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

A) 34

B) 48

C) 50

D) 44

2 / 25

2. ni hisoblang.

A) 3

B) -2

C) 4

D) 2

3 / 25

3. stemadan ni toping.

A) 11/7

B) 7/11

C) 3/7

D) 7/3

4 / 25

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

A) -2

B) -4

C) 6

D) 8

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5. tengsizlikni yeching.

A) (-∞;-1/2)∪(-1/2;3)∪(3;∞)

B) xℇR

C) (-∞;-1/2)∪(-1/2;∞)

D) (-∞;3)∪(3;∞)

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6. Agar cheksiz kamayuvchi geometrik progressiyaning hadlari yig`indisi ga teng bo`lsa, uning hadlari kublari yig`indisining hadlari kvadratlari yig`indisiga nisbatini toping.

A) 3

B) 4

C) 2

D) 1

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7. 20 dan 250 gacha sonlarichida 4 ga bo`linadigan, lekin 6 ga bo`linmaydigan nechta natural son bor?

A) 39

B) 30

C) 48

D) 33

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

A) 20/69

B) 0

C) -48

D) 8

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9. 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) 126

C) 135

D) 145

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

A) -10

B) -5

C) -40

D) -20

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11. 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) 6

C) 12

D) 9

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12. Sonlarni o`sish tartibida yozing.

A) b

B) a

C) c

D) c

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

A) 3

B) 1

C) 4

D) 2

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14. 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) 12

C) 16

D) 21

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15. 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) 64

C) 4

D) 36

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

A) 18

B) 15

C) 29

D) 5

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17. Tenglamalar sistemasi nechta yechimga ega?

A) 1

B) 4

C) 6

D) 2

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

A) 24

B) 7

C) 20

D) 27

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

A) 1

B) 4

C) 3

D) 2

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

A) cos40°

B) –cos40°

C) –sin40°

D) sin40°

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23. 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) 3

B) 5

C) 4

D) 2

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24. y = −3x − 10 va y = 0,5x −3 to‘g‘ri chiziqlar va absissa o‘qi bilan chegaralangan uchburchak yuzini toping.

A) 18,6

B) 56/3

C) 28/3

D) 9,6

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25. ning qiymatini toping

A) 3

B) 1

C) 7

D) 5

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