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Matematika olimpiada Tuman 2022-2023 o'quv yili

10-sinf Matematika olimpiada №4

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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. Hisoblang:

A) 3

B) 4

C) 2

D) 1

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

A) 16

B) 12

C) 15

D) 14

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4. Tenglamalar sistemasi nechta yechimga ega?

A) 8

B) 6

C) 10

D) 12

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5. a,b,c−ABC uchburchakning tomonlari. Agar a⁴ + b⁴ + c⁴ + 32 = 2(a²b² + b²c² + a²c²) bo‘lsa, ABC uchburchak yuzini toping.

A) √2

B) 2√2

C) 1

D) √3

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

A) 11

B) 12

C) 9

D) 6

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

A) 48

B) 54

C) 40

D) 36

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8. Soddalashtiring:

A) a+b

B) 2a

C) a-b

D) 2b

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9. tenglama nechta haqiqiy yechimga ega?

A) 4

B) 3

C) 2

D) 1

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10. 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

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11. Chizmada ABCD −parallelolgramm. DE ni ntoping.

A) 6

B) 4

C) 9

D) 5

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12. Tenglamani yeching:

A) 8/17

B) -1

C) 0

D) 15/17

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

7 ∆ 1 operatsiya natijasini toping.

A) 592

B) 125

C) 32

D) 86

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14. Soddalashtiring: bunda, |?| < 3

A) 9-2?

B) 9

C) 1-2?

D) 2? − 9

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

A) 3

B) 6

C) 2

D) 5

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16. Tenglamani yeching:

A) 4

B) 5

C) 2

D) 3

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

A) 51

B) 4

C) 53

D) 49

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18. 1,2,3,4…..,2021,2022 sonlar orasidan nechtasi 3 ga ham, 7 ga ham bo‘linmaydi?

A) 1128

B) 1156

C) 1098

D) 1084

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

A) 53

B) 4

C) 51

D) 49

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

A) 2 va 3

B) 3

C) 3 va 15

D) 3 va 10

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21. Agar bo'lsa, ni toping.

A) 4

B) 3.5

C) 5

D) 4.5

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22. 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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23. 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) 7

C) 5

D) 6

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

A) 5

B) 40

C) 20

D) 10

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

A) 20

B) 18

C) 19

D) 21

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

A) 2

B) 3

C) 4

D) 5

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28. 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) 12

B) 11

C) 14

D) 13

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