9-sinf Matematika olimpiada №2

Avgust 19, 2024

16 Ko'rishlar 1 izoh

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Vaqtingiz tugadi!

9-sinf Matematika olimpiada №2

2019-yil tuman bosqichida tushgan savollar

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1. 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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2. ni hisoblang.

A) 3

B) -2

C) 4

D) 2

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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. 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) 9

D) 12

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5. Tenglamalar sistemasi nechta yechimga ega?

A) 2

B) 4

C) 1

D) 6

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

A) 1

B) 4

C) 3

D) 2

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7. tengsizlikni yeching.

A) (-∞;-1/2)∪(-1/2;3)∪(3;∞)

B) (-∞;3)∪(3;∞)

C) xℇR

D) (-∞;-1/2)∪(-1/2;∞)

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8. 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) 2

D) 4

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9. f(x) funksiyani toping.

A) 1/(1-x)

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

C) 1/x

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

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

A) –cos40°

B) sin40°

C) –sin40°

D) cos40°

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

A) -5

B) -20

C) -40

D) -10

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

A) 27

B) 7

C) 24

D) 20

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13. 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) 21

B) 12

C) 14

D) 16

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14. Sonlarni o`sish tartibida yozing.

A) a

B) c

C) c

D) b

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

A) 18

B) 29

C) 15

D) 5

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

A) 99

B) 12√3

C) 55

D) 84

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

A) II

B) I

C) IV

D) III

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

A) a=−3

B) a=2 ; a = -3

C) a ≠1

D) a = 1

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

A) 3

B) 4

C) 1

D) 2

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20. 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) 135

B) 145

C) 180

D) 126

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

A) 1

B) 2

C) 3

D) 4

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

A) -2

B) -4

C) 6

D) 8

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23. 20 dan 250 gacha sonlarichida 4 ga bo`linadigan, lekin 6 ga bo`linmaydigan nechta natural son bor?

A) 48

B) 33

C) 30

D) 39

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24. x, y, z tub sonlar uchun xyz = 5(x + y + z) bo’lsa, x² + y² + z² ni hisoblang.

A) 78

B) 55

C) 68

D) 70

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25. Massasi 228 g tuzli aralashma tarkibida 88,2% suv bor. Aralashma tarkibida 81% suv bo’lishi uchun qancha suvni bug’lantirish kerak?

A) 84,6

B) 86,4

C) 72,4

D) 76,4

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