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Matematika olimpiada Tuman 2019-2020 o'quv yili

10-sinf Matematika olimpiada №2

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Avgust 19, 2024

36 Ko'rishlar 1 izoh

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10-sinf Matematika olimpiada №2

2019-yil tuman bosqichida tushgan savollar

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1. $(2x-1)^{2017}$ ko‘phadni standart ko‘rinishda ifodalangandagi koeffitsientlar yig‘indisini toping.

1. $2^{2017}+1$

2. $2^{2017}$

3. $2^{2017}-1$

4.1

A) 4

B) 3

C) 1

D) 2

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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) 7,2 sm

C) 6,4 sm

D) 5,6 sm

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

A) 12

B) 8

C) -2/3

D) 10

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

A) 39

B) 40

C) 43

D) 31

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

A) 1/16

B) 1/64

C) 1/32

D) 1/128

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6. Tenglamaning ildizini nimchoragi nechaga teng ?

A) 20/69

B) 0,5

C) 0,125

D) 0,25

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7. 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) 3

D) 6

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

A) 5

B) 4

C) 2

D) 3

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9. trigonometrik tenglamani yeching.

A) π/12+πk/2; k∈Z

B) π/12+2πk; k∈Z

C) π/6+πk; k∈Z

D) π/12+πk; k∈Z

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

A) 72

B) 70

C) 60

D) 71

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11. 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)

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12. 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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13. Tengsizlikni yeching:

A) (5/3;2)

B) (2/3;2)

C) (1/2;∞)

D) (4/3;3)

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14. Hisoblang:

A) -1/8

B) -1/4

C) 1/4

D) 1/8

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15. bo'lsa kasrning qiymatini hisoblang.

A) √11+1

B) 2-√11

C) √11-1

D) √11-2

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16. Funksiyaning aniqlanish sohasini toping.

A) (-∞;3/4)∪(4; 7]

B) (3/4;7)

C) [3/4;7]

D) (3/4;4)

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17. 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%

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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) 14°

D) 10°

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

A) 16

B) 15

C) 12

D) 14

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

A) 4 ta

B) 2 ta

C) 1 ta

D) 3 ta

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

A) 18

B) 12

C) 6

D) 24

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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) x²-12-3

B) x²+12x+3

C) (x-3)²

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) 4

B) 20

C) 12

D) 10

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24. ifodani soddalshtiring