k∈Z 3 / 25 3. Agar a = √5 + 1 va b = √5 − 1 bo‘lsa, 2a² − ab − a² ifodaning qiymatini toping. A) 3√5 + 6 B) 6√5 + 2 C) 6√5 + 1 D) √5 + 6 4 / 25 4. Funksiyaning eng kichik qiymatini toping. ?(?) = (2? + 6)5 − 4(2? + 6)4, bunda |? + 3| ≤ 2. A) -4⁴ B) -4⁵ C) -2⁹ D) -2¹¹ 5 / 25 5. 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) 443 B) 423 C) 433 D) 444 6 / 25 6. 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) 20/3 C) 120/17 D) 60/7 7 / 25 7. 80 ni qanday musbat butun songa bo‘lganda, hosil bo‘ladigan qoldiq bo‘linmaning 25%iga teng bo‘ladi? A) 11 B) 21 C) 19 D) 10 8 / 25 8. Hisoblang: 1 + 2 ∙ 2 + 3 ∙ 22 + 4 ∙ 23+. … + 100 ∙ 299 A) B B) D C) A D) C 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) 6 C) 4 D) 3 10 / 25 10. (?²+ 4? + 8)² + 3?³ + 14?² + 24? = 0 tenglamaning ildizlari yig’indisini toping. A) -11 B) -6 C) -7 D) -5 11 / 25 11. Quyidagi sonlar orasidan musbat sonni aniqlang. A) A B) B C) D D) C 12 / 25 12. bo‘lsa, ?² + ?² ni toping. A) 20.2 B) 61/20 C) 65/21 D) 20 13 / 25 13. АВС uchburchak ∠C=60° burchagining bissektrisasi 5√3 ga teng. Agar АС : ВС = 5 :2 bo‘lsa, ВС ni toping. A) C B) B C) D D) A 14 / 25 14. Agar ?(?) = ?2021 + 3?2020 + 3?2019 − ?2018 + 1 bo‘lsa, ni toping. A) 2 B) 3 C) 0 D) 1 15 / 25 15. 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) 0.2 C) 0.5 D) 0.6 16 / 25 16. 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) √6/2 B) 4/3 C) √5/2 D) 1.4 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. Agar ? + 4/√?= 17 bo‘lsa, ? + 4√? ni toping. A) 3 B) 1 C) 4 D) 2 19 / 25 19. Sektor perimetri 28 sm ga teng, uning yuzi esa 49 sm2. Sektor yoyining uzunligini toping. A) 7 sm B) 18 sm C) 14 sm D) 12 sm 20 / 25 20. Soddalashtiring: A) III B) I C) IV D) II 21 / 25 21. Hisoblang: A) 2 B) 1.5 C) 0 D) 1 22 / 25 22. Hisoblang: (1 − tg5°)(1 − tg20°)2 + 2(2tg20° + tg5°) A) 4 B) 1 C) 2 D) 3 23 / 25 23. ABC uchburchakning AC tomonida shunday D nuqta olinganki, bunda ∠ABC=∠BDC, 5AB=4BD. Agar BC=10 bo‘lsa, ACni toping. A) 8 B) 10 C) 6 D) 12 24 / 25 24. Hisoblang: A) 95/243 B) 81/109 C) 172/249 D) 85/104 25 / 25 25. Tenglamalar sistemasi nechta yechimga ega? A) 12 B) 6 C) 8 D) 10 0% Testni qayta ishga tushiring Author: InfoMaster Matematika olimpiada