11-sinf Matematika olimpiada №4 Oktabr 18, 2022Oktabr 18, 2022 da chop etilgan InfoMaster tomonidan 11-sinf Matematika olimpiada №4 ga fikr bildirilmagan. 2 123456789101112131415161718192021222324252627282930 Vaqtingiz tugadi! 11-sinf Matematika olimpiada №4 2022-yil 12-oktyabr: 2022-2023 o'quv yilida tuman bosqichida tushgan savollar! 1 / 30 1. 1!+2!+3!+.....+10! sonining oxirgi raqamini toping. A) 6 B) 3 C) 7 D) 0 2 / 30 2. Radiusi 6 ga teng bo`lgan uchta aylana o`zaro tashqi urinishidan hosil bo`lgan egri chiziqli uchburchakka ichki chizilgan aylana radiusini toping. A) 2√2−1 B) 1 C) 6-2√3 D) 4√3-6 3 / 30 3. 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) 18 B) 15 C) 20 D) 10 4 / 30 4. Hisoblang: A) 2 B) 0 C) 1.5 D) 1 5 / 30 5. Hisoblang: A) 85/104 B) 81/109 C) 172/249 D) 95/243 6 / 30 6. 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) 91 B) 81 C) 40 D) 41 7 / 30 7. ABCD - kvadrat, AC-diagonal. Agar AE=BE+CE ( a + b = c ) bo‘lsa, ∠AEB burchakni toping(chizmaga qarang!). A) 45 B) 50 C) 60 D) 55 8 / 30 8. Soatning minut mili 144° ga burilganda, soatning soat mili qanday burchakka burilada? A) 6° B) 9° C) 12° D) 18° 9 / 30 9. Soddalashtiring: bunda, |?| < 1. A) -2 B) 2a+4 C) 4-2a D) 2-2a 10 / 30 10. Tengsizliklar sistemasinining butun yechimlari sonini toping. A) 4 B) 7 C) 5 D) 6 11 / 30 11. 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) 6 C) 9 D) 8 12 / 30 12. Tenglamani yeching: A) 10/21 B) 0 C) ∅ D) 29/462 13 / 30 13. 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) 85/6 D) 35/3 14 / 30 14. bo’lsa, P(−1) ni toping. A) 115 B) 100 C) 105 D) 120 15 / 30 15. Uchlari A(2; −3), B(6; −1), C(6; 4) va D(2; 2) nuqtalarda bo‘lgan ABCD to‘rtburchak yuzini toping. A) 18 B) 16 C) 15 D) 20 16 / 30 16. Raqamlari yig‘indisi 10 dan kam bo‘lmagan, raqamlari ko‘paytmasi esa 10 dan katta bo‘lmagan uch xonali sonlar nechta? A) 96 B) 89 C) 106 D) 100 17 / 30 17. Soddalashtiring: A) B B) D C) C D) A 18 / 30 18. BC = BE = CD ,∠DAE = 20°, ∠BCD = 60° ,∠ADE = ? (chizmaga qarang) A) 30° B) 20° C) 50° D) 40° 19 / 30 19. Agar bo‘lsa sin²α ni toping. A) C B) A C) D D) B 20 / 30 20. ?(3) ∙ (? − 2) + ?(? − 1) = 3? bo‘lsa, ?(1) ni toping. A) 2 B) 4 C) 6 D) 3 21 / 30 21. Muntazam uchburchak 36 ta yuzi 1 ga teng bo‘lgan kichkina muntazam uchburchaklardan iborat (chizmaga qarang!). ABC uchburchak yuzini toping. A) 12 B) 10 C) 13 D) 11 22 / 30 22. Hisoblang: A) A B) C C) D D) B 23 / 30 23. To‘g‘ri burchakli uchburchakning bir burchagi 60° ga teng. Bu burchakdan chiqarilgan bissektrisaning uzunligi 2 m. Uchburchakning gipotenuzasi uzunligini toping. A) √5 B) √3 C) 2√3 D) √5 +1 24 / 30 24. formula bilan berilgan sonli ketma-ketlikning dastlabki 20 ta hadining o‘rta arifmetigini toping. A) 23/6 B) 22/3 C) 25/6 D) 20/3 25 / 30 25. ABC uchburchakda ctgA+ctgB= 3 va AB= 12 bo‘lsa, ABC uchburchak yuzini toping. A) 521 B) 123 C) 216 D) 265 26 / 30 26. 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 27 / 30 27. 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) 10 B) 6 C) 8 D) 12 28 / 30 28. Soddalashtiring: A) −сtg²1° B) −сtg1° C) -1 D) −сtg13° 29 / 30 29. ∠CAD = 2∠ACD, AC =13a, BD = 5a va AB = CD bo’lsa, 20⋅cos ∠ACD ni toping.(chizmaga qarang!) A) 17 B) 15 C) 16 D) 19 30 / 30 30. a2b5 = 620 tenglikni qanoatlantiruvchi nechta (?; ?) butun sonlar juftligi mavjud? A) 10 B) 8 C) 14 D) 12 0% Author: InfoMaster Matematika olimpiada