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. 750 ning oxirgi ikkita raqamini toping. A) 49 B) 35 C) 51 D) 25 2 / 30 2. 3cos2x-3 sin2x=0 trigonometrik tenglamani yeching. A) π/12+πk; k∈Z B) π/6+πk; k∈Z C) π/12+πk/2; k∈Z) D) π/12+2πk; k∈Z 3 / 30 3. ifodani soddalshtiring A) 2cosα B) cosα C) 2sinα D) 1 4 / 30 4. 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) 211/47 B) 177/48 C) 175/48 D) 3 5 / 30 5. 80 ni qanday musbat butun songa bo‘lganda, hosil bo‘ladigan qoldiq bo‘linmaning 25%iga teng bo‘ladi? A) 10 B) 11 C) 21 D) 19 6 / 30 6. ∠CAD = 2∠ACD, AC =13a, BD = 5a va AB = CD bo’lsa, 20⋅cos ∠ACD ni toping.(chizmaga qarang!) A) 16 B) 15 C) 19 D) 17 7 / 30 7. Raqamlari yig‘indisi 10 dan kam bo‘lmagan, raqamlari ko‘paytmasi esa 10 dan katta bo‘lmagan uch xonali sonlar nechta? A) 100 B) 106 C) 96 D) 89 8 / 30 8. formula bilan berilgan sonli ketma-ketlikning dastlabki 20 ta hadining o‘rta arifmetigini toping. A) 22/3 B) 23/6 C) 25/6 D) 20/3 9 / 30 9. bo’lsa, P(−1) ni toping. A) 120 B) 100 C) 105 D) 115 10 / 30 10. To‘g‘ri burchakli uchburchakning bir burchagi 60° ga teng. Bu burchakdan chiqarilgan bissektrisaning uzunligi 2 m. Uchburchakning gipotenuzasi uzunligini toping. A) 2√3 B) √5 +1 C) √3 D) √5 11 / 30 11. Soatning minut mili 144° ga burilganda, soatning soat mili qanday burchakka burilada? A) 9° B) 18° C) 12° D) 6° 12 / 30 12. Agar ifodaning qiymatini toping. A) 0.05 B) 0.8 C) 20 D) 4 13 / 30 13. Tenglamani yeching: A) 10/21 B) 0 C) 29/462 D) ∅ 14 / 30 14. Soddalashtiring: A) −сtg13° B) −сtg²1° C) -1 D) −сtg1° 15 / 30 15. Soddalashtiring: bunda, |?| < 1. A) 2-2a B) 4-2a C) 2a+4 D) -2 16 / 30 16. 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) 3 B) 9 C) 6 D) 8 17 / 30 17. ?(3) ∙ (? − 2) + ?(? − 1) = 3? bo‘lsa, ?(1) ni toping. A) 4 B) 3 C) 2 D) 6 18 / 30 18. BC = BE = CD ,∠DAE = 20°, ∠BCD = 60° ,∠ADE = ? (chizmaga qarang) A) 40° B) 30° C) 50° D) 20° 19 / 30 19. Tengsizliklar sistemasinining butun yechimlari sonini toping. A) 6 B) 7 C) 4 D) 5 20 / 30 20. ABCD - kvadrat, AC-diagonal. Agar AE=BE+CE ( a + b = c ) bo‘lsa, ∠AEB burchakni toping(chizmaga qarang!). A) 60 B) 55 C) 45 D) 50 21 / 30 21. un ketma-ketlik quyidagicha berilgan: u1 = 1, un+1 = un + 8n. U holda, u50 −u30 ni toping. A) 5320 B) 6320 C) 6230 D) 6320 22 / 30 22. Agar bo‘lsa sin²α ni toping. A) B B) A C) C D) D 23 / 30 23. Arifmetik progressiyada ?2 = 12, ?7 − ?4 = 9 bo‘lsa, ?19 ni toping. A) 56 B) 54 C) 63 D) 61 24 / 30 24. Uchlari A(2; −3), B(6; −1), C(6; 4) va D(2; 2) nuqtalarda bo‘lgan ABCD to‘rtburchak yuzini toping. A) 20 B) 16 C) 18 D) 15 25 / 30 25. ? soniga teskari bo‘lgan son ? ning 9% ini tashkil qiladi. ? ni toping. (?u yerda, ? > 0) A) 8/3 B) 13/3 C) 16/3 D) 10/3 26 / 30 26. (3 − cos²x− 2sinx)(lg²y+ 2lgy+ 4) ≤ 3 bo‘lsa, sin²x+ 20y+ 1 ni toping. A) 3 B) 2 C) 5 D) 4 27 / 30 27. ABC uchburchakda ctgA+ctgB= 3 va AB= 12 bo‘lsa, ABC uchburchak yuzini toping. A) 216 B) 265 C) 521 D) 123 28 / 30 28. Muntazam uchburchak 36 ta yuzi 1 ga teng bo‘lgan kichkina muntazam uchburchaklardan iborat (chizmaga qarang!). ABC uchburchak yuzini toping. A) 10 B) 11 C) 12 D) 13 29 / 30 29. 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) 41 D) 91 30 / 30 30. O‘tkir burchakli uchburchakning ikki tomon uzunliklari ayirmasi 8, bu tomonlarning uchinchi tomondagi proyeksiyalari mos ravishda 8 va 20 ga teng. Berilgan uchburchakka tashqi chizilgan aylana radiusini toping. A) 83/6 B) 37/3 C) 35/3 D) 85/6 0% tomonidan Wordpress Quiz plugin Matematika olimpiada, Tuman 2022-2023 o'quv yili
