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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

1 / 25

1. Hisoblang:

A) 1

B) 4

C) 2

D) 3

2 / 25

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

A) 8,1 sm

B) 5,6 sm

C) 7,2 sm

D) 6,4 sm

3 / 25

3. Funksiyaning aniqlanish sohasini toping.

A) (-∞;3/4)∪(4; 7]

B) (3/4;7)

C) [3/4;7]

D) (3/4;4)

4 / 25

4. ifodani soddalshtiring

A) cosα

B) 2sinα

C) 1

D) 2cosα

5 / 25

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

A) 1/16

B) 1/32

C) 1/64

D) 1/128

6 / 25

6. trigonometrik tenglamani yeching.

A) π/12+2πk; k∈Z

B) π/12+πk; k∈Z

C) π/6+πk; k∈Z

D) π/12+πk/2; k∈Z

7 / 25

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

A) 2

B) 3

C) 4

D) 5

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

A) 10°

B) 14°

C) 7°

D) 17°

10 / 25

10. Tenglamaning ildizini nimchoragi nechaga teng ?

A) 0,125

B) 0,25

C) 0,5

D) 20/69

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11. 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) 65%

B) 70%

C) 60%

D) 50%

12 / 25

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) 6

C) 3

D) 4

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

A) 8

B) -2/3

C) 12

D) 10

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14. 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

15 / 25

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

A) I

B) II

C) III

D) IV

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16. 2x²-2ax+1=0 kvadrat tenglama ildizlari uchun

tengliko`rinlibo`lsa, a ni toping.

A) -1

B) 1

C) 7

D) -3

17 / 25

17. 7(kx−2)=7k+2(x−8) tenglama k ning qanday qiymatlarida ildizga ega bo`lmaydi?

A) (−∞; 2/7)

B) ∅

C) k=2/7

D) (2/7; ∞)

18 / 25

18. bo'lsa kasrning qiymatini hisoblang.

A) √11-2

B) √11+1

C) 2-√11

D) √11-1

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

A) 12

B) 14

C) 16

D) 15

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20. [2x-1]=x tenglamani butun yechimlar sonini toping. Bu yerda [a]− a sonining butun qismi.

A) 4 ta

B) 3 ta

C) 1 ta

D) 2 ta

21 / 25

21. Hisoblang:

A) 1/4

B) -1/4

C) -1/8

D) 1/8

22 / 25

22. Tengsizlikni yeching:

A) (2/3;2)

B) (1/2;∞)

C) (4/3;3)

D) (5/3;2)

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

A) 6

B) 12

C) 24

D) 18

25 / 25

25. 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) 20

B) 4

C) 10

D) 12