11-sinf Matematika olimpiada №2 Iyul 17, 2022Iyul 17, 2022 da chop etilgan InfoMaster tomonidan 11-sinf Matematika olimpiada №2 ga fikr bildirilmagan. 0 12345678910111213141516171819202122232425 Vaqtingiz tugadi! 11-sinf Matematika olimpiada №2 2019-yil tuman bosqichida tushgan savollar 1 / 25 1. ko‘phadning barcha koeffitsientlari va ozod hadining yig‘indisini toping. A) 125 B) -238 C) 245 D) -247 2 / 25 2. 32017 sonning oxirgi ikkita raqamini toping. A) 03 B) 13 C) 63 D) 83 3 / 25 3. Poyezd 3 minutda 7 kilometrmasofani , motosikl 5 minutda 7 kilometrmasofanibosibo`tdi. Mototsikltezligipoyezdtezliginingnecha % initashkilqiladi? A) 71% B) 61% C) 70% D) 60% 4 / 25 4. Bitta tekislikda yotuvchi n ta turli tog`ri chiziq o`tkazilgan. Ularning ixtiyoriy ikkitasi parallel emas va ixtiyoriy uchtasi bitta nuqtadan o`tmaydi ,ya`ni bitta nuqtada kesishmaydi. Bu to`g`ri chiziqlar tekislikni 1276 qismga ajratadi. n ni aniqlang? A) 50 B) 52 C) 51 D) 49 5 / 25 5. ni hisoblang. A) 12 B) 13 C) -13 D) -12 6 / 25 6. Agar 2a =27, 3c=16 bo’lsa a ∙ ? ning qiymatini toping. A) 11 B) 13 C) 12 D) 10 7 / 25 7. f(x)=x³/3-x²-35x+2 funksiya uchun f `(x)=0 bo`lsa x ni toping. A) −7 va −5 B) −7 va 5 C) 5 va 7 D) −5 va 7 8 / 25 8. 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) 18 B) 288 C) 72 D) 234 9 / 25 9. funksiyaning boshlang`ich funksiyasini toping. A) III B) II C) IV D) I 10 / 25 10. 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) (√3-1)/2 C) 7-4√3 D) (1+√3)/2 11 / 25 11. Ifodani soddalashtiring: A) 1+√(a+1) B) 0 C) √(a²-1) D) 1−√(a-1) 12 / 25 12. y=6sin2x+sin12x funksiyaning hosilasini toping. A) 24cos7xcos5x B) 24sin7xsin5x C) 24sin5xcos7x D) −24sin7xcos5x 13 / 25 13. |x²+2x-8|=3a tenglama a ning qanday qiymatlarida 3 ta haqiqiy yechimga ega bo`ladi. A) (0;3) B) a>3, a=0 C) a=3 D) 1 14 / 25 14. Agar f(g(x))= − x+13 bo`lsa, f(x) va g(x) to`g`ri chiziqlar orasidagi burchakni toping . A) π/2 B) π/4 C) π/3 D) 0 15 / 25 15. f(x)=70cosxcos6x uchun boshlang`ich funksiya toping. A) 7cos5x−5cos7x+c B) 7sin5x−5sin7x+c C) 7sin5x+5sin7x+C D) −7cos5x−5cos7x+c 16 / 25 16. 3cos2x-3 sin2x=0 trigonometrik tenglamani yeching. A) π/12+πk; k∈Z B) π/6+πk; k∈Z C) π/12+πk/2; k∈Z) D) π/12+2πk; k∈Z 17 / 25 17. 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) 216 B) 100 C) 45 D) 27 18 / 25 18. 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) 6 B) √30 C) 12√30 D) √10 19 / 25 19. 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) 15/7 C) 2√2 D) 25/12 20 / 25 20. 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) 20 B) 18 C) 10 D) 15 21 / 25 21. Radiusi 6 ga teng bo`lgan uchta aylana o`zaro tashqi urinishidan hosil bo`lgan egri chiziqli uchburchakka ichki chizilgan aylana radiusini toping. A) 6-2√3 B) 4√3-6 C) 1 D) 2√2−1 22 / 25 22. Tenglamani yeching: |x²-3x-2|=x²+3|x+2|+4 A) [−2;∞) B) [−2;0] C) (−∞;−2] D) [2;∞) 23 / 25 23. funksiyaning aniqlanish sohasini toping. A) (-∞;4/3)∪(4/3;∞) B) (2/3;∞) C) (-∞;2/3)∪(2/3;∞) D) (-∞;4/3) 24 / 25 24. ifodani soddalshtiring A) cosα B) 1 C) 2cosα D) 2sinα 25 / 25 25. Tenglamani yeching: A) πk; −arcctg4+πk; k∈Z B) π −arcctg4+πk; k∈Z C) arccos0,8+2πk; k∈Z D) πk; π−arcctg4+πk; k∈Z 0% Testni qayta ishga tushiring Author: InfoMaster Matematika olimpiada