9-sinf Matematika olimpiada №2

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9-sinf Matematika olimpiada №2

2019-yil tuman bosqichida tushgan savollar

1 / 25

1. Agar bo‘lsa, ko‘paytmani hisoblang.

A) 1/33

B) 1/35

C) -1

D) 31/35

2 / 25

2. Teng yonli trapetsiyaning diagonali uni ikkita teng yonli uchburchakka ajratadi. Trapetsiyaning burchaklarini toping.

1. $82^{0},98^{0}$

2. $135^{0},45^{0}$

3. $100^{0},80^{0}$

4. $72^{0},108^{0}$

A) 2

B) 3

C) 4

D) 1

3 / 25

3. Hisoblang:

A) 1,5

B) 5

C) 0,5

D) 1

4 / 25

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

A) -5

B) -10

C) -40

D) -20

5 / 25

5. Agar a-b =|x| + 3 bo’lsa a va b lar uchun to’g’ri munosabatni aniqlang.

A) a

B) a>b

C) a ≤ b

D) a=b+1

6 / 25

6. 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) 16

C) 64

D) 36

7 / 25

7. tengsizlikni yeching.

A) (-∞;-1/2)∪(-1/2;∞)

B) (-∞;-1/2)∪(-1/2;3)∪(3;∞)

C) xℇR

D) (-∞;3)∪(3;∞)

8 / 25

8. 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) 12

B) 21

C) 14

D) 16

9 / 25

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

A) 29

B) 5

C) 18

D) 15

10 / 25

10. 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) 2

B) 4

C) 5

D) 3

11 / 25

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

A) a=−3

B) a = 1

C) a=2 ; a = -3

D) a ≠1

12 / 25

12. f(x) funksiyani toping.

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

B) 1/x

C) 1/(1-x)

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

13 / 25

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

A) 4

B) 3

C) 2

D) 1

14 / 25

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

A) III

B) II

C) IV

D) I

15 / 25

15. Tenglamalar sistemasi nechta yechimga ega?

A) 1

B) 4

C) 6

D) 2

16 / 25

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

A) 84

B) 55

C) 99

D) 12√3

17 / 25

17. 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) 4

C) 3

D) 1

18 / 25

18. Sonlarni o`sish tartibida yozing.

A) b

B) c

C) c

D) a

19 / 25

19. 20 dan 250 gacha sonlarichida 4 ga bo`linadigan, lekin 6 ga bo`linmaydigan nechta natural son bor?

A) 33

B) 48

C) 39

D) 30

20 / 25

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

A) 20/69

B) -48

C) 8

D) 0

21 / 25

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

A) 6

B) 8

C) -4

D) -2

22 / 25

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

A) cos40°

B) –sin40°

C) sin40°

D) –cos40°

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

A) 4

B) 3

C) 1

D) 2

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24. ?, ?, ? sonlar to’plami ?⁴ − 2?², ?⁴ − 2?², ?⁴ − 2?² to’plami bilan almashtirildi. Natijada hosil bo’lgan to’plam avvalgisi bilan bir xil bo’ldi. Agar ?, ?, ? sonlarning yig’indisi (−3) ga teng ekani ma’lum bo’lsa, ?, ?, ? sonlar ko‘paytmasini toping.

A) 2

B) 0

C) -1

D) 1

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) 72,4

C) 84,6

D) 86,4

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