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Matematika olimpiada Tuman 2019-2020 o'quv yili

10-sinf Matematika olimpiada №2

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Avgust 19, 2024

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10-sinf Matematika olimpiada №2

2019-yil tuman bosqichida tushgan savollar

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1. Agar bo‘lsa, ni toping.

A) -3

B) -1

C) -7

D) -5

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2. Ninachi va chivin to‘g‘ri chiziq bo‘ylab harakatlanmoqda. Ninachi chivinni quvib yetmoqchi. Ninachining tezligi 1,2 m/s va chivinniki 30 sm/s. Necha sekunddan so‘ng ular orasidagi masofa 6,5 m dan 20 sm gacha qisqaradi?

A) 7 s

B) 8 s

C) 6 s

D) 5 s

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3. ifodani soddalshtiring

A) cosα

B) 1

C) 2sinα

D) 2cosα

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

A) 60

B) 70

C) 71

D) 72

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5. 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) 70%

B) 65%

C) 50%

D) 60%

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6. 2x²-2ax+1=0 kvadrat tenglama ildizlari uchun

tengliko`rinlibo`lsa, a ni toping.

A) -1

B) 1

C) -3

D) 7

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

A) 5

B) 2

C) 4

D) 3

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8. Funksiyaning aniqlanish sohasini toping.

A) (-∞;3/4)∪(4; 7]

B) [3/4;7]

C) (3/4;4)

D) (3/4;7)

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

A) 1/32

B) 1/64

C) 1/16

D) 1/128

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

A) 18

B) 6

C) 24

D) 12

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11. Hisoblang:

A) 1/8

B) -1/4

C) -1/8

D) 1/4

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

A) 14°

B) 7°

C) 17°

D) 10°

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13. Tengsizlikni yeching:

A) (5/3;2)

B) (2/3;2)

C) (1/2;∞)

D) (4/3;3)

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14. 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

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

A) -2/3

B) 10

C) 8

D) 12

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17. bo'lsa kasrning qiymatini hisoblang.

A) √11+1

B) 2-√11

C) √11-1

D) √11-2

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18. [2x-1]=x tenglamani butun yechimlar sonini toping. Bu yerda [a]− a sonining butun qismi.

A) 1 ta

B) 3 ta

C) 2 ta

D) 4 ta

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

A) III

B) I

C) II

D) IV

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20. 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) 3

C) 4

D) 6

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21. Tenglamaning ildizini nimchoragi nechaga teng ?

A) 0,5

B) 20/69

C) 0,25

D) 0,125

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

A) 39

B) 43

C) 31

D) 40

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23. 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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24. 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) x²+12x+3

C) x²-12-3

D) (x+3)²

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