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 66 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. bo‘lsa, nimaga teng? A) 3 B) 7 C) 9 D) 5 2 / 25 2. ABCD tetraedrning D uchidagi barcha yassi burchaklari to`g`ri. Shu tetraedrda kub shunday ichki chizilganki, kubning bitta uchi D nuqtada, unga qarama−qarshi uchi esa ABC yoqda yotibdi. Agar DA=5, DB=6 va DC=10 bo`lsa, kub qirrasining uzunligini toping. A) 2√2 B) 15/7 C) 2 D) 25/12 3 / 25 3. 100 dan kichik musbat butun sonlar orasida 2 ga ham, 3 ga ham, 7 ga ham bo‘linmaydigan nechta son mavjud? A) 27 B) 29 C) 28 D) 26 4 / 25 4. Aylanaga АВС uchburchak ichki chizilgan. Uchburchakning СС1medianasining davomi aylanani ? nuqtada kesib o‘tadi. ni toping. A) 1 B) 2 C) √5 D) 4 5 / 25 5. 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) √6/2 C) 1.4 D) 4/3 6 / 25 6. Aylananing ОА, ОВ, ОС radiuslari o‘tkazilgan. Agar bo‘lsa, АОВ burchakni toping. A) 30° B) 60° C) 90° D) 120° 7 / 25 7. Hisoblang: 1 + 2 ∙ 2 + 3 ∙ 22 + 4 ∙ 23+. … + 100 ∙ 299 A) D B) B C) A D) C 8 / 25 8. 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 9 / 25 9. bo‘lsa, ?² + ?² ni toping. A) 65/21 B) 61/20 C) 20.2 D) 20 10 / 25 10. Tenglamalar sistemasi nechta yechimga ega? A) 6 B) 12 C) 8 D) 10 11 / 25 11. Soddalashtiring: A) 3cos2x B) 3sin2x C) cosx D) 3cosx 12 / 25 12. Agar ?(?) = ?2021 + 3?2020 + 3?2019 − ?2018 + 1 bo‘lsa, ni toping. A) 3 B) 1 C) 0 D) 2 13 / 25 13. 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) 53 C) 55 D) 65 14 / 25 14. Agar ? + 4/√?= 17 bo‘lsa, ? + 4√? ni toping. A) 3 B) 1 C) 2 D) 4 15 / 25 15. Funksiyaning eng kichik qiymatini toping. ?(?) = (2? + 6)5 − 4(2? + 6)4, bunda |? + 3| ≤ 2. A) -2⁹ B) -4⁵ C) -2¹¹ D) -4⁴ 16 / 25 16. Agar a = √5 + 1 va b = √5 − 1 bo‘lsa, 2a² − ab − a² ifodaning qiymatini toping. A) 6√5 + 1 B) 6√5 + 2 C) 3√5 + 6 D) √5 + 6 17 / 25 17. Quyidagi sonlar orasidan musbat sonni aniqlang. A) A B) B C) D D) C 18 / 25 18. Hisoblang: A) 0 B) 2 C) 1 D) 1.5 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) 12 C) 6 D) 8 20 / 25 20. Hisoblang: (1 − tg5°)(1 − tg20°)2 + 2(2tg20° + tg5°) A) 2 B) 3 C) 4 D) 1 21 / 25 21. 80 ni qanday musbat butun songa bo‘lganda, hosil bo‘ladigan qoldiq bo‘linmaning 25%iga teng bo‘ladi? A) 19 B) 21 C) 11 D) 10 22 / 25 22. 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 23 / 25 23. Sektor perimetri 28 sm ga teng, uning yuzi esa 49 sm2. Sektor yoyining uzunligini toping. A) 12 sm B) 14 sm C) 7 sm D) 18 sm 24 / 25 24. 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) 260/17 D) 120/17 25 / 25 25. Soddalashtiring: A) 2sinα B) 1 C) 2 D) cosα 0% Testni qayta ishga tushiring Author: InfoMaster Foydali bo'lsa mamnunmiz
