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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. tenglama ildizlari yig‘indisini toping.

A) 2

B) 1

C) 3

D) 0

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2. Funksiyaning aniqlanish sohasini toping.

A) (-∞;3/4)∪(4; 7]

B) (3/4;4)

C) [3/4;7]

D) (3/4;7)

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3. bo'lsa kasrning qiymatini hisoblang.

A) √11-1

B) √11+1

C) √11-2

D) 2-√11

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4. Ayirmasi noldan farqli bo‘lgan arifmetik progressiyaning 4-hadidan boshlab 14- hadigacha bo‘lgan hadlar yig‘indisi 77 ga teng. Progressiyaning 7 ga teng bo‘lgan had nomerini toping.

A) 9

B) 10

C) 8

D) 11

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5. ?² + |? − 3| ≤ |?2 + ?| − 3 tengsizlikni yeching.

A) x>3

B) x ≤ 3

C) x<0

D) 3 ≤ x

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6. Tenglamani yeching:

A) 5

B) 3

C) 4

D) 2

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7. Agar bo'lsa, ni toping.

A) 5

B) 4

C) 4.5

D) 3.5

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8. Tenglamani yeching:

A) 0

B) 8/17

C) -1

D) 15/17

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

A) 2

B) 3

C) 4

D) 1

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10. Soddalashtiring: bunda, |?| < 3

A) 2? − 9

B) 9

C) 9-2?

D) 1-2?

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

A) 51

B) 53

C) 4

D) 49

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12. 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) 13

C) 11

D) 12

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

A) 3

B) 6

C) 2

D) 5

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

A) 51

B) 4

C) 49

D) 53

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15. Soddalashtiring:

A) 2a

B) a+b

C) a-b

D) 2b

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16. ? 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 10

D) 3 va 15

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

A) 20

B) 40

C) 5

D) 10

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

A) 19

B) 18

C) 21

D) 20

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

A) 4

B) 5

C) 2

D) 3

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20. ? 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

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21. Agar ni toping.

A) 0.8

B) 4

C) 0.16

D) 8

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22. tenglama nechta haqiqiy yechimga ega?

A) 4

B) 1

C) 2

D) 3

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

A) 9

B) 12

C) 6

D) 11

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

A) 720

B) 990

C) 900

D) 810

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25. 1,2,3,4…..,2021,2022 sonlar orasidan nechtasi 3 ga ham, 7 ga ham bo‘linmaydi?

A) 1128

B) 1084

C) 1156

D) 1098

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

A) 2

B) 4

C) 3

D) 5

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

A) IV

B) III

C) I

D) II

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28. 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 + 2

C) y = x² − 8x + 14

D) y = x² − 8x − 2

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

A) 53

B) 54

C) 55

D) 56

30 / 30

30. 4 ga karrali va o‘nli yozuvida 4, 5, 6, 8 raqamlari bo‘lmagan to‘rt xonali sonlar nechta?

A) 150

B) 180

C) 210

D) 120

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10-sinf Matematika olimpiada №4

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