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. Tenglamani yeching: |x+6|=|x+10|

A) -6

B) 4

C) -8

D) 6

2 / 25

2. P(x) ko‘phadni x-a ga bo‘lgandagi qoldiqni toping.

A) P(x-a)

B) P(x)

C) P(a)

D) 0

3 / 25

3. To‘g‘ri burchakli uchburchakka ichki chizilgan aylana urinish nuqtasida gipotenuzani 5 va 12 ga teng kesmalarga ajratadi. Uchburchak yuzini toping

A) 65

B) 48

C) 35

D) 60

4 / 25

4. 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) 1

B) 3

C) 0,5

D) 2

5 / 25

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

A) 55

B) 12√3

C) 84

D) 99

6 / 25

6. 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) 135

C) 126

D) 145

7 / 25

7. 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

8 / 25

8. Tenglamalar sistemasi nechta yechimga ega?

A) 6

B) 2

C) 1

D) 4

9 / 25

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

A) -48

B) 0

C) 8

D) 20/69

10 / 25

10. tengsizlikni yeching.

A) (-∞;3)∪(3;∞)

B) (-∞;-1/2)∪(-1/2;∞)

C) (-∞;-1/2)∪(-1/2;3)∪(3;∞)

D) xℇR

11 / 25

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

A) 1

B) 3

C) 4

D) 2

12 / 25

12. Sonlarni o`sish tartibida yozing.

A) b

B) a

C) c

D) c

13 / 25

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

A) -5

B) -40

C) -20

D) -10

14 / 25

14. f(x) funksiyani toping.

A) 1/x

B) 1/(1-x)

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

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

15 / 25

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

A) -2

B) 6

C) 8

D) -4

16 / 25

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

A) a = 1

B) a ≠1

C) a=−3

D) a=2 ; a = -3

17 / 25

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

A) 29

B) 15

C) 5

D) 18

18 / 25

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

A) 2

B) 3

C) 1

D) 4

19 / 25

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

A) III

B) IV

C) II

D) I

20 / 25

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

A) 20

B) 24

C) 7

D) 27

21 / 25

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

A) –cos40°

B) –sin40°

C) sin40°

D) cos40°

22 / 25

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

A) 39

B) 48

C) 33

D) 30

23 / 25

23. 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

24 / 25

24. ning qiymatini toping

A) 3

B) 7

C) 1

D) 5

25 / 25

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

A) 4

B) 2

C) 3

D) 1

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