10-sinf Matematika olimpiada №2

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1. Teng yonli uchburchakning asosi 12 sm, yon tomoni 18 sm. Yon tomonlariga bissektrisalar tushirilgan. Bissektrisalarning tomonlari bilan kesishgan nuqtalari orasidagoi masofani toping.

A) 7,2 sm

B) 6,4 sm

C) 5,6 sm

D) 8,1 sm

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2. Sonlarni o‘sish tartibida joylashtiring: $a=sin,b=cos22,c=sin61^{0}$

A) a,c,b

B) b,a,c

C) c,b,a

D) b,c,a

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3. 7(kx−2)=7k+2(x−8) tenglama k ning qanday qiymatlarida ildizga ega bo`lmaydi?

A) k=2/7

B) (2/7; ∞)

C) (−∞; 2/7)

D) ∅

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4. Ta`lim muassasida barcha o`quvchilar kamida bitta ingliz yoki nemis tilida so`zlashа oladilar. Ayrimlari ikkala tilni ham biladilar. O`quvchilarning 85%i ingliz tilini, 75%i nemis tilini biladilar. Ikkala tilni ham biladigan o`quvchilar barcha o`quvchilarning necha % ini tashkil etadi.

A) 50%

B) 60%

C) 70%

D) 65%

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5. trigonometrik tenglamani yeching.

A) π/12+2πk; k∈Z

B) π/12+πk; k∈Z

C) π/12+πk/2; k∈Z

D) π/6+πk; k∈Z

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6. Berilgan funksiyaga teskari funksiyani aniqlang. f(x)=x^2f²(x)+f(x)

A) III

B) IV

C) I

D) II

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7. Uchburchakning ikki tomoni 12 va 13 sm ga, ular orasidagi burchak kosinusi 5/13 ga teng bo`lsa, uning yuzini toping.

A) 71

B) 70

C) 72

D) 60

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8. Tenglamaning ildizini nimchoragi nechaga teng ?

A) 20/69

B) 0,125

C) 0,25

D) 0,5

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9. tengsizlik yechimi bo`la oladigan tub sonlar nechta?

A) 3

B) 4

C) 5

D) 2

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10. bo'lsa kasrning qiymatini hisoblang.

A) √11-2

B) √11+1

C) 2-√11

D) √11-1

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11. Tengsizlikni yeching:

A) (4/3;3)

B) (2/3;2)

C) (5/3;2)

D) (1/2;∞)

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12. Agar x²(a²+b²+9)+2(a+b+3)x+3=0 tenglama haqiqiy yechimga ega bo`lsa, a+b ni toping.

A) 2

B) 4

C) 6

D) 3

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13. [2x-1]=x tenglamani butun yechimlar sonini toping. Bu yerda [a]− a sonining butun qismi.

A) 2 ta

B) 3 ta

C) 4 ta

D) 1 ta

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14. Funksiyaning aniqlanish sohasini toping.

A) (3/4;7)

B) (-∞;3/4)∪(4; 7]

C) [3/4;7]

D) (3/4;4)

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15. f(x)=x²-4x va f(x)=-2x²+8x-p funksiyalar umumiy uchga ega bo`lsa, p ning qiymatini toping.

A) 24

B) 18

C) 6

D) 12

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16. ifodani soddalshtiring

A) 2sinα

B) cosα

C) 1

D) 2cosα

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17. Ko`paytmani hisoblang. cos12°cos24°cos36°cos48°cos60°cos72°cos84°

A) 1/32

B) 1/128

C) 1/16

D) 1/64

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18. Uchburchakning ikkita burchagi mos ravishda 38^o va 52^oga teng. Uchinchi burchagi uchidan tushirilgan bissektrisa va mediana orasidagi burchakni toping.

A) 7°

B) 17°

C) 10°

D) 14°

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19. Hisoblang:

A) 1/4

B) -1/4

C) -1/8

D) 1/8

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20. Beshta a₁, a₂, a₃, a₄, a₅ tub sonlar ayirmasi 6 ga teng bo`lgan arifmetik progressiyani tashkil qiladi. 2a₂+a₃ni toping.

A) 39

B) 31

C) 43

D) 40

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21. Agar f(g(x))=x²-6x+6 va f(x)=x−3 funksiyalar berilgan bo`lsa, g(x) funksiya ko`rinishini aniqlang.

A) (x+3)²

B) (x-3)²

C) x²-12-3

D) x²+12x+3

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22. Korxona xom−ashyuo qimmatlashgani sababli maxsulot narxi 20% ga oshirildi, biroq mijojlar soni 20 % ga kamayib ketdi. Shunda korxona narxni qanchadir foizga kamaytirib mijozlari sonini 25% ga oshirishga erishdi. Shundan keyin korxona tushumi narx o`zgarmasdan oldingi tushumga qaraganda 8% ga oshgan bo`lsa, yangi narx necha foizga kamaytirilgan?

A) 4

B) 20

C) 12

D) 10

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23. Agar f(x+1) =7+3x funksiya uchun f (a)=2 tenglik o`rinli bo`lsa, a ning qiymatini toping.

A) 10

B) 12

C) 8

D) -2/3

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24. Uchburchakning tomonlari 7 va 11 ga, uchinchi tomonining medianasi √21 ga teng. Uchburchakning uchunchi tomonini toping.

A) 15

B) 12

C) 16

D) 14

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25. 2x²-2ax+1=0 kvadrat tenglama ildizlari uchun

tengliko`rinlibo`lsa, a ni toping.

A) -1

B) 1

C) 7

D) -3

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10-sinf Matematika olimpiada №2

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