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 14 Ko'rishlar 2 izohlar SaqlashSaqlanganOlib tashlandi 0 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. Agar va bo‘lsa, ni toping. A) 31 B) 25 C) 11 D) 39 2 / 30 2. ABCD tetraedrning D uchidagi barcha yassi burchaklari to`g`ri. Shu tetraedrda kub shunday ichki chizilganki, kubning bitta uchi D nuqtada, unga qarama−qarshi uchi esa ABC yoqda yotibdi. Agar DA=5, DB=6 va DC=10 bo`lsa, kub qirrasining uzunligini toping. A) 2 B) 2√2 C) 15/7 D) 25/12 3 / 30 3. Agar 2a =27, 3c=16 bo’lsa a ∙ ? ning qiymatini toping. A) 13 B) 10 C) 12 D) 11 4 / 30 4. Agar ? + 4/√?= 17 bo‘lsa, ? + 4√? ni toping. A) 3 B) 2 C) 1 D) 4 5 / 30 5. Aylananing ОА, ОВ, ОС radiuslari o‘tkazilgan. Agar bo‘lsa, АОВ burchakni toping. A) 30° B) 90° C) 120° D) 60° 6 / 30 6. Soatning minut mili 144° ga burilganda, soatning soat mili qanday burchakka burilada? A) 12° B) 6° C) 18° D) 9° 7 / 30 7. BC = BE = CD ,∠DAE = 20°, ∠BCD = 60° ,∠ADE = ? (chizmaga qarang) A) 30° B) 50° C) 20° D) 40° 8 / 30 8. ? 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 9 / 30 9. ∠CAD = 2∠ACD, AC =13a, BD = 5a va AB = CD bo’lsa, 20⋅cos ∠ACD ni toping.(chizmaga qarang!) A) 15 B) 19 C) 17 D) 16 10 / 30 10. Soddalashtiring: bunda, |?| < 1. A) -2 B) 4-2a C) 2-2a D) 2a+4 11 / 30 11. 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 12 / 30 12. un ketma-ketlik quyidagicha berilgan: u1 = 1, un+1 = un + 8n. U holda, u50 −u30 ni toping. A) 5320 B) 6320 C) 6230 D) 6320 13 / 30 13. ABC uchburchakda ctgA+ctgB= 3 va AB= 12 bo‘lsa, ABC uchburchak yuzini toping. A) 265 B) 123 C) 521 D) 216 14 / 30 14. a2b5 = 620 tenglikni qanoatlantiruvchi nechta (?; ?) butun sonlar juftligi mavjud? A) 14 B) 8 C) 10 D) 12 15 / 30 15. Soddalashtiring: A) −сtg²1° B) -1 C) −сtg13° D) −сtg1° 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) √5 B) √5 +1 C) √3 D) 2√3 17 / 30 17. 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 18 / 30 18. 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) 81 C) 40 D) 91 19 / 30 19. Tengsizliklar sistemasinining butun yechimlari sonini toping. A) 6 B) 7 C) 4 D) 5 20 / 30 20. 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) 20 C) 18 D) 16 21 / 30 21. bo’lsa, P(−1) ni toping. A) 100 B) 120 C) 115 D) 105 22 / 30 22. 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) 8 C) 3 D) 6 23 / 30 23. Tenglamani yeching: A) ∅ B) 29/462 C) 0 D) 10/21 24 / 30 24. ?(3) ∙ (? − 2) + ?(? − 1) = 3? bo‘lsa, ?(1) ni toping. A) 6 B) 4 C) 2 D) 3 25 / 30 25. Hisoblang: A) D B) B C) A D) C 26 / 30 26. 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) 35/3 B) 83/6 C) 37/3 D) 85/6 27 / 30 27. formula bilan berilgan sonli ketma-ketlikning dastlabki 20 ta hadining o‘rta arifmetigini toping. A) 25/6 B) 20/3 C) 22/3 D) 23/6 28 / 30 28. (3 − cos²x− 2sinx)(lg²y+ 2lgy+ 4) ≤ 3 bo‘lsa, sin²x+ 20y+ 1 ni toping. A) 5 B) 4 C) 3 D) 2 29 / 30 29. Agar ifodaning qiymatini toping. A) 4 B) 0.8 C) 0.05 D) 20 30 / 30 30. 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) 11 D) 13 0% tomonidan Wordpress Quiz plugin Author: InfoMaster