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. tenglamaning ildizlari yig‘indisini toping. A) 6 B) -2 C) -6 D) 10 2 / 30 2. Perimetri 4 ga o`tkir burchagi 30oga va shu burchak qarshisidagi tomoni √3 ga teng bo`lgan uchburchakka ichki chizlgan aylana radiusini toping. A) 4√3+7 B) (1+√3)/2 C) (√3-1)/2 D) 7-4√3 3 / 30 3. |x²+2x-8|=3a tenglama a ning qanday qiymatlarida 3 ta haqiqiy yechimga ega bo`ladi. A) a>3, a=0 B) a=3 C) (0;3) D) 1 4 / 30 4. Agar a = √5 + 1 va b = √5 − 1 bo‘lsa, 2a² − ab − a² ifodaning qiymatini toping. A) 6√5 + 1 B) √5 + 6 C) 3√5 + 6 D) 6√5 + 2 5 / 30 5. To‘g‘ri burchakli uchburchakka ichki va tashqi chizilgan aylana radiuslari nisbati 2 : 5 bo‘lsa, uchburchakning katta o‘tkir burchagining kosinusini toping. A) 0.2 B) 0.8 C) 0.6 D) 0.5 6 / 30 6. Tengsizliklar sistemasinining butun yechimlari sonini toping. A) 5 B) 7 C) 4 D) 6 7 / 30 7. bo’lsa, P(−1) ni toping. A) 120 B) 105 C) 100 D) 115 8 / 30 8. ?(3) ∙ (? − 2) + ?(? − 1) = 3? bo‘lsa, ?(1) ni toping. A) 4 B) 2 C) 6 D) 3 9 / 30 9. Soatning minut mili 144° ga burilganda, soatning soat mili qanday burchakka burilada? A) 12° B) 6° C) 9° D) 18° 10 / 30 10. 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 11 / 30 11. To‘g‘ri burchakli uchburchakning bir burchagi 60° ga teng. Bu burchakdan chiqarilgan bissektrisaning uzunligi 2 m. Uchburchakning gipotenuzasi uzunligini toping. A) √5 +1 B) 2√3 C) √3 D) √5 12 / 30 12. Muntazam uchburchak 36 ta yuzi 1 ga teng bo‘lgan kichkina muntazam uchburchaklardan iborat (chizmaga qarang!). ABC uchburchak yuzini toping. A) 11 B) 12 C) 10 D) 13 13 / 30 13. (3 − cos²x− 2sinx)(lg²y+ 2lgy+ 4) ≤ 3 bo‘lsa, sin²x+ 20y+ 1 ni toping. A) 4 B) 2 C) 5 D) 3 14 / 30 14. ABC uchburchakda ctgA+ctgB= 3 va AB= 12 bo‘lsa, ABC uchburchak yuzini toping. A) 123 B) 265 C) 216 D) 521 15 / 30 15. 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) 6 D) 9 16 / 30 16. ? soniga teskari bo‘lgan son ? ning 9% ini tashkil qiladi. ? ni toping. (?u yerda, ? > 0) A) 16/3 B) 10/3 C) 8/3 D) 13/3 17 / 30 17. 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 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) 91 B) 81 C) 41 D) 40 19 / 30 19. 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 20 / 30 20. un ketma-ketlik quyidagicha berilgan: u1 = 1, un+1 = un + 8n. U holda, u50 −u30 ni toping. A) 6320 B) 6230 C) 5320 D) 6320 21 / 30 21. Soddalashtiring: bunda, |?| < 1. A) 2-2a B) -2 C) 2a+4 D) 4-2a 22 / 30 22. 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) 12 B) 6 C) 8 D) 10 23 / 30 23. BC = BE = CD ,∠DAE = 20°, ∠BCD = 60° ,∠ADE = ? (chizmaga qarang) A) 30° B) 50° C) 40° D) 20° 24 / 30 24. Soddalashtiring: A) B B) D C) C D) A 25 / 30 25. Agar bo‘lsa sin²α ni toping. A) D B) B C) C D) A 26 / 30 26. 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) 18 C) 20 D) 16 27 / 30 27. 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) 106 D) 89 28 / 30 28. a2b5 = 620 tenglikni qanoatlantiruvchi nechta (?; ?) butun sonlar juftligi mavjud? A) 14 B) 10 C) 8 D) 12 29 / 30 29. Arifmetik progressiyada ?2 = 12, ?7 − ?4 = 9 bo‘lsa, ?19 ni toping. A) 54 B) 56 C) 63 D) 61 30 / 30 30. formula bilan berilgan sonli ketma-ketlikning dastlabki 20 ta hadining o‘rta arifmetigini toping. A) 22/3 B) 23/6 C) 20/3 D) 25/6 0% tomonidan Wordpress Quiz plugin Author: InfoMaster