11-sinf Matematika olimpiada №3 Oktabr 4, 2022Avgust 19, 2024 da chop etilgan InfoMaster tomonidan 11-sinf Matematika olimpiada №3 ga 3 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. va a,b>0 bo‘lsa, ifodaning eng kichik qiymatini toping. A) 1 B) 4 C) 3 D) 2 2 / 25 2. Asosi ga teng bo`lgan muntazam to`rtburchakli piramidaning uchidan o`tkazilgan kesma asos tomonini 2:4 nisbatda bo`ladi va asos tekisligi bilan 60o li burchakhosilqiladi. Piramidahajmini toping. A) √30 B) 12√30 C) 6 D) √10 3 / 25 3. Agar a = √5 + 1 va b = √5 − 1 bo‘lsa, 2a² − ab − a² ifodaning qiymatini toping. A) √5 + 6 B) 6√5 + 2 C) 3√5 + 6 D) 6√5 + 1 4 / 25 4. 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 5 / 25 5. Tenglama nechta yechimga ega? Bunda, x ∈ (1; 47) A) 15 B) 12 C) 16 D) 14 6 / 25 6. Soddalashtiring: A) II B) I C) IV D) III 7 / 25 7. Funksiyaning eng kichik qiymatini toping. ?(?) = (2? + 6)5 − 4(2? + 6)4, bunda |? + 3| ≤ 2. A) -4⁵ B) -2⁹ C) -2¹¹ D) -4⁴ 8 / 25 8. Sektor perimetri 28 sm ga teng, uning yuzi esa 49 sm2. Sektor yoyining uzunligini toping. A) 14 sm B) 7 sm C) 18 sm D) 12 sm 9 / 25 9. Agar ?(?) = ?2021 + 3?2020 + 3?2019 − ?2018 + 1 bo‘lsa, ni toping. A) 0 B) 1 C) 3 D) 2 10 / 25 10. 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) 444 B) 423 C) 433 D) 443 11 / 25 11. Hisoblang: A) 1.5 B) 1 C) 2 D) 0 12 / 25 12. 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) 26 D) 29 13 / 25 13. Soddalashtiring: A) 1 B) cosα C) 2sinα D) 2 14 / 25 14. bo‘lsa, ?² + ?² ni toping. A) 61/20 B) 20 C) 20.2 D) 65/21 15 / 25 15. 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) √6/2 B) 1.4 C) 4/3 D) √5/2 16 / 25 16. 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) 6 C) 4 D) 3 17 / 25 17. Hisoblang: (1 − tg5°)(1 − tg20°)2 + 2(2tg20° + tg5°) A) 3 B) 4 C) 2 D) 1 18 / 25 18. 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) D D) C 19 / 25 19. 80 ni qanday musbat butun songa bo‘lganda, hosil bo‘ladigan qoldiq bo‘linmaning 25%iga teng bo‘ladi? A) 10 B) 19 C) 11 D) 21 20 / 25 20. (?²+ 4? + 8)² + 3?³ + 14?² + 24? = 0 tenglamaning ildizlari yig’indisini toping. A) -11 B) -5 C) -7 D) -6 21 / 25 21. Agar ? + 4/√?= 17 bo‘lsa, ? + 4√? ni toping. A) 2 B) 1 C) 3 D) 4 22 / 25 22. Quyidagi sonlar orasidan musbat sonni aniqlang. A) D B) A C) C D) B 23 / 25 23. ABC uchburchakning AC tomonida shunday D nuqta olinganki, bunda ∠ABC=∠BDC, 5AB=4BD. Agar BC=10 bo‘lsa, ACni toping. A) 12 B) 10 C) 6 D) 8 24 / 25 24. 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) 0.2 C) 0.8 D) 0.6 25 / 25 25. Soddalashtiring: A) 3sin2x B) 3cosx C) cosx D) 3cos2x 0% Testni qayta ishga tushiring tomonidan Wordpress Quiz plugin Matematika olimpiada, Viloyat 2021-2022 o'quv yili
