10-sinf Matematika olimpiada №4

Oktabr 18, 2022Avgust 19, 2024 InfoMaster 39 fikr bildirilgan

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1. tenglama ildizlari yig‘indisini toping.

A) 2

B) 1

C) 0

D) 3

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

A) 12

B) 6

C) 24

D) 18

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4. Uchburchak tomonlarining uzunliklari berilgan tenglamaning ildizlariga mos keladi. ?³ − 24?² + 183? − 440 = 0. Uchburchakning yuzini hisoblang.

A) 4√21

B) 35

C) 2√21

D) √21

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5. ABC uchburchakning AC tomonida D nuqta olingan, bunda ∠ABC = ∠BDC. Agar AD = 10, CD = 8 bo‘lsa, BC ni toping.

A) 10

B) 9

C) 12

D) 15

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6. Soddalashtiring: bunda, |?| < 3

A) 2? − 9

B) 9-2?

C) 1-2?

D) 9

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7. tenglama nechta haqiqiy yechimga ega?

A) 2

B) 4

C) 1

D) 3

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8. Ikki son o’rtasidagi ∆ operatsiyasiga ko‘ra quyidagi natijalar olindi:

7 ∆ 1 operatsiya natijasini toping.

A) 32

B) 592

C) 125

D) 86

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9. Agar bo'lsa, ni toping.

A) 5

B) 3.5

C) 4.5

D) 4

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10. 1,2,3,4…..,2021,2022 sonlar orasidan nechtasi 3 ga ham, 7 ga ham bo‘linmaydi?

A) 1098

B) 1084

C) 1128

D) 1156

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11. ?₁ va ?₂ sonlari ?² − 7? − 1 = 0 tenglama ildizlari bo‘lsa, ?²₁ + ?²₂ni toping.

A) 49

B) 53

C) 4

D) 51

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12. 4 ga karrali va o‘nli yozuvida 4, 5, 6, 8 raqamlari bo‘lmagan to‘rt xonali sonlar nechta?

A) 180

B) 210

C) 150

D) 120

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13. ?₁ va ?₂ sonlari ?² − 7? − 1 = 0 tenglama ildizlari bo‘lsa, ?²₁ + ?²₂ni toping.

A) 49

B) 4

C) 51

D) 53

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14. tenglama bilan berilgan aylananing markazi koordinata tekisligining qaysi choragida yotadi?

A) IV

B) I

C) II

D) III

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15. Chizmada AE = 2, BE= 6, DE= 3. Aylana diametrini toping.

A) 2√45

B) √65

C) √25

D) 36

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16. f(x) = ax² + b funksiya grafigi A(-1;5) va B(2;-1) nuqtalardan o‘tadi. f(5 − f(1)) ning qiymatini toping.

A) 2

B) 5

C) 7

D) 6

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17. Raqamlari yig‘indisi 3 ga teng bo‘lgan o‘n xonali natural sonlar nechta?

A) 53

B) 55

C) 56

D) 54

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18. Tenglamani yeching:

A) 5

B) 2

C) 4

D) 3

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19. Supermarketda reklama aksiyasi o‘tkazilmoqda: 3 ta shokolad sotib olgan xaridorga 4-shokolad sovg‘a tariqasida qo‘shib beriladi. Bitta shokolad narxi 28000 so‘m. Xaridor 300 000 so‘m evaziga eng ko‘pi bilan nechta shokolad xarid qila oladi?

A) 14

B) 12

C) 13

D) 11

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20. k parametrning qanday musbat qiymatida 20x²+ ?x + 5 = 0 tenglama bitta ildizga ega?

A) 20

B) 5

C) 10

D) 40

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21. Qavariq o‘n ikki burchakning diagonallar sonini toping.

A) 48

B) 40

C) 54

D) 36

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22. bo‘lsa, f (5 − f (1− f (1− f (0)))) ni toping.

A) 20

B) 18

C) 21

D) 19

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23. ∠BAD= ∠ABD= 20∘, ∠DBC= 110∘, ∠BCD= 30∘ va AB= 2, CD=?

A) 1

B) 2

C) 4

D) 3

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24. Agar ni toping.

A) 0.16

B) 0.8

C) 4

D) 8

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25. ?³?³ = 1024 tenglikni qanoatlantiruvchi nechta (?; b) butun sonlar juftligi mavjud?

A) 2

B) 5

C) 4

D) 3

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26. y = 4x² − 3x − 5 parabolaga x(0; 0) nuqtaga nisbatan simmetrik bo‘lgan parabola tenglamasini ko‘rsating.

A) y= 4x² − 3x + 5

B) y=-4x² − 3x+ 5

C) y= 4x² + 3x - 5

D) y= -4x² − 3x - 5

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27. ? parametrning qanday musbat qiymatlarida ?² − (? + 3)? + 3? + 11 = 0 tenglamaning barcha ildizlari butun sonlardan iborat bo‘ladi?

A) 3 va 15

B) 3

C) 3 va 10

D) 2 va 3

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28. ? parametrning qanday musbat qiymatlarida ?² − (? + 3)? + 3? + 11 = 0 tenglamaning barcha ildizlari butun sonlardan iborat bo‘ladi?

A) 15

B) 16

C) 3

D) 10

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29. Uchinchi raqami to‘rtinchi raqamidan 1 ga kichik bo‘lgan to‘rt xonali sonlar sonini toping

A) 990

B) 900

C) 810

D) 720

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30. bo’lsa, (2? − 3)² ifodaning qiymatini toping.

A) 3

B) 2

C) 5

D) 6

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