Uy » Online olimpiada » Matematika olimpiada » 11-sinf Matematika olimpiada №2 Matematika olimpiadaTuman 2019-2020 o'quv yili 11-sinf Matematika olimpiada №2 InfoMaster Avgust 19, 2024 16 Ko'rishlar 3 izohlar SaqlashSaqlanganOlib tashlandi 0 0 12345678910111213141516171819202122232425 Vaqtingiz tugadi! 11-sinf Matematika olimpiada №2 2019-yil tuman bosqichida tushgan savollar 1 / 25 1. a,b-to‘g‘ri burchakli uchburchakning katetlari va h-gipotenuzaga tushirilgan balandligi bo‘lsa, yig‘indini toping. A) 2 B) 4 C) 1 D) 3 2 / 25 2. ko‘phadning barcha koeffitsientlari va ozod hadining yig‘indisini toping. A) -238 B) 245 C) -247 D) 125 3 / 25 3. 3cos2x-3 sin2x=0 trigonometrik tenglamani yeching. A) π/12+πk/2; k∈Z) B) π/12+2πk; k∈Z C) π/12+πk; k∈Z D) π/6+πk; k∈Z 4 / 25 4. Tenglamani yeching: |x²-3x-2|=x²+3|x+2|+4 A) [2;∞) B) [−2;0] C) (−∞;−2] D) [−2;∞) 5 / 25 5. Ifodani soddalashtiring: A) 0 B) 1−√(a-1) C) 1+√(a+1) D) √(a²-1) 6 / 25 6. Radiusi 6 ga teng bo`lgan uchta aylana o`zaro tashqi urinishidan hosil bo`lgan egri chiziqli uchburchakka ichki chizilgan aylana radiusini toping. A) 1 B) 2√2−1 C) 6-2√3 D) 4√3-6 7 / 25 7. Agar lg5=a va lg3=b bo`lsa, log308 ni toping. A) 1+b B) (1−a)(1+b) C) (3(1-a))/(1+b) D) 3(1−a) 8 / 25 8. funksiyaning aniqlanish sohasini toping. A) (-∞;4/3) B) (-∞;4/3)∪(4/3;∞) C) (-∞;2/3)∪(2/3;∞) D) (2/3;∞) 9 / 25 9. ifodani soddalshtiring A) 2sinα B) 2cosα C) 1 D) cosα 10 / 25 10. ni hisoblang. A) -13 B) -12 C) 12 D) 13 11 / 25 11. 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 12 / 25 12. |x²+2x-8|=3a tenglama a ning qanday qiymatlarida 3 ta haqiqiy yechimga ega bo`ladi. A) 1 B) a>3, a=0 C) (0;3) D) a=3 13 / 25 13. y=6sin2x+sin12x funksiyaning hosilasini toping. A) 24sin7xsin5x B) 24sin5xcos7x C) 24cos7xcos5x D) −24sin7xcos5x 14 / 25 14. Tenglamani yeching: A) πk; π−arcctg4+πk; k∈Z B) π −arcctg4+πk; k∈Z C) πk; −arcctg4+πk; k∈Z D) arccos0,8+2πk; k∈Z 15 / 25 15. 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) 7-4√3 C) (1+√3)/2 D) 4√3+7 16 / 25 16. 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√2 B) 15/7 C) 2 D) 25/12 17 / 25 17. 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) 12√30 C) √10 D) √30 18 / 25 18. 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) 49 C) 51 D) 52 19 / 25 19. 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 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) 10 B) 15 C) 20 D) 18 21 / 25 21. f(x)=70cosxcos6x uchun boshlang`ich funksiya toping. A) −7cos5x−5cos7x+c B) 7cos5x−5cos7x+c C) 7sin5x+5sin7x+C D) 7sin5x−5sin7x+c 22 / 25 22. 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 23 / 25 23. Agar 2a =27, 3c=16 bo’lsa a ∙ ? ning qiymatini toping. A) 10 B) 13 C) 12 D) 11 24 / 25 24. Poyezd 3 minutda 7 kilometrmasofani , motosikl 5 minutda 7 kilometrmasofanibosibo`tdi. Mototsikltezligipoyezdtezliginingnecha % initashkilqiladi? A) 70% B) 60% C) 71% D) 61% 25 / 25 25. Tengsizlikni yeching. A) (2/3;2) B) (4/3;3) C) (1/2;∞) D) (5/3;2) 0% Testni qayta ishga tushiring Tomonidan Wordpress Quiz plugin Author: InfoMaster Foydali bo'lsa mamnunmiz