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

1 / 25

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) 400

B) 200

C) 100

D) 300

2 / 25

2. Yuzi 96 sm², balandliklari 6 sm va 8 sm bo‘lgan parallelogrammning perimetrini toping.

A) 50 sm

B) 56 sm

C) 40 sm

D) 20 sm

3 / 25

3. Agar bo‘lsa, ni hisoblang.

A) 3

B) ±4

C) -4

D) 4

4 / 25

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

A) -10

B) -5

C) -20

D) -40

5 / 25

5. 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) 2

C) 3

D) 4

6 / 25

6. Tenglamalar sistemasi nechta yechimga ega?

A) 1

B) 2

C) 6

D) 4

7 / 25

7. 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) 64

B) 36

C) 4

D) 16

8 / 25

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

A) –cos40°

B) cos40°

C) –sin40°

D) sin40°

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9. 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) 6

B) 4

C) 12

D) 9

10 / 25

10. 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) 145

B) 180

C) 126

D) 135

11 / 25

11. 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) 16

B) 12

C) 14

D) 21

12 / 25

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

A) 27

B) 24

C) 7

D) 20

13 / 25

13. 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

14 / 25

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

A) 20/69

B) 0

C) 8

D) -48

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15. tengsizlikni yeching.

A) (-∞;-1/2)∪(-1/2;3)∪(3;∞)

B) (-∞;-1/2)∪(-1/2;∞)

C) (-∞;3)∪(3;∞)

D) xℇR

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16. f(x) funksiyani toping.

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

B) 1/(1-x)

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

D) 1/x

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

A) 18

B) 29

C) 15

D) 5

18 / 25

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

A) 8

B) 6

C) -2

D) -4

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19. Sonlarni o`sish tartibida yozing.

A) c

B) a

C) b

D) c

20 / 25

20. 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) 3

C) 1

D) 2

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

A) 4

B) 1

C) 2

D) 3

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

A) a = 1

B) a ≠1

C) a=2 ; a = -3

D) a=−3

23 / 25

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

A) 39

B) 30

C) 33

D) 48

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

A) 1

B) 3

C) 4

D) 2

25 / 25

25. olti xonali son 72 ga bo’linsa, ? + ? ni toping.

A) 15

B) 12

C) 10

D) 13

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