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Matematika olimpiada Tuman 2020-2021 o'quv yili

9-sinf Matematika olimpiada №1

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Avgust 23, 2024

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9-sinf Matematika olimpiada №1

2020-2021 o'quv yil tuman bosqichida tushgan savollar

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1. Hisoblang:

A) 0,5

B) 1,5

C) 1

D) 5

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2. To‘g‘ri burchakli uchburchakka ichki chizilgan aylana urinish nuqtasida gipotenuzani 5 va 12 ga teng kesmalarga ajratadi. Uchburchak yuzini toping

A) 65

B) 48

C) 35

D) 60

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3. Rombning diagonallari 6 va 8 ga teng bo‘lsa, uning tomonini toping.

A) 3

B) 6

C) 8

D) 5

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4. ni hisoblang.

A) -2

B) 4

C) 2

D) 3

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

A) 2

B) 0

C) -1

D) 1

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6. Agar bo‘lsa, ni hisoblang.

A) -4

B) 4

C) 3

D) ±4

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7. Uchburchakning perimetri 24 sm ga teng bo‘lib, uning tomonlari uzunliklari arifmetik progressiya tashkil etadi. Shu uchburchakning kichik tomoni 6 sm bo‘lsa, uchburchak turini aniqlang.

A) Bunday uchburchak yo’q

B) To‘g‘ri burchakli

C) O’tmas burchakli

D) O’tkir burchakli

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8. Parallellogrammning 5 ga teng bo‘lgan diagonali uning 12 ga teng bo‘lgan tomoniga perpendikulyar. Parallelogrammning perimetrini toping.

A) 48

B) 50

C) 34

D) 44

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9. Agar (3-a)(3-b)(3-c)=(3+a)(3+b)(3+c) bo‘lsa, $(ab)^{-1}+(bc)^{-1}+(ac)^{-1}$ ni hisoblang. (Bunda $abc\neq 0$ ).

A) -1/9

B) 1/9

C) -1/3

D) 1/27

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10. stemadan ni toping.

A) 7/11

B) 11/7

C) 7/3

D) 3/7

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11. 60⁰ li burchakka bir-biriga tashqaridan urinuvchi ikkita aylana ichki chizilgan. Kichik aylananing radiusi ga teng. Katta aylananing radiusini toping.

A) 3r

B) 2r

C) 5r

D) 4r

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12. 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) 2

B) 4

C) 1

D) 3

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13. Tarkibida 85% suv bo‘lgan 0,5 t sellyuloza qorishmasida 75% suv bo‘lgan qorishma olish uchun necha kg suvni bug‘lantirish kerak?

A) 100

B) 400

C) 300

D) 200

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14. Abituriyentga 36 ta masala berildi. To‘g‘ri yechilgan har biriga 3 ball beriladi. Noto‘g‘risiga 2 ball chegiriladi. 88 ball to‘plashi uchun o‘quvchi nechta masalani to‘g‘ri yechishi kerak?

A) 38

B) 32

C) 34

D) 30

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15. bo‘lsa, ifodaning qiymatini toping

A) 3/16

B) 2/3

C) 15/16

D) 13/16

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16. Geometrik progressiyada dastlabki to‘rtta hadlari mos ravishda 6; 24; 96; bo‘lsa, ni toping.

A) 15

B) 22

C) 16

D) 14

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17. P(x) ko‘phadni x-a ga bo‘lgandagi qoldiqni toping.

A) P(x)

B) P(a)

C) P(x-a)

D) 0

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18. Asoslari 18 va 12 ga teng bo‘lgan teng yonli trapetsiyaning diagonallari o‘zaro perpendikulyar. Trapetsiyaning yuzini toping

A) 225

B) 400

C) 150

D) 125

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19. Tenglamani yeching: |x+6|=|x+10|

A) -8

B) 4

C) -6

D) 6

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20. Hovuzga uchta quvur o‘tkazilgan. Birinchisi hovuzni 12 soatda, ikkinchisi 8 soatda to‘ldiradi. Uchinchisi hovuzni 1 sutkada bo‘shatadi. Agar uchala quvur birgalikda ochib qo‘yilsa, bo‘sh hovuzning yarmi qancha vaqt(soat)da to‘ladi?

A) 2

B) 3

C) 1,5

D) 2,5

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21. Ifodaning eng kichik qiymatini toping: