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Matematika olimpiada Tuman 2022-2023 o'quv yili

10-sinf Matematika olimpiada №4

InfoMaster

Avgust 19, 2024

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10-sinf Matematika olimpiada №4

2022-yil 12-oktabr:

2022-2023 o'quv yili tuman bosqichida tushgan savollar!

1 / 30

1. ABC uchburchakda AB=BC,AM -mediana. Agar AB+MB=9 va MC+AC=7 bo‘lsa, uning asosini toping.

A) 6

B) 4

C) 5

D) 7

2 / 30

2. Tengsizlikni yeching:

A) (1/2;∞)

B) (2/3;2)

C) (5/3;2)

D) (4/3;3)

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3. 2x²-2ax+1=0 kvadrat tenglama ildizlari uchun

tengliko`rinlibo`lsa, a ni toping.

A) 7

B) -1

C) -3

D) 1

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4. ABCD to‘rtburchakda А va В burchaklar- to‘g‘ri, tg∠D = 3/4 va ВС = AD/2 = АВ + 2 bo‘lsa, АС ni toping.

A) 15

B) 8

C) 9

D) 10

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5. Agar ni toping.

A) 0.8

B) 0.9

C) 0.96

D) 0.81

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6. Tenglamani yeching:

A) -1

B) 0

C) 15/17

D) 8/17

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7. tenglama nechta haqiqiy yechimga ega?

A) 4

B) 1

C) 3

D) 2

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

A) 49

B) 51

C) 53

D) 4

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

A) 53

B) 49

C) 51

D) 4

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10. Agar bo'lsa, ni toping.

A) 3.5

B) 4

C) 5

D) 4.5

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11. Soddalashtiring:

A) a-b

B) 2a

C) 2b

D) a+b

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12. ?³?³ = 1024 tenglikni qanoatlantiruvchi nechta (?; b) butun sonlar juftligi mavjud?

A) 3

B) 4

C) 5

D) 2

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

A) 5

B) 20

C) 10

D) 40

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

A) 3

B) 3 va 15

C) 3 va 10

D) 2 va 3

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15. Chizmada ABCD −parallelolgramm. DE ni ntoping.

A) 4

B) 9

C) 5

D) 6

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16. Soddalashtiring: bunda, |?| < 3

A) 9

B) 9-2?

C) 2? − 9

D) 1-2?

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17. Agar ni toping.

A) 0.8

B) 8

C) 0.16

D) 4

18 / 30

18. ABCD qavariq to‘rtburchakka aylana ichki chizilgan. Agar АВ = 7, BC= 11 bo‘lsa, CD − AD ni toping.

A) 2

B) 3

C) 5

D) 4

19 / 30

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

A) III

B) IV

C) I

D) II

20 / 30

20. y = x²− 2 parabolaga y = 2 to‘g‘ri chiziqqa nisbatan simmetrik bo‘lgan parabola tenglamasini tuzing.

A) y = x² + 8x + 2

B) y = x² − 8x + 14

C) y = x² + 8x − 14

D) y = x² − 8x − 2

21 / 30

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

A) 48

B) 40

C) 54

D) 36

22 / 30

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

A) 6

B) 2

C) 3

D) 5

23 / 30

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

7 ∆ 1 operatsiya natijasini toping.

A) 125

B) 592

C) 86

D) 32

24 / 30

24. 1,2,3,4…..,2021,2022 sonlar orasidan nechtasi 3 ga ham, 7 ga ham bo‘linmaydi?

A) 1156

B) 1128

C) 1084

D) 1098

25 / 30

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

A) √65

B) 2√45

C) √25

D) 36

26 / 30

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

A) 18

B) 21

C) 20

D) 19

27 / 30

27. ABCD qavariq to‘rtburchakda ∠BAD= ∠CDA= 60∘, ∠BDA= ∠CAB, AB= 2 va CD= 9 bo‘lsa, AD ni toping.

A) 9

B) 11

C) 12

D) 6

28 / 30

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

A) 10

B) 3

C) 15

D) 16

29 / 30

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

A) 55

B) 56

C) 53

D) 54

30 / 30

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

A) 5

B) 6

C) 7

D) 2

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2022-yil 12-oktabr:

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