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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. 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’tkir burchakli

B) O’tmas burchakli

C) Bunday uchburchak yo’q

D) To‘g‘ri burchakli

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2. 60⁰ li burchakka bir-biriga tashqaridan urinuvchi ikkita aylana ichki chizilgan. Kichik aylananing radiusi ga teng. Katta aylananing radiusini toping.

A) 4r

B) 2r

C) 5r

D) 3r

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

A) 3

B) 8

C) 5

D) 6

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

A) 40 sm

B) 20 sm

C) 50 sm

D) 56 sm

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5. Tenglamaning natural sonlardagi yechimida ni toping:

A) 2

B) 5

C) 3

D) 4

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

A) 150

B) 125

C) 400

D) 225

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7. 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) 200

D) 300

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8. Ifodaning eng kichik qiymatini toping:

A) -12

B) 4

C) -4

D) 12

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9. 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) 2,5

D) 1,5

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

A) 1

B) -1

C) 0

D) 2

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

A) 1/33

B) -1

C) 31/35

D) 1/35

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

A) 22

B) 16

C) 15

D) 14

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13. stemadan ni toping.

A) 11/7

B) 7/3

C) 3/7

D) 7/11

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14. 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) -1/3

C) 1/27

D) 1/9

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15. bo‘lsa, ifodaning qiymatini toping

A) 15/16

B) 3/16

C) 13/16

D) 2/3

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

A) -8

B) -6

C) 6

D) 4

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

A) 34

B) 44

C) 50

D) 48

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18. Agar bo‘lsa, ni hisoblang.

A) 3

B) ±4

C) 4

D) -4

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

A) P(a)

B) P(x)

C) P(x-a)

D) 0

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21. ni hisoblang.

A) 2

B) 3

C) -2

D) 4

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22. 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) 4

D) 2

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

A) 35

B) 48

C) 60

D) 65

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24. Hisoblang: