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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!

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1. Agar ikkita teng tomonli uchburchakning tomonlari uchun munosabat o‘rinli bo‘lsa, katta uchburchak yuzini kichik uchburchak yuziga nisbatini toping.

A) 7

B) 8

C) 9

D) 6

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

A) 2

B) 4

C) 5

D) 3

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

A) 14°

B) 17°

C) 10°

D) 7°

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4. 10²⁰²² − 2²⁰²¹ ayirmani 24 ga bo‘lgandagi qoldiqni toping.

A) 0

B) 16

C) 8

D) 12

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5. Agar ?₁ = 6? − 6 va у₂//?₁ hamda у₂ to‘g‘ri chiziq ?(6; 6) nuqtadan o‘tsa, ?₂ ni toping.

A) −6? + 42

B) 6? − 30

C) −6? + 6

D) 6? − 24

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

A) 150

B) 210

C) 120

D) 180

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

A) 5

B) 3

C) 2

D) 6

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

A) 3

B) 4

C) 2

D) 1

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9. Agar bo'lsa, ni toping.

A) 5

B) 4.5

C) 3.5

D) 4

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

A) III

B) I

C) IV

D) II

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

A) 5

B) 4

C) 3

D) 2

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12. Tenglamani yeching:

A) 15/17

B) -1

C) 0

D) 8/17

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

A) 55

B) 53

C) 54

D) 56

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15. Tenglamani yeching:

A) 2

B) 3

C) 5

D) 4

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16. 1,2,3,4…..,2021,2022 sonlar orasidan nechtasi 3 ga ham, 7 ga ham bo‘linmaydi?

A) 1098

B) 1128

C) 1156

D) 1084

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

7 ∆ 1 operatsiya natijasini toping.

A) 592

B) 125

C) 86

D) 32

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

A) 12

B) 6

C) 11

D) 9

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

A) 10

B) 5

C) 40

D) 20

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

A) 7

B) 2

C) 6

D) 5

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

A) 2√45

B) √25

C) 36

D) √65

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

A) y = x² − 8x + 14

B) y = x² + 8x − 14

C) y = x² + 8x + 2

D) y = x² − 8x − 2

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23. Chizmada ABCD −parallelolgramm. DE ni ntoping.

A) 9

B) 6

C) 5

D) 4

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

A) 54

B) 48

C) 40

D) 36

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

A) 10

B) 16

C) 3

D) 15

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27. Soddalashtiring: bunda, |?| < 3

A) 9-2?

B) 9

C) 2? − 9

D) 1-2?

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

A) 990

B) 720

C) 810

D) 900

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

A) 3 va 10

B) 3 va 15

C) 2 va 3

D) 3

30 / 30

30. tenglama nechta haqiqiy yechimga ega?

A) 3

B) 4

C) 1

D) 2

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