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 101 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) 3 B) 2 C) Ø D) 5 2 / 25 2. Perimetri 4 ga o`tkir burchagi 30oga va shu burchak qarshisidagi tomoni √3 ga teng bo`lgan uchburchakka ichki chizlgan aylana radiusini toping. A) 7-4√3 B) (√3-1)/2 C) (1+√3)/2 D) 4√3+7 3 / 25 3. Soddalashtiring: A) 2sinα B) 1 C) cosα D) 2 4 / 25 4. Aylananing ОА, ОВ, ОС radiuslari o‘tkazilgan. Agar bo‘lsa, АОВ burchakni toping. A) 60° B) 120° C) 30° D) 90° 5 / 25 5. Agar ? + 4/√?= 17 bo‘lsa, ? + 4√? ni toping. A) 2 B) 4 C) 1 D) 3 6 / 25 6. АВС uchburchak ∠C=60° burchagining bissektrisasi 5√3 ga teng. Agar АС : ВС = 5 :2 bo‘lsa, ВС ni toping. A) D B) A C) B D) C 7 / 25 7. 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 8 / 25 8. Soddalashtiring: A) 3cosx B) 3cos2x C) 3sin2x D) cosx 9 / 25 9. 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 10 / 25 10. Tenglamalar sistemasi nechta yechimga ega? A) 10 B) 6 C) 8 D) 12 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) 3 C) 211/47 D) 177/48 12 / 25 12. Tenglama nechta yechimga ega? Bunda, x ∈ (1; 47) A) 15 B) 12 C) 14 D) 16 13 / 25 13. Hisoblang: 1 + 2 ∙ 2 + 3 ∙ 22 + 4 ∙ 23+. … + 100 ∙ 299 A) B B) D C) A D) C 14 / 25 14. 80 ni qanday musbat butun songa bo‘lganda, hosil bo‘ladigan qoldiq bo‘linmaning 25%iga teng bo‘ladi? A) 10 B) 21 C) 11 D) 19 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. Hisoblang: A) 85/104 B) 172/249 C) 95/243 D) 81/109 17 / 25 17. Hisoblang: A) 2 B) 0 C) 1.5 D) 1 18 / 25 18. Aylanaga АВС uchburchak ichki chizilgan. Uchburchakning СС1medianasining davomi aylanani ? nuqtada kesib o‘tadi. ni toping. A) 2 B) 4 C) √5 D) 1 19 / 25 19. 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 20 / 25 20. Soddalashtiring: A) III B) IV C) I D) II 21 / 25 21. 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 22 / 25 22. 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 23 / 25 23. Hisoblang: (1 − tg5°)(1 − tg20°)2 + 2(2tg20° + tg5°) A) 1 B) 2 C) 4 D) 3 24 / 25 24. bo‘lsa, ?² + ?² ni toping. A) 65/21 B) 61/20 C) 20 D) 20.2 25 / 25 25. Quyidagi sonlar orasidan musbat sonni aniqlang. A) D B) C C) B D) A 0% Testni qayta ishga tushiring Author: InfoMaster Foydali bo'lsa mamnunmiz
