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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. ifodani a=4, b=5 bo‘lgandagi qiymatini toping.

A) 2

B) 1

C) -1

D) 0

2 / 30

2. Tenglamalar sistemasi nechta yechimga ega?

A) 4

B) 6

C) 2

D) 1

3 / 30

3. bo‘lsa, 3? + ? ni toping.

A) 7,5

B) 5

C) 2,5

D) 10

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4. ABC uchburchakda AB=10, BC=3, AC=√89. B burchakning kosinusini toping.

A) 1/4

B) 1/5

C) 1/3

D) 1/2

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5. tengsizlikning butun yechimlari yig‘indisini toping.

A) 12

B) 18

C) 21

D) 20

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

A) 63

B) 81

C) 55

D) 95

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7. Chizmada ∠AOD = 120∘, ∠BOD = 3∠AOB ?a ∠AOC = 2∠COD bo‘lsa, ∠BOC burchak nimaga teng?

A) 45°

B) 60°

C) 30°

D) 50°

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

A) 2

B) 3

C) 0

D) 1

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

A) 11

B) 9

C) 8

D) 10

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

A) 25

B) 15

C) 9

D) 10

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11. Soddalashtiring:

A) B

B) A

C) D

D) C

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12. Soddalashtiring

A) 9

B) 0

C) 6

D) 5

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13. a = 0,12(12), ? = 0,1(21), c = 0,12(11). Agar a+ b+ c= 0, x₁x₂x₃x₄... x₂₀₂₁x₂₀₂₂x_2023...bo‘lsa, x₂₀₂₂ni toping (bunda, x₁, x₂... raqamlar).

A) 9

B) 6

C) 5

D) 2

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14. ABCD to‘rtburchakda: AB=CD, BC= AD. Agar A burchak B burchakdan 4 marta katta bo‘lsa, to‘rtburchakning A burchagini toping.

A) 132°

B) 124°

C) 144°

D) 148°

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15. Soddalashtiring:

A) C

B) D

C) B

D) A

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16. Hisoblang:

A) 0

B) -6

C) 5

D) 8

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

A) 160°

B) 150°

C) 100°

D) 120°

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18. −16 ≤ 2(y − 7) ≤ 0 va −7 ≤ x ≤ 8 bo‘lsa, x² − y² ifodaning eng kichik qiymatini toping.

A) 2

B) 0

C) 3

D) 1

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19. ABC uchburchakning AE va BF medianalari P nuqtada kesishadi. Agar ABC uchburchak yuzi 36 bo‘lsa, PEСF to‘rtburchak yuzini toping.

A) 6

B) 18

C) 9

D) 12

20 / 30

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

A) 7

B) 9

C) 8

D) 10

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

A) (1/3 ; 1,2)

B) (0; 2,5)

C) (1/6 ; 1,5)

D) (1/6 ; 1,1)

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22. Agar bo'lsa, ning qiymatini toping.

A) -4

B) 0

C) 5

D) 6

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23. Soddalashtiring:

A) D

B) A

C) B

D) C

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24. Agar 3x − y = 7 va 5x + 4y = 21 bo‘lsa, 24x + 9y ni hisoblang.

A) 69

B) 78

C) 90

D) 84

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25. Tenglamani yeching:

A) 29/220

B) 0

C) 10/11

D) Ø

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

A) 3

B) 5

C) 7

D) 2

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

A) 14

B) 16

C) 12

D) 18

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28. 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) 25

B) 26

C) 27

D) 28

29 / 30

29. Chizmadagi uchburchaklar sonini toping.