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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. Tenglamaning natural sonlardagi yechimida ni toping:

A) 5

B) 4

C) 3

D) 2

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

A) P(x)

B) P(a)

C) 0

D) P(x-a)

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3. Hisoblang:

A) 1,5

B) 1

C) 0,5

D) 5

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

A) 44

B) 50

C) 48

D) 34

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5. 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) 34

B) 30

C) 38

D) 32

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6. Yuzi 96 sm², balandliklari 6 sm va 8 sm bo‘lgan parallelogrammning perimetrini toping.

A) 20 sm

B) 56 sm

C) 50 sm

D) 40 sm

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7. bo‘lsa, ifodaning qiymatini toping

A) 2/3

B) 3/16

C) 13/16

D) 15/16

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8. 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) 3

D) 1

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

A) -6

B) -8

C) 6

D) 4

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

A) 22

B) 15

C) 14

D) 16

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12. 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) O’tmas burchakli

B) Bunday uchburchak yo’q

C) To‘g‘ri burchakli

D) O’tkir burchakli

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13. 60⁰ li burchakka bir-biriga tashqaridan urinuvchi ikkita aylana ichki chizilgan. Kichik aylananing radiusi ga teng. Katta aylananing radiusini toping.

A) 2r

B) 5r

C) 4r

D) 3r

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

A) 150

B) 225

C) 125

D) 400

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

A) 60

B) 35

C) 48

D) 65

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

A) 8

B) 5

C) 3

D) 6

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17. Ifodaning eng kichik qiymatini toping:

A) 12

B) -4

C) -12

D) 4

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18. 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) 2,5

B) 2

C) 3

D) 1,5

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19. Agar bo‘lsa, ni hisoblang.