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 30 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. tenglama t ning qanday qiymatida uchta ildizga ega bo‘ladi? A) 5 B) Ø C) 2 D) 3 2 / 25 2. 3cos2x-3 sin2x=0 trigonometrik tenglamani yeching. A) π/12+2πk; k∈Z B) π/12+πk; k∈Z C) π/6+πk; k∈Z D) π/12+πk/2; k∈Z) 3 / 25 3. Aylananing ОА, ОВ, ОС radiuslari o‘tkazilgan. Agar bo‘lsa, АОВ burchakni toping. A) 30° B) 60° C) 90° D) 120° 4 / 25 4. Hisoblang: A) 81/109 B) 172/249 C) 95/243 D) 85/104 5 / 25 5. Aylanaga АВС uchburchak ichki chizilgan. Uchburchakning СС1medianasining davomi aylanani ? nuqtada kesib o‘tadi. ni toping. A) 2 B) 1 C) √5 D) 4 6 / 25 6. Soddalashtiring: A) 1 B) 2sinα C) cosα D) 2 7 / 25 7. 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) 65 B) 73 C) 53 D) 55 8 / 25 8. Soddalashtiring: A) 3cosx B) cosx C) 3cos2x D) 3sin2x 9 / 25 9. Soddalashtiring: A) IV B) III C) I D) II 10 / 25 10. Quyidagi sonlar orasidan musbat sonni aniqlang. A) A B) D C) C D) B 11 / 25 11. 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 12 / 25 12. Agar a = √5 + 1 va b = √5 − 1 bo‘lsa, 2a² − ab − a² ifodaning qiymatini toping. A) √5 + 6 B) 6√5 + 2 C) 3√5 + 6 D) 6√5 + 1 13 / 25 13. Tenglama nechta yechimga ega? Bunda, x ∈ (1; 47) A) 12 B) 16 C) 15 D) 14 14 / 25 14. 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) 211/47 B) 3 C) 177/48 D) 175/48 15 / 25 15. Hisoblang: (1 − tg5°)(1 − tg20°)2 + 2(2tg20° + tg5°) A) 1 B) 3 C) 4 D) 2 16 / 25 16. Agar ? + 4/√?= 17 bo‘lsa, ? + 4√? ni toping. A) 1 B) 3 C) 4 D) 2 17 / 25 17. 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) 10 D) 6 18 / 25 18. bo‘lsa, ?² + ?² ni toping. A) 20.2 B) 61/20 C) 65/21 D) 20 19 / 25 19. Hisoblang: 1 + 2 ∙ 2 + 3 ∙ 22 + 4 ∙ 23+. … + 100 ∙ 299 A) A B) B C) C D) D 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) 1.4 B) √6/2 C) 4/3 D) √5/2 21 / 25 21. 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) 0.2 C) 0.8 D) 0.5 22 / 25 22. Sektor perimetri 28 sm ga teng, uning yuzi esa 49 sm2. Sektor yoyining uzunligini toping. A) 14 sm B) 18 sm C) 12 sm D) 7 sm 23 / 25 23. 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) 60/7 D) 120/17 24 / 25 24. Funksiyaning eng kichik qiymatini toping. ?(?) = (2? + 6)5 − 4(2? + 6)4, bunda |? + 3| ≤ 2. A) -2¹¹ B) -4⁵ C) -2⁹ D) -4⁴ 25 / 25 25. Tenglamalar sistemasi nechta yechimga ega? A) 12 B) 8 C) 6 D) 10 0% Testni qayta ishga tushiring Author: InfoMaster Foydali bo'lsa mamnunmiz
