11-sinf Matematika olimpiada №3 Oktabr 4, 2022Oktabr 4, 2022 da chop etilgan InfoMaster tomonidan 11-sinf Matematika olimpiada №3 ga fikr bildirilmagan. 0 12345678910111213141516171819202122232425 Vaqtingiz tugadi! 11-sinf Matematika olimpiada №3 2021-2022 o'quv yilida viloyat bosqichida tushgan savollar 1 / 25 1. Koordinata boshidan o‘tuvchi, simmetriya o‘qi ordinata o‘qiga parallel, cho‘qqisi y=x va y+x-2=0 to‘g‘ri chiziqlar kesishgan nuqtada bo‘lgan parabolaning tenglamasini toping. A) y=-x²-2x B) y=-x²+2x C) y=x²-2x D) y=-x²+1 2 / 25 2. funksiyaning aniqlanish sohasini toping. A) (-∞;4/3) B) (2/3;∞) C) (-∞;2/3)∪(2/3;∞) D) (-∞;4/3)∪(4/3;∞) 3 / 25 3. Funksiyaning eng kichik qiymatini toping. ?(?) = (2? + 6)5 − 4(2? + 6)4, bunda |? + 3| ≤ 2. A) -2⁹ B) -2¹¹ C) -4⁵ D) -4⁴ 4 / 25 4. Aylanaga АВС uchburchak ichki chizilgan. Uchburchakning СС1medianasining davomi aylanani ? nuqtada kesib o‘tadi. ni toping. A) 4 B) 1 C) √5 D) 2 5 / 25 5. 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 6 / 25 6. 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) 175/48 C) 177/48 D) 211/47 7 / 25 7. Soddalashtiring: A) 2 B) 2sinα C) 1 D) cosα 8 / 25 8. Quyidagi sonlar orasidan musbat sonni aniqlang. A) B B) D C) C D) A 9 / 25 9. Aylananing ОА, ОВ, ОС radiuslari o‘tkazilgan. Agar bo‘lsa, АОВ burchakni toping. A) 30° B) 90° C) 120° D) 60° 10 / 25 10. Agar a = √5 + 1 va b = √5 − 1 bo‘lsa, 2a² − ab − a² ifodaning qiymatini toping. A) √5 + 6 B) 3√5 + 6 C) 6√5 + 1 D) 6√5 + 2 11 / 25 11. Tenglamalar sistemasi nechta yechimga ega? A) 6 B) 12 C) 8 D) 10 12 / 25 12. (?²+ 4? + 8)² + 3?³ + 14?² + 24? = 0 tenglamaning ildizlari yig’indisini toping. A) -7 B) -5 C) -6 D) -11 13 / 25 13. 80 ni qanday musbat butun songa bo‘lganda, hosil bo‘ladigan qoldiq bo‘linmaning 25%iga teng bo‘ladi? A) 21 B) 11 C) 10 D) 19 14 / 25 14. 100 dan kichik musbat butun sonlar orasida 2 ga ham, 3 ga ham, 7 ga ham bo‘linmaydigan nechta son mavjud? A) 27 B) 28 C) 29 D) 26 15 / 25 15. Hisoblang: 1 + 2 ∙ 2 + 3 ∙ 22 + 4 ∙ 23+. … + 100 ∙ 299 A) B B) A C) D D) C 16 / 25 16. Tenglama nechta yechimga ega? Bunda, x ∈ (1; 47) A) 16 B) 12 C) 14 D) 15 17 / 25 17. 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) √5/2 C) √6/2 D) 1.4 18 / 25 18. Agar ?(?) = ?2021 + 3?2020 + 3?2019 − ?2018 + 1 bo‘lsa, ni toping. A) 1 B) 3 C) 0 D) 2 19 / 25 19. Hisoblang: A) 81/109 B) 172/249 C) 95/243 D) 85/104 20 / 25 20. Soddalashtiring: A) 3sin2x B) 3cosx C) cosx D) 3cos2x 21 / 25 21. Agar ? + 4/√?= 17 bo‘lsa, ? + 4√? ni toping. A) 3 B) 2 C) 1 D) 4 22 / 25 22. Sektor perimetri 28 sm ga teng, uning yuzi esa 49 sm2. Sektor yoyining uzunligini toping. A) 14 sm B) 7 sm C) 12 sm D) 18 sm 23 / 25 23. bo‘lsa, ?² + ?² ni toping. A) 65/21 B) 61/20 C) 20.2 D) 20 24 / 25 24. 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 25 / 25 25. 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 0% Testni qayta ishga tushiring Author: InfoMaster Matematika olimpiada