11-sinf Matematika olimpiada №4 Oktabr 18, 2022Avgust 19, 2024 da chop etilgan InfoMaster tomonidan 11-sinf Matematika olimpiada №4 ga 3 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. ABC uchburchakka aylana tashqi chizilgan. Uchburchakning AM medianasi aylana bilan K nuqtada kesishguncha davom ettirilgan. Agar AM=18,MK=8,BK=10 bo‘lsa, AC tomonini toping. A) 16 B) 12 C) 14 D) 15 2 / 30 2. Bir savdogar 1 mеtrini 1200 tiyindan olgan matosini yuvib, kuritgandan so`ng 1800 tiyindan sotyapti. Mato yuvilib kuritilganidan so`ng 20 foizi qisqardi. Bularga ko`ra savdogar nеcha foiz foyda ko`radi? A) 10 B) 18 C) 15 D) 20 3 / 30 3. Agar 2a =27, 3c=16 bo’lsa a ∙ ? ning qiymatini toping. A) 10 B) 13 C) 12 D) 11 4 / 30 4. bo‘lsa, ?² + ?² ni toping. A) 61/20 B) 20.2 C) 65/21 D) 20 5 / 30 5. Agar a = √5 + 1 va b = √5 − 1 bo‘lsa, 2a² − ab − a² ifodaning qiymatini toping. A) 6√5 + 1 B) 3√5 + 6 C) 6√5 + 2 D) √5 + 6 6 / 30 6. Soddalashtiring: A) −сtg1° B) -1 C) −сtg²1° D) −сtg13° 7 / 30 7. 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) 9 B) 3 C) 8 D) 6 8 / 30 8. 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 9 / 30 9. bo’lsa, P(−1) ni toping. A) 120 B) 100 C) 115 D) 105 10 / 30 10. a2b5 = 620 tenglikni qanoatlantiruvchi nechta (?; ?) butun sonlar juftligi mavjud? A) 12 B) 14 C) 8 D) 10 11 / 30 11. ABC uchburchakda ctgA+ctgB= 3 va AB= 12 bo‘lsa, ABC uchburchak yuzini toping. A) 265 B) 521 C) 123 D) 216 12 / 30 12. (3 − cos²x− 2sinx)(lg²y+ 2lgy+ 4) ≤ 3 bo‘lsa, sin²x+ 20y+ 1 ni toping. A) 2 B) 4 C) 3 D) 5 13 / 30 13. Soddalashtiring: bunda, |?| < 1. A) 4-2a B) 2-2a C) 2a+4 D) -2 14 / 30 14. Soatning minut mili 144° ga burilganda, soatning soat mili qanday burchakka burilada? A) 12° B) 9° C) 18° D) 6° 15 / 30 15. 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 16 / 30 16. 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 17 / 30 17. BC = BE = CD ,∠DAE = 20°, ∠BCD = 60° ,∠ADE = ? (chizmaga qarang) A) 20° B) 40° C) 30° D) 50° 18 / 30 18. ABCD - kvadrat, AC-diagonal. Agar AE=BE+CE ( a + b = c ) bo‘lsa, ∠AEB burchakni toping(chizmaga qarang!). A) 50 B) 60 C) 45 D) 55 19 / 30 19. Soddalashtiring: A) A B) C C) B D) D 20 / 30 20. Arifmetik progressiyada ?2 = 12, ?7 − ?4 = 9 bo‘lsa, ?19 ni toping. A) 56 B) 63 C) 54 D) 61 21 / 30 21. 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) √5 D) 2√3 22 / 30 22. Tenglamani yeching: A) 0 B) 29/462 C) 10/21 D) ∅ 23 / 30 23. Agar ifodaning qiymatini toping. A) 20 B) 4 C) 0.05 D) 0.8 24 / 30 24. ?(3) ∙ (? − 2) + ?(? − 1) = 3? bo‘lsa, ?(1) ni toping. A) 4 B) 2 C) 3 D) 6 25 / 30 25. 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) 10 C) 12 D) 8 26 / 30 26. 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) 40 B) 81 C) 91 D) 41 27 / 30 27. 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) 35/3 C) 83/6 D) 85/6 28 / 30 28. Hisoblang: A) A B) D C) B D) C 29 / 30 29. Uchlari A(2; −3), B(6; −1), C(6; 4) va D(2; 2) nuqtalarda bo‘lgan ABCD to‘rtburchak yuzini toping. A) 15 B) 16 C) 18 D) 20 30 / 30 30. Tengsizliklar sistemasinining butun yechimlari sonini toping. A) 6 B) 7 C) 4 D) 5 0% tomonidan Wordpress Quiz plugin Matematika olimpiada, Tuman 2022-2023 o'quv yili
