11-sinf Matematika olimpiada №4 Oktabr 18, 2022Oktabr 18, 2022 da chop etilgan InfoMaster tomonidan 11-sinf Matematika olimpiada №4 ga fikr bildirilmagan. 1 123456789101112131415161718192021222324252627282930 Vaqtingiz tugadi! 11-sinf Matematika olimpiada №4 2022-yil 12-oktyabr: 2022-2023 o'quv yilida tuman bosqichida tushgan savollar! 1 / 30 1. tenglama nechta ildizga ega? A) 4 B) 1 C) 2 D) 3 2 / 30 2. Poyezd 3 minutda 7 kilometrmasofani , motosikl 5 minutda 7 kilometrmasofanibosibo`tdi. Mototsikltezligipoyezdtezliginingnecha % initashkilqiladi? A) 70% B) 71% C) 61% D) 60% 3 / 30 3. Ifodani soddalashtiring: A) 0 B) 1−√(a-1) C) 1+√(a+1) D) √(a²-1) 4 / 30 4. Tenglama nechta yechimga ega? Bunda, x ∈ (1; 47) A) 12 B) 14 C) 16 D) 15 5 / 30 5. (?²+ 4? + 8)² + 3?³ + 14?² + 24? = 0 tenglamaning ildizlari yig’indisini toping. A) -6 B) -11 C) -7 D) -5 6 / 30 6. Tenglamani yeching: A) 10/21 B) 29/462 C) ∅ D) 0 7 / 30 7. ∠CAD = 2∠ACD, AC =13a, BD = 5a va AB = CD bo’lsa, 20⋅cos ∠ACD ni toping.(chizmaga qarang!) A) 19 B) 16 C) 15 D) 17 8 / 30 8. Hisoblang: A) A B) B C) D D) C 9 / 30 9. ABCD - kvadrat, AC-diagonal. Agar AE=BE+CE ( a + b = c ) bo‘lsa, ∠AEB burchakni toping(chizmaga qarang!). A) 55 B) 60 C) 50 D) 45 10 / 30 10. a2b5 = 620 tenglikni qanoatlantiruvchi nechta (?; ?) butun sonlar juftligi mavjud? A) 8 B) 12 C) 10 D) 14 11 / 30 11. Soddalashtiring: bunda, |?| < 1. A) -2 B) 4-2a C) 2a+4 D) 2-2a 12 / 30 12. ?(3) ∙ (? − 2) + ?(? − 1) = 3? bo‘lsa, ?(1) ni toping. A) 6 B) 2 C) 4 D) 3 13 / 30 13. 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) 15 C) 16 D) 18 14 / 30 14. Agar bo‘lsa sin²α ni toping. A) C B) B C) A D) D 15 / 30 15. Tengsizliklar sistemasinining butun yechimlari sonini toping. A) 6 B) 5 C) 7 D) 4 16 / 30 16. To‘g‘ri burchakli uchburchakning bir burchagi 60° ga teng. Bu burchakdan chiqarilgan bissektrisaning uzunligi 2 m. Uchburchakning gipotenuzasi uzunligini toping. A) √3 B) √5 +1 C) 2√3 D) √5 17 / 30 17. (3 − cos²x− 2sinx)(lg²y+ 2lgy+ 4) ≤ 3 bo‘lsa, sin²x+ 20y+ 1 ni toping. A) 4 B) 5 C) 3 D) 2 18 / 30 18. bo’lsa, P(−1) ni toping. A) 100 B) 120 C) 115 D) 105 19 / 30 19. Soddalashtiring: A) -1 B) −сtg²1° C) −сtg1° D) −сtg13° 20 / 30 20. Raqamlari yig‘indisi 10 dan kam bo‘lmagan, raqamlari ko‘paytmasi esa 10 dan katta bo‘lmagan uch xonali sonlar nechta? A) 100 B) 96 C) 89 D) 106 21 / 30 21. Soddalashtiring: A) D B) C C) A D) B 22 / 30 22. 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) 37/3 B) 83/6 C) 35/3 D) 85/6 23 / 30 23. 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) 3 C) 9 D) 6 24 / 30 24. ABC uchburchakda ctgA+ctgB= 3 va AB= 12 bo‘lsa, ABC uchburchak yuzini toping. A) 265 B) 123 C) 521 D) 216 25 / 30 25. un ketma-ketlik quyidagicha berilgan: u1 = 1, un+1 = un + 8n. U holda, u50 −u30 ni toping. A) 5320 B) 6230 C) 6320 D) 6320 26 / 30 26. Arifmetik progressiyada ?2 = 12, ?7 − ?4 = 9 bo‘lsa, ?19 ni toping. A) 54 B) 61 C) 63 D) 56 27 / 30 27. 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 28 / 30 28. ? = ?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 29 / 30 29. BC = BE = CD ,∠DAE = 20°, ∠BCD = 60° ,∠ADE = ? (chizmaga qarang) A) 20° B) 50° C) 30° D) 40° 30 / 30 30. Soatning minut mili 144° ga burilganda, soatning soat mili qanday burchakka burilada? A) 12° B) 18° C) 9° D) 6° 0% Author: InfoMaster Matematika olimpiada