9-sinf Matematika olimpiada №2

Avgust 19, 2024

36 Ko'rishlar 1 izoh

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Vaqtingiz tugadi!

9-sinf Matematika olimpiada №2

2019-yil tuman bosqichida tushgan savollar

1 / 25

1. Hisoblang:

A) 1,5

B) 0,5

C) 1

D) 5

2 / 25

2. Agar bo‘lsa, ni hisoblang.

A) ±4

B) 3

C) -4

D) 4

3 / 25

3. stemadan ni toping.

A) 7/11

B) 7/3

C) 3/7

D) 11/7

4 / 25

4. f(x) funksiyani toping.

A) 1/x

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

C) 1/(1-x)

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

5 / 25

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

A) –cos40°

B) cos40°

C) –sin40°

D) sin40°

6 / 25

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

A) 7

B) 27

C) 24

D) 20

7 / 25

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

A) -20

B) -5

C) -40

D) -10

8 / 25

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

A) 18

B) 15

C) 5

D) 29

9 / 25

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

A) 1

B) 2

C) 3

D) 4

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

A) 84

B) 99

C) 55

D) 12√3

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11. 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) 2

D) 4

12 / 25

12. 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) 2

D) 3

13 / 25

13. Tenglamalar sistemasi nechta yechimga ega?

A) 6

B) 1

C) 2

D) 4

14 / 25

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) 21

B) 12

C) 14

D) 16

15 / 25

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

A) a = 1

B) a=2 ; a = -3

C) a ≠1

D) a=−3

17 / 25

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

A) 8

B) 20/69

C) 0

D) -48

18 / 25

18. 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) 64

C) 16

D) 36

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19. 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) 135

D) 126

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

A) -2

B) -4

C) 8

D) 6

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21. 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) 9

C) 12

D) 6

22 / 25

22. 20 dan 250 gacha sonlarichida 4 ga bo`linadigan, lekin 6 ga bo`linmaydigan nechta natural son bor?

A) 48

B) 30

C) 39

D) 33

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

A) 4

B) 3

C) 1

D) 2

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24. Teng yonli ABC (AC=BC) uchburchakning AC tomonida D nuqta olingan. K - BD kesma va AH balandlik kesishgan nuqta. Agar AD=AK bo‘lsa, u holda DBA burchakni toping.

A) 45°

B) 30°

C) 60°

D) 75°

25 / 25

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

A) 76,4

B) 86,4

C) 72,4

D) 84,6

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