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 55 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. 1!+2!+3!+.....+10! sonining oxirgi raqamini toping. A) 7 B) 3 C) 0 D) 6 2 / 25 2. Tengsizlikni yeching. A) (2/3;2) B) (5/3;2) C) (1/2;∞) D) (4/3;3) 3 / 25 3. Agar ? + 4/√?= 17 bo‘lsa, ? + 4√? ni toping. A) 4 B) 1 C) 2 D) 3 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) 60/7 B) 20/3 C) 120/17 D) 260/17 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) 0.2 C) 0.6 D) 0.8 6 / 25 6. АВС uchburchak ∠C=60° burchagining bissektrisasi 5√3 ga teng. Agar АС : ВС = 5 :2 bo‘lsa, ВС ni toping. A) A B) B C) D D) C 7 / 25 7. bo‘lsa, ?² + ?² ni toping. A) 20 B) 61/20 C) 65/21 D) 20.2 8 / 25 8. Soddalashtiring: A) 1 B) cosα C) 2sinα D) 2 9 / 25 9. Tenglamalar sistemasi nechta yechimga ega? A) 8 B) 10 C) 12 D) 6 10 / 25 10. Hisoblang: (1 − tg5°)(1 − tg20°)2 + 2(2tg20° + tg5°) A) 4 B) 2 C) 1 D) 3 11 / 25 11. 80 ni qanday musbat butun songa bo‘lganda, hosil bo‘ladigan qoldiq bo‘linmaning 25%iga teng bo‘ladi? A) 19 B) 11 C) 10 D) 21 12 / 25 12. 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 13 / 25 13. Quyidagi sonlar orasidan musbat sonni aniqlang. A) A B) C C) B D) D 14 / 25 14. Soddalashtiring: A) II B) I C) III D) IV 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. Hisoblang: A) 85/104 B) 81/109 C) 95/243 D) 172/249 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) 1.4 D) √6/2 18 / 25 18. Hisoblang: A) 1 B) 0 C) 2 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) 12 B) 10 C) 6 D) 8 20 / 25 20. Funksiyaning eng kichik qiymatini toping. ?(?) = (2? + 6)5 − 4(2? + 6)4, bunda |? + 3| ≤ 2. A) -4⁵ B) -2¹¹ C) -2⁹ D) -4⁴ 21 / 25 21. 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) 443 B) 433 C) 444 D) 423 22 / 25 22. Soddalashtiring: A) cosx B) 3cos2x C) 3sin2x D) 3cosx 23 / 25 23. 100 dan kichik musbat butun sonlar orasida 2 ga ham, 3 ga ham, 7 ga ham bo‘linmaydigan nechta son mavjud? A) 28 B) 26 C) 29 D) 27 24 / 25 24. Agar ?(?) = ?2021 + 3?2020 + 3?2019 − ?2018 + 1 bo‘lsa, ni toping. A) 3 B) 2 C) 1 D) 0 25 / 25 25. Aylananing ОА, ОВ, ОС radiuslari o‘tkazilgan. Agar bo‘lsa, АОВ burchakni toping. A) 30° B) 90° C) 120° D) 60° 0% Testni qayta ishga tushiring Author: InfoMaster Foydali bo'lsa mamnunmiz
