9-sinf Matematika olimpiada №2

Avgust 19, 2024

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Vaqtingiz tugadi!

9-sinf Matematika olimpiada №2

2019-yil tuman bosqichida tushgan savollar

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1. 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) 1,5

B) 2,5

C) 3

D) 2

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

A) 1

B) 0

C) -1

D) 2

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4. Funksiya berilgan. f(f(−1)) ni toping.

A) 15

B) 5

C) 29

D) 18

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5. Sonlarni o`sish tartibida yozing.

A) c

B) b

C) a

D) c

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6. Agar bo’lsa , x va y sonlarning ko’paytmasini toping.

A) 6

B) 8

C) -2

D) -4

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7. Agar x²−8x+20z+4z²+41=0 tenglik o`rinli bo`lsa, xz ni toping.

A) -20

B) -40

C) -10

D) -5

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8. tengsizlikni yeching.

A) (-∞;3)∪(3;∞)

B) (-∞;-1/2)∪(-1/2;3)∪(3;∞)

C) xℇR

D) (-∞;-1/2)∪(-1/2;∞)

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9. Hisoblang: cos 10^o− 2 cos 50^o− cos 70^o

A) sin40°

B) cos40°

C) –sin40°

D) –cos40°

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10. ABC uchburchakda O nuqta AD medianava BE bissektrisalar kesishishnuqtasi. AOEva BOD uchburchaklar yuzlari mos ravishda 1 va 3 ga teng bo`lsa, EOC uchburchakning yuzini toping.

A) 5

B) 3

C) 4

D) 2

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11. Bahodir o`zidagi 411 dona yong`oqni 4 ta bolaga bo`lib berdi. Agar Sanjar va O`ktamning olgan yong`oqlari soni 2 va 3 sonlariga to`g`ri proporsional ,O`ktam va Sohibning yong`oqlari 7 va 5 sonlariga teskari proporsional , Sanjar va G`anisherning yong`oqlari esa 9 va 4 sonlariga teskari proporsional ekanligi ma`lum bo`lsa, G`anisher nechta yong`oq olgan?

A) 180

B) 145

C) 126

D) 135

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12. ABCD parallelogramda AB=10, AD=16. BC tomonga AE va DF bissektrisalar o`tkazilganbo`lib, ular G nuqtada kesishadi. E va F nuqtalar BC tomonda bo`lsa, AGD va FGE uchgburchaklar yuzalari nisbatini toping.

A) 16

B) 4

C) 64

D) 36

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13. Muntazam uchburchakning ichidagi nuqtadan tomonlarigacha bo`lgan masofalar yig`indisi 6 ga teng bo`lsa, uchburchak yuzini toping.

A) 55

B) 12√3

C) 99

D) 84

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14. Birinchi quvurdan ikkinchi quvurga qaraganda ikki barobar ko’p suv oqadi.Ikkalasi birgalikda bo’sh hovuzni 12 soatda to’ldiradi.Birinchi quvur hovuzning uchdan bir qismini necha soatda to’ldiradi?

A) 4

B) 12

C) 9

D) 6

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15. Agar arifmetik progressiyada bo`lsa, ayirmani toping.

A) 4

B) 1

C) 2

D) 3

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16. 20 dan 250 gacha sonlarichida 4 ga bo`linadigan, lekin 6 ga bo`linmaydigan nechta natural son bor?

A) 30

B) 48

C) 33

D) 39

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17. Agar f(x) = (a + b − 4)x³+ 2x²+ (b − 3)x +6 juftfunksiyaberilganbo’lsa, f(b) ningqiymatini toping.

A) 20

B) 27

C) 7

D) 24

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18. ABC uchburchakning AB tomonidan M va N nuqtalar shunday tanlab olinganki, BN=NM=MA. AC tomonidan K va L nuqtalar shunday tanlab olindiki AK=3KL=1,5LC bo'ldi. S_MNLK: S_MNLK=?

A) 0,5

B) 1

C) 3

D) 2

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19. (a²- 9)x = a²+ 2a - 3 tenglama a ningqandayqiymatidacheksizko’pyechimgaega?

A) a = 1

B) a=−3

C) a ≠1

D) a=2 ; a = -3

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20. x₀soni tenglamani ildizi bo`lsa, x²₀ -64 ni toping.

A) 20/69

B) -48

C) 8

D) 0

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21. Agar sin x + cos x = 1,04 tenglik o’rinli bo’lsa, x qaysi chorakda joylashgan?

A) II

B) IV

C) III

D) I

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22. ABCD trapetsiyaning yuzi 36 gateng, asoslari DC=6, AB=2. BC tomonidan E nuqta olingan bo’lib, BE=2EC bo’lsa, ADE uchbutchakning yuzini toping.

A) 14

B) 21

C) 12

D) 16

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23. f(x) funksiyani toping.

A) (1+x)/(1-x)

B) (1-x)/(1+x)

C) 1/(1-x)

D) 1/x

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24. Yozuvida faqat 0 va 1 raqamlaridan iborat va 225 ga qoldiqsiz bo‘linadigan eng kichik natural sonni toping.

A) 11 111 111 100

B) 11 111 111 101

C) 11 111 101 110

D) 11 111 111 110

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25. ABC uchburchakda AL bissektrisa o’tkazildi. AB va BL kesmalarda E va D nuqtalar mos ravishda shunday olinganki, DL=LC, ED∥ AC. Agar
AE=15, AC=12 ekani ma’lum bo’lsa, ED kesma uzunligini toping.

A) 4

B) 3

C) 2

D) 5

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