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

A) 16

B) 14

C) 15

D) 22

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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) 35

B) 65

C) 48

D) 60

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3. bo‘lsa, ifodaning qiymatini toping

A) 13/16

B) 3/16

C) 15/16

D) 2/3

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4. Ifodaning eng kichik qiymatini toping:

A) 4

B) -12

C) 12

D) -4

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

A) 0

B) P(a)

C) P(x)

D) P(x-a)

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6. 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) 3

B) 1

C) 2

D) 4

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7. 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) 1/27

C) -1/9

D) -1/3

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8. Hisoblang:

A) 1

B) 5

C) 1,5

D) 0,5

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

A) 20 sm

B) 40 sm

C) 50 sm

D) 56 sm

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

A) -6

B) 4

C) -8

D) 6

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11. 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) 2,5

C) 1,5

D) 3

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12. 60⁰ li burchakka bir-biriga tashqaridan urinuvchi ikkita aylana ichki chizilgan. Kichik aylananing radiusi ga teng. Katta aylananing radiusini toping.

A) 4r

B) 3r

C) 2r

D) 5r

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

A) 8

B) 3

C) 6

D) 5

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

A) 0

B) -1

C) 2

D) 1

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15. Agar bo‘lsa, ni hisoblang.

A) -4

B) 3

C) ±4

D) 4

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

A) 200

B) 300

C) 100

D) 400

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17. ni hisoblang.

A) -2

B) 2

C) 3

D) 4

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18. 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’tkir burchakli

D) O’tmas burchakli

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19. stemadan ni toping.

A) 3/7

B) 11/7

C) 7/11

D) 7/3

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20. Tenglamaning natural sonlardagi yechimida ni toping:

A) 5

B) 4

C) 3

D) 2

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

A) 48

B) 44

C) 34

D) 50

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22. 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) 32

B) 30

C) 38

D) 34

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23. Agar bo‘lsa, ko‘paytmani hisoblang.