Barcha fanlardan online testlar

Matematika olimpiada Tuman 2022-2023 o'quv yili

11-sinf Matematika olimpiada №4

InfoMaster

Avgust 19, 2024

39 Ko'rishlar 2 izohlar

SaqlashSaqlanganOlib tashlandi 0

11-sinf Matematika olimpiada №4

2022-yil 12-oktyabr:

2022-2023 o'quv yilida tuman bosqichida tushgan savollar!

1 / 30

1. 7⁵⁰ning oxirgi ikkita raqamini toping.

A) 49

B) 25

C) 35

D) 51

2 / 30

2. GH kesmani O nuqta, G nuqtadan boshlab hisoblaganda, 5 : 7 kabi, P nuqtaesa 5:11 kabi nisbatda bo’ladi. O va P nuqtalar orasidagi masofa 30 sm bo’lsa, GH kesmaning uzunligini toping.

A) 288

B) 234

C) 18

D) 72

3 / 30

3. Ifodani soddalashtiring:

A) √(a²-1)

B) 0

C) 1+√(a+1)

D) 1−√(a-1)

4 / 30

4. Berilgan natural son 400 dan katta va 500 dan kichik. Uning raqamlari yig‘indisi 9 va u berilgan sonning raqamlari teskari tartibda yozilgan sonning 47/36 qismiga teng. Berilgan sonni toping.

A) 433

B) 443

C) 444

D) 423

5 / 30

5. Agar ?(?) = ?²⁰²¹ + 3?²⁰²⁰ + 3?²⁰¹⁹ − ?²⁰¹⁸ + 1 bo‘lsa, ni toping.

A) 1

B) 0

C) 2

D) 3

6 / 30

6. To‘g‘ri burchakli uchburchakning bir burchagi 60° ga teng. Bu burchakdan chiqarilgan bissektrisaning uzunligi 2 m. Uchburchakning gipotenuzasi uzunligini toping.

A) √5

B) √5 +1

C) √3

D) 2√3

7 / 30

7. y = x² − 2x + 3 parabolaga y = 3 to‘g‘ri chiziqqa nisbatan simmetrik bo‘lgan parabola tenglamasini tuzing.

A) y =-x² + 2x + 3

B) y = x² − 2x - 3

C) y =-x² + 2x - 3

D) y = -x² − 2x + 3

8 / 30

8. Arifmetik progressiyada ?₂ = 12, ?₇ − ?₄ = 9 bo‘lsa, ?₁₉ni toping.

A) 54

B) 56

C) 63

D) 61

9 / 30

9. formula bilan berilgan sonli ketma-ketlikning dastlabki 20 ta hadining o‘rta arifmetigini toping.

A) 22/3

B) 20/3

C) 23/6

D) 25/6

10 / 30

10. O‘tkir burchakli uchburchakning ikki tomon uzunliklari ayirmasi 8, bu tomonlarning uchinchi tomondagi proyeksiyalari mos ravishda 8 va 20 ga teng. Berilgan uchburchakka tashqi chizilgan aylana radiusini toping.

A) 37/3

B) 83/6

C) 35/3

D) 85/6

11 / 30

11. Agar bo‘lsa sin²α ni toping.

A) A

B) B

C) D

D) C

12 / 30

12. (3 − cos²x− 2sinx)(lg²y+ 2lgy+ 4) ≤ 3 bo‘lsa, sin²x+ 20y+ 1 ni toping.

A) 3

B) 5

C) 4

D) 2

13 / 30

13. Tengsizliklar sistemasinining butun yechimlari sonini toping.

A) 5

B) 7

C) 6

D) 4

14 / 30

14. ABC uchburchakda ctgA+ctgB= 3 va AB= 12 bo‘lsa, ABC uchburchak yuzini toping.

A) 521

B) 123

C) 216

D) 265

15 / 30

15. Soatning minut mili 144° ga burilganda, soatning soat mili qanday burchakka burilada?

A) 12°

B) 9°

C) 18°

D) 6°

16 / 30

16. BC = BE = CD ,∠DAE = 20°, ∠BCD = 60° ,∠ADE = ? (chizmaga qarang)

A) 30°

B) 50°

C) 40°

D) 20°

17 / 30

17. bo’lsa, P(−1) ni toping.

A) 100

B) 115

C) 120

D) 105

18 / 30

18. ABCD - kvadrat, AC-diagonal. Agar AE=BE+CE ( a + b = c ) bo‘lsa, ∠AEB burchakni toping(chizmaga qarang!).

A) 45

B) 55

C) 50

D) 60

19 / 30

19. ∠CAD = 2∠ACD, AC =13a, BD = 5a va AB = CD bo’lsa, 20⋅cos ∠ACD ni toping.(chizmaga qarang!)

A) 16

B) 15

C) 19

D) 17

20 / 30

20. Soddalashtiring:

A) −сtg²1°

B) -1

C) −сtg1°

D) −сtg13°

21 / 30

21. Natural son roppa-rosa 2 ta tub bo‘luvchiga, bu sonning kvadrati esa 45 ta turli natural bo‘luvchiga ega. Berilgan sonning kubi eng ko‘pi bilan nechta natural bo‘luvchiga ega bo‘lishi mumkin?

A) 41

B) 40

C) 81

D) 91

22 / 30

22. Raqamlari yig‘indisi 10 dan kam bo‘lmagan, raqamlari ko‘paytmasi esa 10 dan katta bo‘lmagan uch xonali sonlar nechta?

A) 100

B) 89

C) 106

D) 96

23 / 30

23. Muntazam uchburchak 36 ta yuzi 1 ga teng bo‘lgan kichkina muntazam uchburchaklardan iborat (chizmaga qarang!). ABC uchburchak yuzini toping.

A) 10

B) 12

C) 13

D) 11

24 / 30

24. u_nketma-ketlik quyidagicha berilgan: u₁ = 1, u_n+1 = u_n + 8n. U holda, u₅₀ −u₃₀ ni toping.

A) 6230

B) 6320

C) 5320

D) 6320

25 / 30

25. ?(3) ∙ (? − 2) + ?(? − 1) = 3? bo‘lsa, ?(1) ni toping.

A) 3

B) 6

C) 4

D) 2

26 / 30

26. Soddalashtiring: bunda, |?| < 1.

A) 2-2a

B) -2

C) 4-2a

D) 2a+4

27 / 30

27. Doskaga ?₁, ?₂, ?₃, . . . , ?₂₀₀ sonlari yozilgan. Ma’lumki, ?₁ = 3, ?₂ = 9. Agar ixtiyoriy n natural son uchun ?_n+2 = ?_n+1 − ?_n tenglik o‘rinli bo‘lsa, ?₂₀₀ ni toping.