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 40 Ko'rishlar 1 izoh SaqlashSaqlanganOlib tashlandi 0 0 12345678910111213141516171819202122232425 Vaqtingiz tugadi! 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) -247 B) 245 C) -238 D) 125 2 / 25 2. GH kesmani O nuqta, G nuqtadan boshlab hisoblaganda, 5 : 7 kabi, P nuqtaesa 5:11 kabi nisbatda bo’ladi. O va P nuqtalar orasidagi masofa 30 sm bo’lsa, GH kesmaning uzunligini toping. A) 18 B) 234 C) 72 D) 288 3 / 25 3. Soddalashtiring: A) cosx B) 3cosx C) 3cos2x D) 3sin2x 4 / 25 4. 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 5 / 25 5. Tenglamalar sistemasi nechta yechimga ega? A) 10 B) 6 C) 8 D) 12 6 / 25 6. Quyidagi sonlar orasidan musbat sonni aniqlang. A) B B) A C) D D) C 7 / 25 7. Hisoblang: A) 85/104 B) 172/249 C) 95/243 D) 81/109 8 / 25 8. 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 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) 4/3 B) √6/2 C) 1.4 D) √5/2 10 / 25 10. Agar ?(?) = ?2021 + 3?2020 + 3?2019 − ?2018 + 1 bo‘lsa, ni toping. A) 0 B) 2 C) 3 D) 1 11 / 25 11. Agar ? + 4/√?= 17 bo‘lsa, ? + 4√? ni toping. A) 1 B) 3 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) 11 B) 19 C) 21 D) 10 13 / 25 13. bo‘lsa, ?² + ?² ni toping. A) 61/20 B) 20 C) 20.2 D) 65/21 14 / 25 14. АВС uchburchak ∠C=60° burchagining bissektrisasi 5√3 ga teng. Agar АС : ВС = 5 :2 bo‘lsa, ВС ni toping. A) A B) D C) C D) B 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) 0.2 B) 0.5 C) 0.6 D) 0.8 16 / 25 16. 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) 20/3 D) 120/17 17 / 25 17. Hisoblang: (1 − tg5°)(1 − tg20°)2 + 2(2tg20° + tg5°) A) 3 B) 2 C) 1 D) 4 18 / 25 18. 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) 73 B) 65 C) 55 D) 53 19 / 25 19. ABC uchburchakning AC tomonida shunday D nuqta olinganki, bunda ∠ABC=∠BDC, 5AB=4BD. Agar BC=10 bo‘lsa, ACni toping. A) 10 B) 8 C) 6 D) 12 20 / 25 20. Aylanaga АВС uchburchak ichki chizilgan. Uchburchakning СС1medianasining davomi aylanani ? nuqtada kesib o‘tadi. ni toping. A) 4 B) 2 C) 1 D) √5 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) 211/47 C) 3 D) 177/48 22 / 25 22. Tenglama nechta yechimga ega? Bunda, x ∈ (1; 47) A) 16 B) 12 C) 14 D) 15 23 / 25 23. Hisoblang: A) 1.5 B) 0 C) 2 D) 1 24 / 25 24. Funksiyaning eng kichik qiymatini toping. ?(?) = (2? + 6)5 − 4(2? + 6)4, bunda |? + 3| ≤ 2. A) -2⁹ B) -4⁴ C) -2¹¹ D) -4⁵ 25 / 25 25. (?²+ 4? + 8)² + 3?³ + 14?² + 24? = 0 tenglamaning ildizlari yig’indisini toping. A) -6 B) -11 C) -5 D) -7 0% Testni qayta ishga tushiring Author: InfoMaster Foydali bo'lsa mamnunmiz
