9-sinf Matematika olimpiada №2

Avgust 19, 2024

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9-sinf Matematika olimpiada №2

2019-yil tuman bosqichida tushgan savollar

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1. 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) 100

C) 300

D) 400

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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) 48

C) 65

D) 60

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3. 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) 3

C) 1

D) 4

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4. 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) 126

B) 135

C) 180

D) 145

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

A) -20

B) -10

C) -5

D) -40

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6. 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) 4

B) 16

C) 64

D) 36

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

A) a=2 ; a = -3

B) a=−3

C) a = 1

D) a ≠1

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

A) 8

B) 6

C) -4

D) -2

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9. 20 dan 250 gacha sonlarichida 4 ga bo`linadigan, lekin 6 ga bo`linmaydigan nechta natural son bor?

A) 30

B) 48

C) 39

D) 33

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

A) 24

B) 27

C) 7

D) 20

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11. f(x) funksiyani toping.

A) 1/(1-x)

B) 1/x

C) (1-x)/(1+x)

D) (1+x)/(1-x)

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

A) 5

B) 15

C) 18

D) 29

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13. 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) 4

B) 2

C) 3

D) 5

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

A) 99

B) 12√3

C) 84

D) 55

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15. 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) 2

C) 1

D) 3

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

A) 0

B) 8

C) 20/69

D) -48

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17. 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) 12

B) 21

C) 14

D) 16

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18. tengsizlikni yeching.

A) (-∞;-1/2)∪(-1/2;∞)

B) (-∞;3)∪(3;∞)

C) xℇR

D) (-∞;-1/2)∪(-1/2;3)∪(3;∞)

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

A) –sin40°

B) cos40°

C) sin40°

D) –cos40°

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

A) III

B) II

C) IV

D) I

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

A) 4

B) 3

C) 2

D) 1

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22. Sonlarni o`sish tartibida yozing.

A) c

B) c

C) b

D) a

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23. ax²+bc+c=0 kvadrat tenglama bitta manfiy, bitta musbat ildizga ega bo`lsa, quyidagilardan qaysibiri to`g`ri?(D=b²−4ac)

A) 4

B) 1

C) 3

D) 2

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24. ∠ABC = 90°, AD=2√6, CE=2√3, AG=GC, DF=FE bo‘lsa, FG ni toping.

A) 3

B) 2

C) 1

D) 4

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25. ABC teng yonli uchburchakning AC asosida D nuqta olingan, bunda CD = 2 va CL bissektrisa (L ∈ AB) DL kesmaga perpendikulyar. AL ni toping.

A) 3

B) 1

C) 5

D) 2

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