11-sinf Matematika olimpiada №3 Oktabr 4, 2022Avgust 19, 2024 da chop etilgan InfoMaster tomonidan 11-sinf Matematika olimpiada №3 ga 9 fikr bildirilgan 0 12345678910111213141516171819202122232425 Vaqtingiz tugadi! Tomonidan yaratilgan InfoMaster 11-sinf Matematika olimpiada №3 2021-2022 o'quv yilida viloyat bosqichida tushgan savollar 1 / 25 1. 750 ning oxirgi ikkita raqamini toping. A) 49 B) 25 C) 35 D) 51 2 / 25 2. GH kesmani O nuqta, G nuqtadan boshlab hisoblaganda, 5 : 7 kabi, P nuqtaesa 5:11 kabi nisbatda bo’ladi. O va P nuqtalar orasidagi masofa 30 sm bo’lsa, GH kesmaning uzunligini toping. A) 234 B) 288 C) 72 D) 18 3 / 25 3. Aylananing ОА, ОВ, ОС radiuslari o‘tkazilgan. Agar bo‘lsa, АОВ burchakni toping. A) 90° B) 120° C) 30° D) 60° 4 / 25 4. ABC uchburchakning AC tomonida shunday D nuqta olinganki, bunda ∠ABC=∠BDC, 5AB=4BD. Agar BC=10 bo‘lsa, ACni toping. A) 8 B) 10 C) 12 D) 6 5 / 25 5. To‘g‘ri burchakli uchburchakka ichki va tashqi chizilgan aylana radiuslari nisbati 2 : 5 bo‘lsa, uchburchakning katta o‘tkir burchagining kosinusini toping. A) 0.5 B) 0.6 C) 0.8 D) 0.2 6 / 25 6. Hisoblang: 1 + 2 ∙ 2 + 3 ∙ 22 + 4 ∙ 23+. … + 100 ∙ 299 A) A B) B C) D D) C 7 / 25 7. Agar ? + 4/√?= 17 bo‘lsa, ? + 4√? ni toping. A) 3 B) 2 C) 4 D) 1 8 / 25 8. (?²+ 4? + 8)² + 3?³ + 14?² + 24? = 0 tenglamaning ildizlari yig’indisini toping. A) -11 B) -5 C) -7 D) -6 9 / 25 9. 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) 177/48 C) 3 D) 211/47 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) 65 B) 73 C) 55 D) 53 11 / 25 11. Funksiyaning eng kichik qiymatini toping. ?(?) = (2? + 6)5 − 4(2? + 6)4, bunda |? + 3| ≤ 2. A) -2⁹ B) -4⁵ C) -4⁴ D) -2¹¹ 12 / 25 12. Agar ?(?) = ?2021 + 3?2020 + 3?2019 − ?2018 + 1 bo‘lsa, ni toping. A) 1 B) 2 C) 0 D) 3 13 / 25 13. 80 ni qanday musbat butun songa bo‘lganda, hosil bo‘ladigan qoldiq bo‘linmaning 25%iga teng bo‘ladi? A) 11 B) 19 C) 10 D) 21 14 / 25 14. bo‘lsa, ?² + ?² ni toping. A) 61/20 B) 20.2 C) 20 D) 65/21 15 / 25 15. Uchburchakning tomonlari 10, 24 va 26. Aylananing markazi uchburchakning katta tomonida yotadi va ikki kichik tomonlari bu aylanaga urinadi. Aylana radiusini toping. A) 60/7 B) 260/17 C) 20/3 D) 120/17 16 / 25 16. Tenglamalar sistemasi nechta yechimga ega? A) 8 B) 10 C) 6 D) 12 17 / 25 17. АВС uchburchak ∠C=60° burchagining bissektrisasi 5√3 ga teng. Agar АС : ВС = 5 :2 bo‘lsa, ВС ni toping. A) B B) A C) C D) D 18 / 25 18. Aylanaga АВС uchburchak ichki chizilgan. Uchburchakning СС1medianasining davomi aylanani ? nuqtada kesib o‘tadi. ni toping. A) 4 B) 1 C) √5 D) 2 19 / 25 19. 100 dan kichik musbat butun sonlar orasida 2 ga ham, 3 ga ham, 7 ga ham bo‘linmaydigan nechta son mavjud? A) 27 B) 26 C) 29 D) 28 20 / 25 20. Quyidagi sonlar orasidan musbat sonni aniqlang. A) A B) B C) C D) D 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) 4 B) 3 C) 5 D) 6 22 / 25 22. Hisoblang: A) 1.5 B) 1 C) 0 D) 2 23 / 25 23. Sektor perimetri 28 sm ga teng, uning yuzi esa 49 sm2. Sektor yoyining uzunligini toping. A) 12 sm B) 18 sm C) 7 sm D) 14 sm 24 / 25 24. Agar a = √5 + 1 va b = √5 − 1 bo‘lsa, 2a² − ab − a² ifodaning qiymatini toping. A) 3√5 + 6 B) √5 + 6 C) 6√5 + 1 D) 6√5 + 2 25 / 25 25. Soddalashtiring: A) 2sinα B) cosα C) 2 D) 1 0% Testni qayta ishga tushiring Author: InfoMaster Matematika olimpiada, Viloyat 2021-2022 o'quv yili
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