11-sinf Matematika olimpiada №4 Oktabr 18, 2022Avgust 19, 2024 da chop etilgan InfoMaster tomonidan 11-sinf Matematika olimpiada №4 ga 2 fikr bildirilgan 0 123456789101112131415161718192021222324252627282930 Vaqtingiz tugadi! Tomonidan yaratilgan InfoMaster 11-sinf Matematika olimpiada №4 2022-yil 12-oktyabr: 2022-2023 o'quv yilida tuman bosqichida tushgan savollar! 1 / 30 1. tenglama nechta natural yechimga ega? A) 4 B) 2 C) 3 D) 1 2 / 30 2. y=6sin2x+sin12x funksiyaning hosilasini toping. A) 24sin5xcos7x B) 24sin7xsin5x C) 24cos7xcos5x D) −24sin7xcos5x 3 / 30 3. |x²+2x-8|=3a tenglama a ning qanday qiymatlarida 3 ta haqiqiy yechimga ega bo`ladi. A) (0;3) B) a>3, a=0 C) a=3 D) 1 4 / 30 4. Agar a = √5 + 1 va b = √5 − 1 bo‘lsa, 2a² − ab − a² ifodaning qiymatini toping. A) 3√5 + 6 B) 6√5 + 2 C) 6√5 + 1 D) √5 + 6 5 / 30 5. Tenglama nechta yechimga ega? Bunda, x ∈ (1; 47) A) 16 B) 15 C) 12 D) 14 6 / 30 6. Soddalashtiring: bunda, |?| < 1. A) -2 B) 2a+4 C) 2-2a D) 4-2a 7 / 30 7. a2b5 = 620 tenglikni qanoatlantiruvchi nechta (?; ?) butun sonlar juftligi mavjud? A) 10 B) 12 C) 14 D) 8 8 / 30 8. Doskaga ?1, ?2, ?3, . . . , ?200 sonlari yozilgan. Ma’lumki, ?1 = 3, ?2 = 9. Agar ixtiyoriy n natural son uchun ?n+2 = ?n+1 − ?n tenglik o‘rinli bo‘lsa, ?200 ni toping. A) 6 B) 3 C) 8 D) 9 9 / 30 9. Agar bo‘lsa sin²α ni toping. A) D B) B C) C D) A 10 / 30 10. ∠CAD = 2∠ACD, AC =13a, BD = 5a va AB = CD bo’lsa, 20⋅cos ∠ACD ni toping.(chizmaga qarang!) A) 16 B) 17 C) 19 D) 15 11 / 30 11. un ketma-ketlik quyidagicha berilgan: u1 = 1, un+1 = un + 8n. U holda, u50 −u30 ni toping. A) 5320 B) 6320 C) 6320 D) 6230 12 / 30 12. ?(3) ∙ (? − 2) + ?(? − 1) = 3? bo‘lsa, ?(1) ni toping. A) 3 B) 4 C) 2 D) 6 13 / 30 13. Tengsizliklar sistemasinining butun yechimlari sonini toping. A) 7 B) 6 C) 4 D) 5 14 / 30 14. BC = BE = CD ,∠DAE = 20°, ∠BCD = 60° ,∠ADE = ? (chizmaga qarang) A) 40° B) 20° C) 30° D) 50° 15 / 30 15. Natural son roppa-rosa 2 ta tub bo‘luvchiga, bu sonning kvadrati esa 45 ta turli natural bo‘luvchiga ega. Berilgan sonning kubi eng ko‘pi bilan nechta natural bo‘luvchiga ega bo‘lishi mumkin? A) 81 B) 40 C) 91 D) 41 16 / 30 16. ABC uchburchakda ctgA+ctgB= 3 va AB= 12 bo‘lsa, ABC uchburchak yuzini toping. A) 216 B) 265 C) 123 D) 521 17 / 30 17. bo’lsa, P(−1) ni toping. A) 120 B) 105 C) 115 D) 100 18 / 30 18. Muntazam uchburchak 36 ta yuzi 1 ga teng bo‘lgan kichkina muntazam uchburchaklardan iborat (chizmaga qarang!). ABC uchburchak yuzini toping. A) 10 B) 12 C) 13 D) 11 19 / 30 19. y = x² − 2x + 3 parabolaga y = 3 to‘g‘ri chiziqqa nisbatan simmetrik bo‘lgan parabola tenglamasini tuzing. A) y = -x² − 2x + 3 B) y =-x² + 2x + 3 C) y = x² − 2x - 3 D) y =-x² + 2x - 3 20 / 30 20. Hisoblang: A) C B) B C) D D) A 21 / 30 21. Soddalashtiring: A) −сtg²1° B) -1 C) −сtg1° D) −сtg13° 22 / 30 22. Soatning minut mili 144° ga burilganda, soatning soat mili qanday burchakka burilada? A) 6° B) 9° C) 18° D) 12° 23 / 30 23. ? soniga teskari bo‘lgan son ? ning 9% ini tashkil qiladi. ? ni toping. (?u yerda, ? > 0) A) 13/3 B) 10/3 C) 16/3 D) 8/3 24 / 30 24. Tenglamani yeching: A) ∅ B) 29/462 C) 0 D) 10/21 25 / 30 25. Raqamlari yig‘indisi 10 dan kam bo‘lmagan, raqamlari ko‘paytmasi esa 10 dan katta bo‘lmagan uch xonali sonlar nechta? A) 96 B) 89 C) 106 D) 100 26 / 30 26. Agar ifodaning qiymatini toping. A) 20 B) 0.05 C) 4 D) 0.8 27 / 30 27. Arifmetik progressiyada ?2 = 12, ?7 − ?4 = 9 bo‘lsa, ?19 ni toping. A) 63 B) 56 C) 61 D) 54 28 / 30 28. formula bilan berilgan sonli ketma-ketlikning dastlabki 20 ta hadining o‘rta arifmetigini toping. A) 23/6 B) 25/6 C) 22/3 D) 20/3 29 / 30 29. (3 − cos²x− 2sinx)(lg²y+ 2lgy+ 4) ≤ 3 bo‘lsa, sin²x+ 20y+ 1 ni toping. A) 3 B) 4 C) 2 D) 5 30 / 30 30. ABCD - kvadrat, AC-diagonal. Agar AE=BE+CE ( a + b = c ) bo‘lsa, ∠AEB burchakni toping(chizmaga qarang!). A) 60 B) 45 C) 50 D) 55 0% tomonidan Wordpress Quiz plugin Matematika olimpiada, Tuman 2022-2023 o'quv yili
