11-sinf Matematika olimpiada №4 Oktabr 18, 2022Avgust 19, 2024 da chop etilgan InfoMaster tomonidan 11-sinf Matematika olimpiada №4 ga 5 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. funksiyaning qiymatlar to‘plamini toping. A) [-1;3] B) [-2;2] C) [1;3] D) [1;4] 2 / 30 2. Poyezd 3 minutda 7 kilometrmasofani , motosikl 5 minutda 7 kilometrmasofanibosibo`tdi. Mototsikltezligipoyezdtezliginingnecha % initashkilqiladi? A) 71% B) 61% C) 70% D) 60% 3 / 30 3. ni hisoblang. A) -13 B) -12 C) 13 D) 12 4 / 30 4. (?²+ 4? + 8)² + 3?³ + 14?² + 24? = 0 tenglamaning ildizlari yig’indisini toping. A) -7 B) -11 C) -6 D) -5 5 / 30 5. 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) √5/2 B) 4/3 C) √6/2 D) 1.4 6 / 30 6. Tengsizliklar sistemasinining butun yechimlari sonini toping. A) 5 B) 7 C) 4 D) 6 7 / 30 7. BC = BE = CD ,∠DAE = 20°, ∠BCD = 60° ,∠ADE = ? (chizmaga qarang) A) 50° B) 20° C) 40° D) 30° 8 / 30 8. 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) 85/6 B) 35/3 C) 37/3 D) 83/6 9 / 30 9. Tenglamani yeching: A) 29/462 B) 10/21 C) 0 D) ∅ 10 / 30 10. ? = ?² − 2? + 3 parabolaga ? = 3 to‘g‘ri chiziqqa nisbatan simmetrik bo‘lgan parabola tenglamasini tuzing. A) ? = ?² − 2? - 3 B) ? = -?² − 2? + 3 C) ? =-?² + 2? - 3 D) ? =-?² + 2? + 3 11 / 30 11. Agar bo‘lsa sin²α ni toping. A) A B) C C) D D) B 12 / 30 12. Uchlari A(2; −3), B(6; −1), C(6; 4) va D(2; 2) nuqtalarda bo‘lgan ABCD to‘rtburchak yuzini toping. A) 16 B) 18 C) 15 D) 20 13 / 30 13. 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 14 / 30 14. un ketma-ketlik quyidagicha berilgan: u1 = 1, un+1 = un + 8n. U holda, u50 −u30 ni toping. A) 6320 B) 5320 C) 6230 D) 6320 15 / 30 15. 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) 89 D) 96 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) 8 B) 9 C) 3 D) 6 17 / 30 17. (3 − cos²x− 2sinx)(lg²y+ 2lgy+ 4) ≤ 3 bo‘lsa, sin²x+ 20y+ 1 ni toping. A) 4 B) 5 C) 2 D) 3 18 / 30 18. formula bilan berilgan sonli ketma-ketlikning dastlabki 20 ta hadining o‘rta arifmetigini toping. A) 22/3 B) 20/3 C) 25/6 D) 23/6 19 / 30 19. Soddalashtiring: A) -1 B) −сtg13° C) −сtg1° D) −сtg²1° 20 / 30 20. 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 21 / 30 21. Agar ifodaning qiymatini toping. A) 4 B) 20 C) 0.8 D) 0.05 22 / 30 22. Arifmetik progressiyada ?2 = 12, ?7 − ?4 = 9 bo‘lsa, ?19 ni toping. A) 54 B) 61 C) 63 D) 56 23 / 30 23. ABC uchburchakda ctgA+ctgB= 3 va AB= 12 bo‘lsa, ABC uchburchak yuzini toping. A) 216 B) 265 C) 521 D) 123 24 / 30 24. ? soniga teskari bo‘lgan son ? ning 9% ini tashkil qiladi. ? ni toping. (?u yerda, ? > 0) A) 8/3 B) 13/3 C) 10/3 D) 16/3 25 / 30 25. ABCD - kvadrat, AC-diagonal. Agar AE=BE+CE ( a + b = c ) bo‘lsa, ∠AEB burchakni toping(chizmaga qarang!). A) 45 B) 60 C) 55 D) 50 26 / 30 26. ∠CAD = 2∠ACD, AC =13a, BD = 5a va AB = CD bo’lsa, 20⋅cos ∠ACD ni toping.(chizmaga qarang!) A) 17 B) 19 C) 16 D) 15 27 / 30 27. Soatning minut mili 144° ga burilganda, soatning soat mili qanday burchakka burilada? A) 9° B) 12° C) 6° D) 18° 28 / 30 28. Soddalashtiring: bunda, |?| < 1. A) 2a+4 B) 4-2a C) 2-2a D) -2 29 / 30 29. a2b5 = 620 tenglikni qanoatlantiruvchi nechta (?; ?) butun sonlar juftligi mavjud? A) 8 B) 12 C) 10 D) 14 30 / 30 30. bo’lsa, P(−1) ni toping. A) 120 B) 115 C) 105 D) 100 0% Author: InfoMaster Matematika olimpiada, Tuman 2022-2023 o'quv yili
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