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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!

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1. Teng yonli trapetsiyaning diagonali uni ikkita teng yonli uchburchakka ajratadi. Trapetsiyaning burchaklarini toping.

1. $82^{0},98^{0}$

2. $135^{0},45^{0}$

3. $100^{0},80^{0}$

4. $72^{0},108^{0}$

A) 1

B) 3

C) 4

D) 2

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2. 20 dan 250 gacha sonlarichida 4 ga bo`linadigan, lekin 6 ga bo`linmaydigan nechta natural son bor?

A) 33

B) 30

C) 48

D) 39

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3. To’g’riburchakli uchburchakning o’tkir burchaklaridan chiquvchi medianalar √156 va √89 ga teng bo’lsa, uchburchak gipotenuzasini toping.

A) 12

B) 14

C) 13

D) 15

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4. To‘g‘ri burchakli ABC uchburchakning katetlari 8 ga va 10 ga teng. Shu uchburchakning C to‘g‘ri burchagi uchidan CE mediana va CD bissektrisa o‘tkazilgan. CDE uchburchakning yuzini toping.

A) 17/5

B) 16/7

C) 19/8

D) 20/9

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5. Aylanaga ichki chizilgan trapetsiyaning diagonallari o‘zaro perpendikulyar. Trapetsiya asoslari 1:7 nisbatda va perimetri 18 ga teng bo‘lsa, trapetsiya yuzini toping.

A) 18

B) 22

C) 16

D) 13

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6. Soddalashtiring

A) 5

B) 0

C) 9

D) 6

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

A) 1

B) 0

C) 3

D) 2

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

A) 148°

B) 144°

C) 132°

D) 124°

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9. 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) 16

C) 14

D) 12

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

A) 10

B) 9

C) 8

D) 7

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11. Ikkinchi raqami uchinchi raqamidan 4 marta katta, birinchi raqami esa ikkinchi raqamidan 3 ta kam bo‘lgan uch xonali sonlar nechta?

A) 2

B) 1

C) 3

D) 4

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

A) 6

B) 12

C) 18

D) 9

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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) 5

B) 2

C) 6

D) 9

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14. Soddalashtiring:

A) C

B) A

C) B

D) D

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

A) 2

B) 0

C) 3

D) 1

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16. Hisoblang:

A) -6

B) 8

C) 5

D) 0

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

A) 7

B) 5

C) 2

D) 3

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

A) 25

B) 10

C) 15

D) 9

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

A) 9

B) 10

C) 11

D) 8

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20. Chizmadagi uchburchaklar sonini toping.

A) 30

B) 24

C) 26

D) 28

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

12 ∆ 1 operatsiya natijasini toping.

A) 125

B) 121

C) 132

D) 136

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22. Hisoblang:

A) -22/12

B) -4/3

C) -5/4

D) -11/6

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

A) 95

B) 63

C) 55

D) 81

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

A) 100°

B) 160°

C) 120°

D) 150°

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25. 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 ; 1,1)

D) (1/6 ; 1,5)

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26. Soddalashtiring:

A) B

B) D

C) C

D) A

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27. Soddalashtiring:

A) C

B) B

C) A

D) D

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

A) (0; 2,5)

B) (1/6 ; 1,1)

C) (1/6 ; 1,5)

D) (1/3 ; 1,2)

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29. 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) 2197

B) 2199

C) 2200

D) 2198

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30. Agar bo'lsa, ning qiymatini toping.