11-sinf Matematika olimpiada №2 Iyul 17, 2022Iyul 17, 2022 da chop etilgan InfoMaster tomonidan 11-sinf Matematika olimpiada №2 ga fikr bildirilmagan. 17 12345678910111213141516171819202122232425 Vaqtingiz tugadi! Tomonidan yaratilgan InfoMaster 11-sinf Matematika olimpiada №2 2019-yil tuman bosqichida tushgan savollar 1 / 25 1. Perimetri 4 ga o`tkir burchagi 30oga va shu burchak qarshisidagi tomoni √3 ga teng bo`lgan uchburchakka ichki chizlgan aylana radiusini toping. A) (√3-1)/2 B) (1+√3)/2 C) 7-4√3 D) 4√3+7 2 / 25 2. Asosi ga teng bo`lgan muntazam to`rtburchakli piramidaning uchidan o`tkazilgan kesma asos tomonini 2:4 nisbatda bo`ladi va asos tekisligi bilan 60o li burchakhosilqiladi. Piramidahajmini toping. A) √10 B) 12√30 C) √30 D) 6 3 / 25 3. Tengsizlikni yeching. A) (4/3;3) B) (1/2;∞) C) (5/3;2) D) (2/3;2) 4 / 25 4. Agar f(g(x))= − x+13 bo`lsa, f(x) va g(x) to`g`ri chiziqlar orasidagi burchakni toping . A) π/3 B) π/2 C) 0 D) π/4 5 / 25 5. Ifodani soddalashtiring: A) 1−√(a-1) B) √(a²-1) C) 1+√(a+1) D) 0 6 / 25 6. f(x)=x³/3-x²-35x+2 funksiya uchun f `(x)=0 bo`lsa x ni toping. A) −7 va 5 B) −5 va 7 C) −7 va −5 D) 5 va 7 7 / 25 7. y=6sin2x+sin12x funksiyaning hosilasini toping. A) −24sin7xcos5x B) 24sin7xsin5x C) 24cos7xcos5x D) 24sin5xcos7x 8 / 25 8. 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) 25/12 C) 2√2 D) 15/7 9 / 25 9. |x²+2x-8|=3a tenglama a ning qanday qiymatlarida 3 ta haqiqiy yechimga ega bo`ladi. A) 1 B) a=3 C) a>3, a=0 D) (0;3) 10 / 25 10. 3cos2x-3 sin2x=0 trigonometrik tenglamani yeching. A) π/12+2πk; k∈Z B) π/6+πk; k∈Z C) π/12+πk/2; k∈Z) D) π/12+πk; k∈Z 11 / 25 11. ifodani soddalshtiring A) 2cosα B) cosα C) 1 D) 2sinα 12 / 25 12. Agar 2a =27, 3c=16 bo’lsa a ∙ 𝑐 ning qiymatini toping. A) 13 B) 12 C) 10 D) 11 13 / 25 13. Tenglamani yeching: |x²-3x-2|=x²+3|x+2|+4 A) [−2;∞) B) [2;∞) C) (−∞;−2] D) [−2;0] 14 / 25 14. a+b=−1 a+c=6 va b+c=1 bo`lsa, a² (3b+3c+2a)+b² (3a+3c+2b)+c² (3a+3b+2c) ning son qiymatini toping. A) 45 B) 216 C) 100 D) 27 15 / 25 15. Beshyulduzning uchidagi burchaklarining yig‘indisini toping. A) 240° B) 90° C) 180° D) 270° 16 / 25 16. ni hisoblang. A) -13 B) 13 C) -12 D) 12 17 / 25 17. 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) 20 C) 18 D) 15 18 / 25 18. Radiusi 6 ga teng bo`lgan uchta aylana o`zaro tashqi urinishidan hosil bo`lgan egri chiziqli uchburchakka ichki chizilgan aylana radiusini toping. A) 4√3-6 B) 2√2−1 C) 1 D) 6-2√3 19 / 25 19. funksiyaning aniqlanish sohasini toping. A) (2/3;∞) B) (-∞;4/3)∪(4/3;∞) C) (-∞;2/3)∪(2/3;∞) D) (-∞;4/3) 20 / 25 20. Poyezd 3 minutda 7 kilometrmasofani , motosikl 5 minutda 7 kilometrmasofanibosibo`tdi. Mototsikltezligipoyezdtezliginingnecha % initashkilqiladi? A) 61% B) 70% C) 71% D) 60% 21 / 25 21. GH kesmani O nuqta, G nuqtadan boshlab hisoblaganda, 5 : 7 kabi, P nuqtaesa 5:11 kabi nisbatda bo’ladi. O va P nuqtalar orasidagi masofa 30 sm bo’lsa, GH kesmaning uzunligini toping. A) 72 B) 288 C) 234 D) 18 22 / 25 22. Koordinata boshidan o‘tuvchi, simmetriya o‘qi ordinata o‘qiga parallel, cho‘qqisi y=x va y+x-2=0 to‘g‘ri chiziqlar kesishgan nuqtada bo‘lgan parabolaning tenglamasini toping. A) y=-x²+1 B) y=x²-2x C) y=-x²-2x D) y=-x²+2x 23 / 25 23. funksiyaning boshlang`ich funksiyasini toping. A) IV B) III C) II D) I 24 / 25 24. f(x)=70cosxcos6x uchun boshlang`ich funksiya toping. A) 7sin5x−5sin7x+c B) 7sin5x+5sin7x+C C) 7cos5x−5cos7x+c D) −7cos5x−5cos7x+c 25 / 25 25. Tenglamani yeching: A) π −arcctg4+πk; k∈Z B) arccos0,8+2πk; k∈Z C) πk; −arcctg4+πk; k∈Z D) πk; π−arcctg4+πk; k∈Z 0% Testni qayta ishga tushiring Author: InfoMaster Matematika olimpiada
