11-sinf Matematika olimpiada №3 Oktabr 4, 2022Avgust 19, 2024 da chop etilgan InfoMaster tomonidan 11-sinf Matematika olimpiada №3 ga 3 fikr bildirilgan 0 12345678910111213141516171819202122232425 Vaqtingiz tugadi! Tomonidan yaratilgan InfoMaster 11-sinf Matematika olimpiada №3 2021-2022 o'quv yilida viloyat bosqichida tushgan savollar 1 / 25 1. To‘g‘ri burchakli uchburchakda AC=3, BC=4, CD-balandlik va CE-bissektrisa. DE ni toping. A) 23/35 B) 15/31 C) 21 D) 12/35 2 / 25 2. ifodani soddalshtiring A) 1 B) 2cosα C) cosα D) 2sinα 3 / 25 3. Aylananing ОА, ОВ, ОС radiuslari o‘tkazilgan. Agar bo‘lsa, АОВ burchakni toping. A) 30° B) 90° C) 120° D) 60° 4 / 25 4. 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) 60/7 C) 120/17 D) 20/3 5 / 25 5. 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 6 / 25 6. Tenglamalar sistemasi nechta yechimga ega? A) 8 B) 10 C) 12 D) 6 7 / 25 7. 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) 444 B) 443 C) 433 D) 423 8 / 25 8. Soddalashtiring: A) 2sinα B) 1 C) cosα D) 2 9 / 25 9. bo‘lsa, ?² + ?² ni toping. A) 20.2 B) 61/20 C) 20 D) 65/21 10 / 25 10. Funksiyaning eng kichik qiymatini toping. ?(?) = (2? + 6)5 − 4(2? + 6)4, bunda |? + 3| ≤ 2. A) -4⁴ B) -2¹¹ C) -4⁵ D) -2⁹ 11 / 25 11. 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) 175/48 B) 177/48 C) 3 D) 211/47 12 / 25 12. Tenglama nechta yechimga ega? Bunda, x ∈ (1; 47) A) 15 B) 16 C) 14 D) 12 13 / 25 13. Hisoblang: (1 − tg5°)(1 − tg20°)2 + 2(2tg20° + tg5°) A) 2 B) 3 C) 1 D) 4 14 / 25 14. 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 15 / 25 15. (?²+ 4? + 8)² + 3?³ + 14?² + 24? = 0 tenglamaning ildizlari yig’indisini toping. A) -5 B) -6 C) -7 D) -11 16 / 25 16. Soddalashtiring: A) IV B) III C) II D) I 17 / 25 17. Soddalashtiring: A) 3cos2x B) 3cosx C) cosx D) 3sin2x 18 / 25 18. Quyidagi sonlar orasidan musbat sonni aniqlang. A) B B) D C) A D) C 19 / 25 19. Hisoblang: A) 1.5 B) 0 C) 2 D) 1 20 / 25 20. Hisoblang: 1 + 2 ∙ 2 + 3 ∙ 22 + 4 ∙ 23+. … + 100 ∙ 299 A) D B) C C) A D) B 21 / 25 21. Agar ? + 4/√?= 17 bo‘lsa, ? + 4√? ni toping. A) 4 B) 2 C) 3 D) 1 22 / 25 22. 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) 6 B) 4 C) 3 D) 5 23 / 25 23. 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 24 / 25 24. АВС uchburchak ∠C=60° burchagining bissektrisasi 5√3 ga teng. Agar АС : ВС = 5 :2 bo‘lsa, ВС ni toping. A) C B) A C) D D) B 25 / 25 25. Ikki xonali sonni qandaydir natural songa bo‘lganda bo‘linmada 3 va qoldiqda 8 hosil bo‘ladi. Agar bo‘linuvchining raqamlari o‘rni almashtirilsa va bo‘luvchi son o‘zgarishsiz qoldirilsa, u holda bo‘linmada 2 va qoldiqda 5 hosil bo‘ladi. Bo‘linuvchning dastlabki qiymatini toping. A) 53 B) 73 C) 65 D) 55 0% Testni qayta ishga tushiring tomonidan Wordpress Quiz plugin Matematika olimpiada, Viloyat 2021-2022 o'quv yili
