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 26 Ko'rishlar 1 izoh SaqlashSaqlanganOlib tashlandi 0 8 12345678910111213141516171819202122232425 Vaqtingiz tugadi! 11-sinf Matematika olimpiada №3 2021-2022 o'quv yilida viloyat bosqichida tushgan savollar 1 / 25 1. funksiyaning grafigi qaysi choraklardan o‘tadi? A) I,II B) III,IV C) II,III D) I,II,III,IV 2 / 25 2. 3cos2x-3 sin2x=0 trigonometrik tenglamani yeching. A) π/12+πk; k∈Z B) π/12+πk/2; k∈Z) C) π/6+πk; k∈Z D) π/12+2πk; k∈Z 3 / 25 3. Aylananing ОА, ОВ, ОС radiuslari o‘tkazilgan. Agar bo‘lsa, АОВ burchakni toping. A) 120° B) 60° C) 30° D) 90° 4 / 25 4. Soddalashtiring: A) 3cosx B) 3cos2x C) 3sin2x D) cosx 5 / 25 5. 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) 3 B) 177/48 C) 211/47 D) 175/48 6 / 25 6. Hisoblang: (1 − tg5°)(1 − tg20°)2 + 2(2tg20° + tg5°) A) 1 B) 2 C) 3 D) 4 7 / 25 7. Hisoblang: 1 + 2 ∙ 2 + 3 ∙ 22 + 4 ∙ 23+. … + 100 ∙ 299 A) A B) D C) B D) C 8 / 25 8. bo‘lsa, ?² + ?² ni toping. A) 20 B) 20.2 C) 61/20 D) 65/21 9 / 25 9. (?²+ 4? + 8)² + 3?³ + 14?² + 24? = 0 tenglamaning ildizlari yig’indisini toping. A) -5 B) -7 C) -11 D) -6 10 / 25 10. 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) 55 C) 65 D) 53 11 / 25 11. Hisoblang: A) 1.5 B) 2 C) 1 D) 0 12 / 25 12. Sektor perimetri 28 sm ga teng, uning yuzi esa 49 sm2. Sektor yoyining uzunligini toping. A) 7 sm B) 14 sm C) 12 sm D) 18 sm 13 / 25 13. Hisoblang: A) 95/243 B) 81/109 C) 172/249 D) 85/104 14 / 25 14. 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) 423 B) 444 C) 443 D) 433 15 / 25 15. Aylanaga АВС uchburchak ichki chizilgan. Uchburchakning СС1medianasining davomi aylanani ? nuqtada kesib o‘tadi. ni toping. A) 2 B) 1 C) 4 D) √5 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) 120/17 B) 20/3 C) 60/7 D) 260/17 17 / 25 17. Agar ?(?) = ?2021 + 3?2020 + 3?2019 − ?2018 + 1 bo‘lsa, ni toping. A) 1 B) 3 C) 2 D) 0 18 / 25 18. 100 dan kichik musbat butun sonlar orasida 2 ga ham, 3 ga ham, 7 ga ham bo‘linmaydigan nechta son mavjud? A) 26 B) 28 C) 29 D) 27 19 / 25 19. 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) √5/2 D) 1.4 20 / 25 20. 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) 0.5 C) 0.2 D) 0.8 21 / 25 21. Funksiyaning eng kichik qiymatini toping. ?(?) = (2? + 6)5 − 4(2? + 6)4, bunda |? + 3| ≤ 2. A) -4⁴ B) -4⁵ C) -2⁹ D) -2¹¹ 22 / 25 22. Soddalashtiring: A) I B) IV C) II D) III 23 / 25 23. Quyidagi sonlar orasidan musbat sonni aniqlang. A) B B) A C) C D) D 24 / 25 24. Agar a = √5 + 1 va b = √5 − 1 bo‘lsa, 2a² − ab − a² ifodaning qiymatini toping. A) 6√5 + 2 B) √5 + 6 C) 3√5 + 6 D) 6√5 + 1 25 / 25 25. ABC uchburchakning AC tomonida shunday D nuqta olinganki, bunda ∠ABC=∠BDC, 5AB=4BD. Agar BC=10 bo‘lsa, ACni toping. A) 8 B) 6 C) 12 D) 10 0% Testni qayta ishga tushiring Author: InfoMaster Foydali bo'lsa mamnunmiz
