Uy » Online olimpiada » Matematika olimpiada » 11-sinf Matematika olimpiada №4 Matematika olimpiadaTuman 2022-2023 o'quv yili 11-sinf Matematika olimpiada №4 InfoMaster Avgust 19, 2024 82 Ko'rishlar 2 izohlar SaqlashSaqlanganOlib tashlandi 0 4 123456789101112131415161718192021222324252627282930 Vaqtingiz tugadi! 11-sinf Matematika olimpiada №4 2022-yil 12-oktyabr: 2022-2023 o'quv yilida tuman bosqichida tushgan savollar! 1 / 30 1. Sonlarni kamayish tartibida joylashtiring: A) b>c>a B) c>b>a C) c>a>b D) a>b>c 2 / 30 2. y=6sin2x+sin12x funksiyaning hosilasini toping. A) 24cos7xcos5x B) 24sin5xcos7x C) −24sin7xcos5x D) 24sin7xsin5x 3 / 30 3. Tenglamani yeching: A) πk; π−arcctg4+πk; k∈Z B) πk; −arcctg4+πk; k∈Z C) π −arcctg4+πk; k∈Z D) arccos0,8+2πk; k∈Z 4 / 30 4. 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) 53 B) 65 C) 73 D) 55 5 / 30 5. Tenglama nechta yechimga ega? Bunda, x ∈ (1; 47) A) 12 B) 16 C) 14 D) 15 6 / 30 6. 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) 18 C) 15 D) 16 7 / 30 7. (3 − cos²x− 2sinx)(lg²y+ 2lgy+ 4) ≤ 3 bo‘lsa, sin²x+ 20y+ 1 ni toping. A) 2 B) 4 C) 3 D) 5 8 / 30 8. ABCD - kvadrat, AC-diagonal. Agar AE=BE+CE ( a + b = c ) bo‘lsa, ∠AEB burchakni toping(chizmaga qarang!). A) 55 B) 50 C) 45 D) 60 9 / 30 9. a2b5 = 620 tenglikni qanoatlantiruvchi nechta (?; ?) butun sonlar juftligi mavjud? A) 12 B) 14 C) 10 D) 8 10 / 30 10. Soddalashtiring: A) −сtg²1° B) -1 C) −сtg13° D) −сtg1° 11 / 30 11. Agar ifodaning qiymatini toping. A) 20 B) 0.05 C) 0.8 D) 4 12 / 30 12. Muntazam uchburchak 36 ta yuzi 1 ga teng bo‘lgan kichkina muntazam uchburchaklardan iborat (chizmaga qarang!). ABC uchburchak yuzini toping. A) 13 B) 11 C) 10 D) 12 13 / 30 13. 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) 8 B) 9 C) 6 D) 3 14 / 30 14. Hisoblang: A) D B) B C) A D) C 15 / 30 15. Soddalashtiring: A) A B) C C) B D) D 16 / 30 16. Arifmetik progressiyada ?2 = 12, ?7 − ?4 = 9 bo‘lsa, ?19 ni toping. A) 54 B) 56 C) 61 D) 63 17 / 30 17. Soddalashtiring: bunda, |?| < 1. A) -2 B) 4-2a C) 2a+4 D) 2-2a 18 / 30 18. 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 19 / 30 19. 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) 41 B) 91 C) 81 D) 40 20 / 30 20. To‘g‘ri burchakli uchburchakning bir burchagi 60° ga teng. Bu burchakdan chiqarilgan bissektrisaning uzunligi 2 m. Uchburchakning gipotenuzasi uzunligini toping. A) √5 +1 B) √5 C) 2√3 D) √3 21 / 30 21. ABC uchburchakda ctgA+ctgB= 3 va AB= 12 bo‘lsa, ABC uchburchak yuzini toping. A) 265 B) 521 C) 216 D) 123 22 / 30 22. ? 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 23 / 30 23. Soatning minut mili 144° ga burilganda, soatning soat mili qanday burchakka burilada? A) 9° B) 6° C) 18° D) 12° 24 / 30 24. Nargizada 2 ta olma va 3 ta nok bor. U 5 kun ketma-ket har kuni singliga bittadan meva beradi. Bu ishni necha usul bilan amalga oshirish mumkin? A) 6 B) 12 C) 8 D) 10 25 / 30 25. Tenglamani yeching: A) 29/462 B) 10/21 C) ∅ D) 0 26 / 30 26. ?(3) ∙ (? − 2) + ?(? − 1) = 3? bo‘lsa, ?(1) ni toping. A) 6 B) 3 C) 2 D) 4 27 / 30 27. Agar bo‘lsa sin²α ni toping. A) C B) A C) D D) B 28 / 30 28. Tengsizliklar sistemasinining butun yechimlari sonini toping. A) 7 B) 5 C) 6 D) 4 29 / 30 29. Raqamlari yig‘indisi 10 dan kam bo‘lmagan, raqamlari ko‘paytmasi esa 10 dan katta bo‘lmagan uch xonali sonlar nechta? A) 96 B) 106 C) 100 D) 89 30 / 30 30. BC = BE = CD ,∠DAE = 20°, ∠BCD = 60° ,∠ADE = ? (chizmaga qarang) A) 40° B) 30° C) 50° D) 20° 0% Tomonidan Wordpress Quiz plugin Author: InfoMaster Foydali bo'lsa mamnunmiz