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. bo‘lsa, ifodaning qiymatini toping

A) 15/16

B) 3/16

C) 13/16

D) 2/3

2 / 25

2. Rombning diagonallari 6 va 8 ga teng bo‘lsa, uning tomonini toping.

A) 5

B) 6

C) 8

D) 3

3 / 25

3. Agar (3-a)(3-b)(3-c)=(3+a)(3+b)(3+c) bo‘lsa, $(ab)^{-1}+(bc)^{-1}+(ac)^{-1}$ ni hisoblang. (Bunda $abc\neq 0$ ).

A) -1/9

B) 1/27

C) -1/3

D) 1/9

4 / 25

4. Tenglamalar sistemasi nechta yechimga ega?

A) 4

B) 2

C) 1

D) 6

5 / 25

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

A) 8

B) -4

C) -2

D) 6

6 / 25

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) 2

B) 3

C) 1

D) 4

7 / 25

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

A) 20

B) 24

C) 27

D) 7

8 / 25

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

A) 55

B) 99

C) 12√3

D) 84

9 / 25

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

A) 15

B) 18

C) 29

D) 5

10 / 25

10. 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) 4

C) 36

D) 16

11 / 25

11. 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) 4

B) 2

C) 3

D) 5

12 / 25

12. f(x) funksiyani toping.

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

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

C) 1/(1-x)

D) 1/x

13 / 25

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

A) a ≠1

B) a = 1

C) a=−3

D) a=2 ; a = -3

14 / 25

14. 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) 126

B) 180

C) 145

D) 135

15 / 25

15. tengsizlikni yeching.

A) (-∞;3)∪(3;∞)

B) (-∞;-1/2)∪(-1/2;3)∪(3;∞)

C) xℇR

D) (-∞;-1/2)∪(-1/2;∞)

16 / 25

16. 20 dan 250 gacha sonlarichida 4 ga bo`linadigan, lekin 6 ga bo`linmaydigan nechta natural son bor?

A) 33

B) 30

C) 39

D) 48

17 / 25

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

A) -48

B) 8

C) 0

D) 20/69

18 / 25

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

A) IV

B) II

C) I

D) III

19 / 25

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

A) 3

B) 2

C) 1

D) 4

20 / 25

20. Sonlarni o`sish tartibida yozing.

A) c

B) b

C) a

D) c

21 / 25

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

A) sin40°

B) –cos40°

C) –sin40°

D) cos40°

22 / 25

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

A) 2

B) 3

C) 4

D) 1

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

A) -5

B) -40

C) -20

D) -10

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24. To’g’riburchakli uchburchakning o’tkir burchaklaridan chiquvchi medianalar √156 va √89 ga teng bo’lsa, uchburchak gipotenuzasini toping.

A) 12

B) 14

C) 13

D) 15

25 / 25

25. Hisoblang

A) 15

B) 16

C) 18

D) 11

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