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Matematika olimpiada Tuman 2022-2023 o'quv yili

9-sinf Matematika olimpiada №4

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Avgust 19, 2024

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9-sinf Matematika olimpiada №4

2022-yil 12-oktabr:

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

1 / 30

1. Agar bo‘lsa, ni hisoblang.

A) 3

B) 4

C) -4

D) ±4

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2. Agar arifmetik progressiyada bo`lsa, ayirmani toping.

A) 1

B) 3

C) 2

D) 4

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3. Kataklarning chiziqlari bo’yicha A dan B ga olib boruvchi eng qisqa yo’llar soni nechta?

A) 56

B) 57

C) 55

D) 58

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4. m ning nechta natural qiymatida tengsizlik x ning istalgan qiymatida o’rinli bo’ladi?

A) 1

B) 3

C) 0

D) 2

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5. ?₁ va ?₂ sonlari 2?² − 3? − 2 = 0 tenglamaning ildizlari, |?₁ − ?₂| ni toping.

A) 2

B) 3

C) 2.5

D) 3.5

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6. Raqamlari yig‘indisi 2 ga teng bo‘lgan o‘n xonali natural sonlar nechta?

A) 9

B) 10

C) 25

D) 15

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

12 ∆ 1 operatsiya natijasini toping.

A) 136

B) 132

C) 125

D) 121

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8. Soddalashtiring:

A) B

B) D

C) C

D) A

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9. Agar ac < 0 bo‘lsa, y=ax-bx²-c funksiya grafigi koordinatalar tekisligining qaysi choraklaridan o‘tadi?

A) I, III, IV

B) I,II,III

C) Barcha chorakdan o'tadi?

D) II, III, IV

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10. Soat strelkasi 5 soat vaqt o‘tgandan keyin qanday burchakka buriladi?

A) 160°

B) 100°

C) 150°

D) 120°

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11. Agar AB =12, BC =14, CD = 2 bo’lsa, aylana radiusini aniqlang.

A) 10

B) 9

C) 8

D) 11

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12. Anvar 2 dan boshlab barcha natural sonlarni doskaga yozdi. U yozayotganda to‘la kub bo‘lgan sonlarni qoldirib ketdi (8, 125 kabi). Doskaga 2186-o‘rinda yozilgan sonni toping.

A) 2199

B) 2198

C) 2200

D) 2197

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13. Soddalashtiring

A) 6

B) 9

C) 0

D) 5

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14. Ikkinchi raqami uchinchi raqamidan 1 ta kam bo‘lgan uch xonali sonlar sonini toping.

A) 81

B) 95

C) 63

D) 55

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15. Agar bo'lsa, ning qiymatini toping.

A) 5

B) 6

C) -4

D) 0

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16. −16 ≤ 2(y − 7) ≤ 0 va −7 ≤ x ≤ 8 bo‘lsa, x² − y² ifodaning eng kichik qiymatini toping.

A) 3

B) 0

C) 1

D) 2

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17. Agar a + b − 2c = 0 bo’lsa, ni hisoblang.

A) 1

B) 2

C) 0

D) 3

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18. x₀haqiqiy son x³ +1 = (x² − x −1)² − 4 tenglama ildizi bo‘lsa, (x₀ − 1)² ni toping.

A) 5

B) 2

C) 3

D) 7

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19. Soddalashtiring:

A) A

B) D

C) C

D) B

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20. tengsizlikning (−5; 5) oraliqda nechta butun yechimi mavjud?

A) 7

B) 9

C) 10

D) 8

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21. a parametrning qanday qiymatlarida 9 + 3a, 5 − 2a va 15 − 5a uzunlikdagi kesmalardan uchburchak
yashash mumkin?

A) (1/6 ; 1,5)

B) (0; 2,5)

C) (1/6 ; 1,1)

D) (1/3 ; 1,2)

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22. Uchlari A(2; −3), B(6; 0), C(6; 2) va D(2; 2) nuqtalarda bo‘lgan ABCD to‘rtburchak yuzini toping.

A) 18

B) 14

C) 16

D) 12

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23. a parametrning qanday qiymatlarida 9 + 3a, 5 − 2a va 15 − 5a uzunlikdagi kesmalardan uchburchak
yashash mumkin?

A) (1/3 ; 1,2)

B) (1/6 ; 1,1)

C) (1/6 ; 1,5)

D) (0; 2,5)

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24. Soddalashtiring:

A) D

B) A

C) C

D) B

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25. f(x)=ax+b funksiya grafigi A(-1;3) va B(1;7) nuqtalar orqali o‘tadi. f(4- f( -1)) ni toping

A) 7

B) 10

C) 12

D) 9

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26. Oila erkak kishi, uning ayoli va talaba qizidan iborat. Agar erkak kishining maoshi 2 barobar oshsa, u holda oila daromadi 67%ga ortadi, agar talaba qizning stipendiyasi 3 barobar kamaysa, oila daromadi 4%ga qisqaradi. Ayolning maoshi oila daromadining necha foizni tashkil qiladi?

A) 28

B) 25

C) 27

D) 26

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27. Tenglamani yeching: