11-sinf Matematika olimpiada №2 Iyul 17, 2022Avgust 19, 2024 da chop etilgan InfoMaster tomonidan 11-sinf Matematika olimpiada №2 ga 6 fikr bildirilgan 0 12345678910111213141516171819202122232425 Vaqtingiz tugadi! Tomonidan yaratilgan InfoMaster 11-sinf Matematika olimpiada №2 2019-yil tuman bosqichida tushgan savollar 1 / 25 1. ABC uchburchakka aylana tashqi chizilgan. Uchburchakning AM medianasi aylana bilan K nuqtada kesishguncha davom ettirilgan. Agar AM=18,MK=8,BK=10 bo‘lsa, AC tomonini toping. A) 12 B) 15 C) 16 D) 14 2 / 25 2. To‘g‘ri burchakli uchburchakka ichki va tashqi chizilgan aylanalar radiuslari 2 va 5 ga teng. Katetlarning yig‘indisini toping. A) 12 B) 7 C) 14 D) 9 3 / 25 3. ifodani soddalshtiring A) cosα B) 2cosα C) 1 D) 2sinα 4 / 25 4. Agar lg5=a va lg3=b bo`lsa, log308 ni toping. A) 1+b B) (1−a)(1+b) C) 3(1−a) D) (3(1-a))/(1+b) 5 / 25 5. Tenglamani yeching: A) π −arcctg4+πk; k∈Z B) πk; π−arcctg4+πk; k∈Z C) arccos0,8+2πk; k∈Z D) πk; −arcctg4+πk; k∈Z 6 / 25 6. 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) 27 B) 45 C) 100 D) 216 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) 5 va 7 C) −5 va 7 D) −7 va 5 8 / 25 8. funksiyaning aniqlanish sohasini toping. A) (-∞;2/3)∪(2/3;∞) B) (2/3;∞) C) (-∞;4/3)∪(4/3;∞) D) (-∞;4/3) 9 / 25 9. Tengsizlikni yeching. A) (2/3;2) B) (4/3;3) C) (1/2;∞) D) (5/3;2) 10 / 25 10. 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) 15 B) 18 C) 20 D) 10 11 / 25 11. 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) 6 D) √30 12 / 25 12. ni hisoblang. A) 13 B) -12 C) -13 D) 12 13 / 25 13. |x²+2x-8|=3a tenglama a ning qanday qiymatlarida 3 ta haqiqiy yechimga ega bo`ladi. A) a=3 B) 1 C) (0;3) D) a>3, a=0 14 / 25 14. Agar 2a =27, 3c=16 bo’lsa a ∙ ? ning qiymatini toping. A) 13 B) 11 C) 10 D) 12 15 / 25 15. 3cos2x-3 sin2x=0 trigonometrik tenglamani yeching. A) π/12+2πk; k∈Z B) π/12+πk/2; k∈Z) C) π/12+πk; k∈Z D) π/6+πk; k∈Z 16 / 25 16. funksiyaning boshlang`ich funksiyasini toping. A) II B) I C) III D) IV 17 / 25 17. 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) 25/12 B) 2 C) 2√2 D) 15/7 18 / 25 18. f(x)=70cosxcos6x uchun boshlang`ich funksiya toping. A) −7cos5x−5cos7x+c B) 7cos5x−5cos7x+c C) 7sin5x+5sin7x+C D) 7sin5x−5sin7x+c 19 / 25 19. Perimetri 4 ga o`tkir burchagi 30oga va shu burchak qarshisidagi tomoni √3 ga teng bo`lgan uchburchakka ichki chizlgan aylana radiusini toping. A) 7-4√3 B) (√3-1)/2 C) (1+√3)/2 D) 4√3+7 20 / 25 20. Tenglamani yeching: |x²-3x-2|=x²+3|x+2|+4 A) [−2;0] B) [−2;∞) C) [2;∞) D) (−∞;−2] 21 / 25 21. y=6sin2x+sin12x funksiyaning hosilasini toping. A) −24sin7xcos5x B) 24sin5xcos7x C) 24sin7xsin5x D) 24cos7xcos5x 22 / 25 22. Ifodani soddalashtiring: A) 1−√(a-1) B) √(a²-1) C) 0 D) 1+√(a+1) 23 / 25 23. Agar f(g(x))= − x+13 bo`lsa, f(x) va g(x) to`g`ri chiziqlar orasidagi burchakni toping . A) π/2 B) 0 C) π/3 D) π/4 24 / 25 24. 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) 234 B) 18 C) 288 D) 72 25 / 25 25. Poyezd 3 minutda 7 kilometrmasofani , motosikl 5 minutda 7 kilometrmasofanibosibo`tdi. Mototsikltezligipoyezdtezliginingnecha % initashkilqiladi? A) 70% B) 71% C) 60% D) 61% 0% Testni qayta ishga tushiring tomonidan Wordpress Quiz plugin Matematika olimpiada, Tuman 2019-2020 o'quv yili
