11-sinf Matematika olimpiada №3 Oktabr 4, 2022Oktabr 4, 2022 da chop etilgan InfoMaster tomonidan 11-sinf Matematika olimpiada №3 ga 3 fikr bildirilgan 0 12345678910111213141516171819202122232425 Vaqtingiz tugadi! 11-sinf Matematika olimpiada №3 2021-2022 o'quv yilida viloyat bosqichida tushgan savollar 1 / 25 1. a,b-to‘g‘ri burchakli uchburchakning katetlari va h-gipotenuzaga tushirilgan balandligi bo‘lsa, yig‘indini toping. A) 1 B) 2 C) 3 D) 4 2 / 25 2. Tengsizlikni yeching. A) (1/2;∞) B) (5/3;2) C) (4/3;3) D) (2/3;2) 3 / 25 3. Soddalashtiring: A) II B) III C) I D) IV 4 / 25 4. Hisoblang: (1 − tg5°)(1 − tg20°)2 + 2(2tg20° + tg5°) A) 4 B) 2 C) 1 D) 3 5 / 25 5. bo‘lsa, ?² + ?² ni toping. A) 65/21 B) 20 C) 61/20 D) 20.2 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) 20/3 B) 60/7 C) 120/17 D) 260/17 7 / 25 7. Sektor perimetri 28 sm ga teng, uning yuzi esa 49 sm2. Sektor yoyining uzunligini toping. A) 14 sm B) 18 sm C) 7 sm D) 12 sm 8 / 25 8. Tenglama nechta yechimga ega? Bunda, x ∈ (1; 47) A) 12 B) 14 C) 15 D) 16 9 / 25 9. 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) 4/3 C) 1.4 D) √6/2 10 / 25 10. 100 dan kichik musbat butun sonlar orasida 2 ga ham, 3 ga ham, 7 ga ham bo‘linmaydigan nechta son mavjud? A) 28 B) 26 C) 27 D) 29 11 / 25 11. Soddalashtiring: A) cosx B) 3sin2x C) 3cos2x D) 3cosx 12 / 25 12. 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) 55 D) 65 13 / 25 13. ABC uchburchakning AC tomonida shunday D nuqta olinganki, bunda ∠ABC=∠BDC, 5AB=4BD. Agar BC=10 bo‘lsa, ACni toping. A) 12 B) 8 C) 6 D) 10 14 / 25 14. (?²+ 4? + 8)² + 3?³ + 14?² + 24? = 0 tenglamaning ildizlari yig’indisini toping. A) -7 B) -6 C) -11 D) -5 15 / 25 15. Soddalashtiring: A) 2 B) 2sinα C) cosα D) 1 16 / 25 16. Funksiyaning eng kichik qiymatini toping. ?(?) = (2? + 6)5 − 4(2? + 6)4, bunda |? + 3| ≤ 2. A) -2⁹ B) -4⁵ C) -2¹¹ D) -4⁴ 17 / 25 17. АВС uchburchak ∠C=60° burchagining bissektrisasi 5√3 ga teng. Agar АС : ВС = 5 :2 bo‘lsa, ВС ni toping. A) D B) B C) C D) A 18 / 25 18. Agar a = √5 + 1 va b = √5 − 1 bo‘lsa, 2a² − ab − a² ifodaning qiymatini toping. A) 3√5 + 6 B) 6√5 + 1 C) √5 + 6 D) 6√5 + 2 19 / 25 19. Hisoblang: A) 81/109 B) 85/104 C) 172/249 D) 95/243 20 / 25 20. 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) 444 C) 443 D) 423 21 / 25 21. 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) 3 C) 177/48 D) 211/47 22 / 25 22. Agar ? + 4/√?= 17 bo‘lsa, ? + 4√? ni toping. A) 3 B) 4 C) 2 D) 1 23 / 25 23. Hisoblang: A) 2 B) 0 C) 1 D) 1.5 24 / 25 24. 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) 4 B) 5 C) 3 D) 6 25 / 25 25. Quyidagi sonlar orasidan musbat sonni aniqlang. A) B B) D C) A D) C 0% Testni qayta ishga tushiring Author: InfoMaster Matematika olimpiada
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