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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. tenglamaning ildizi qaysi oraliqda joylashgan?

A) [2;4]

B) [0;2]

C) [-2;0]

D) [4;9]

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2. Tenglamaning ildizini nimchoragi nechaga teng ?

A) 0,5

B) 0,125

C) 20/69

D) 0,25

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3. Hisoblang:

A) 1/4

B) -1/4

C) -1/8

D) 1/8

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4. bo‘lsa ? ning qiymatini toping.

A) 25

B) 12

C) 37

D) 40

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5. tenglama nechta yechimga ega, agar x ∈ (0; 50)?

A) 14

B) 17

C) 15

D) 16

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6. 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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7. 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) 5

C) 6

D) 2

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8. Tenglamani yeching:

A) 0

B) 15/17

C) 8/17

D) -1

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

A) 6

B) 12

C) 11

D) 9

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10. Soddalashtiring: bunda, |?| < 3

A) 2? − 9

B) 1-2?

C) 9

D) 9-2?

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

A) 40

B) 48

C) 36

D) 54

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12. Agar bo'lsa, ni toping.

A) 4

B) 3.5

C) 5

D) 4.5

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13. Soddalashtiring:

A) 2a

B) a-b

C) 2b

D) a+b

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

A) 3 va 15

B) 3

C) 2 va 3

D) 3 va 10

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16. Agar ni toping.

A) 8

B) 0.16

C) 0.8

D) 4

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

7 ∆ 1 operatsiya natijasini toping.

A) 86

B) 125

C) 32

D) 592

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18. Tenglamani yeching:

A) 5

B) 4

C) 3

D) 2

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

A) 4

B) 51

C) 53

D) 49

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

A) 3

B) 4

C) 2

D) 1

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21. Chizmada ABCD −parallelolgramm. DE ni ntoping.

A) 6

B) 5

C) 4

D) 9

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

A) 810

B) 900

C) 990

D) 720

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24. 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 − 2

C) y = x² + 8x − 14

D) y = x² − 8x + 14

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

A) 2

B) 3

C) 5

D) 6

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26. ?³?³ = 1024 tenglikni qanoatlantiruvchi nechta (?; b) butun sonlar juftligi mavjud?

A) 3

B) 4

C) 2

D) 5

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27. 4 ga karrali va o‘nli yozuvida 4, 5, 6, 8 raqamlari bo‘lmagan to‘rt xonali sonlar nechta?

A) 210

B) 150

C) 180

D) 120

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

A) 10

B) 16

C) 15

D) 3

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29. 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) 14

C) 13

D) 11

30 / 30

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

A) 55

B) 56

C) 54

D) 53