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Matematika olimpiada Tuman 2019-2020 o'quv yili

10-sinf Matematika olimpiada №2

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Avgust 19, 2024

13 Ko'rishlar 1 izoh

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10-sinf Matematika olimpiada №2

2019-yil tuman bosqichida tushgan savollar

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1. Tenglama ildizlarining o‘rta arifmetik qiymatini toping:

A) 1

B) 3

C) 5

D) 2

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2. tenglama ildizlari yig‘indisini toping.

A) 2

B) 3

C) 0

D) 1

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

A) 60

B) 72

C) 70

D) 71

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4. ifodani soddalshtiring

A) 2sinα

B) cosα

C) 2cosα

D) 1

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5. Tengsizlikni yeching:

A) (2/3;2)

B) (4/3;3)

C) (1/2;∞)

D) (5/3;2)

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6. bo'lsa kasrning qiymatini hisoblang.

A) √11-2

B) √11+1

C) 2-√11

D) √11-1

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

A) (−∞; 2/7)

B) ∅

C) (2/7; ∞)

D) k=2/7

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

A) 14

B) 16

C) 15

D) 12

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9. 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) 60%

B) 50%

C) 65%

D) 70%

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

A) 14°

B) 10°

C) 17°

D) 7°

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11. Tenglamaning ildizini nimchoragi nechaga teng ?

A) 0,125

B) 0,25

C) 0,5

D) 20/69

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

A) 1/128

B) 1/32

C) 1/16

D) 1/64

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13. trigonometrik tenglamani yeching.

A) π/6+πk; k∈Z

B) π/12+πk; k∈Z

C) π/12+2πk; k∈Z

D) π/12+πk/2; k∈Z

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14. Funksiyaning aniqlanish sohasini toping.

A) (3/4;7)

B) (3/4;4)

C) [3/4;7]

D) (-∞;3/4)∪(4; 7]

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15. [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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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) 8

C) 12

D) 10

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

A) 24

B) 12

C) 6

D) 18

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

A) 4

B) 2

C) 6

D) 3

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

A) I

B) IV

C) III

D) II

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21. Hisoblang:

A) 1/4

B) -1/8

C) 1/8

D) -1/4

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22. 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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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) 12

B) 10

C) 20

D) 4

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24. 2x²-2ax+1=0 kvadrat tenglama ildizlari uchun