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Matematika olimpiada Tuman 2022-2023 o'quv yili

11-sinf Matematika olimpiada №4

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Avgust 19, 2024

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11-sinf Matematika olimpiada №4

2022-yil 12-oktyabr:

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

1 / 30

1. To‘g‘ri burchakli uchburchakda AC=3, BC=4, CD-balandlik va CE-bissektrisa. DE ni toping.

A) 15/31

B) 21

C) 23/35

D) 12/35

2 / 30

2. y=6sin2x+sin12x funksiyaning hosilasini toping.

A) 24sin7xsin5x

B) −24sin7xcos5x

C) 24sin5xcos7x

D) 24cos7xcos5x

3 / 30

3. Agar 2^a=27, 3^c=16 bo’lsa a ∙ ? ning qiymatini toping.

A) 10

B) 13

C) 11

D) 12

4 / 30

4. Tenglama nechta yechimga ega? Bunda, x ∈ (1; 47)

A) 16

B) 12

C) 15

D) 14

5 / 30

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

A) 1

B) 0

C) 3

D) 2

6 / 30

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

A) 96

B) 106

C) 89

D) 100

7 / 30

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

A) 17

B) 16

C) 15

D) 19

8 / 30

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

A) 4-2a

B) 2a+4

C) 2-2a

D) -2

9 / 30

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

A) 12

B) 11

C) 13

D) 10

10 / 30

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

A) 25/6

B) 22/3

C) 20/3

D) 23/6

11 / 30

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

A) 45

B) 50

C) 55

D) 60

12 / 30

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

A) 123

B) 521

C) 265

D) 216

13 / 30

13. Hisoblang:

A) A

B) D

C) C

D) B

14 / 30

14. Nargizada 2 ta olma va 3 ta nok bor. U 5 kun ketma-ket har kuni singliga bittadan meva beradi. Bu ishni necha usul bilan amalga oshirish mumkin?

A) 6

B) 10

C) 12

D) 8

15 / 30

15. Soddalashtiring:

A) -1

B) −сtg1°

C) −сtg²1°

D) −сtg13°

16 / 30

16. 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) 81

B) 40

C) 41

D) 91

17 / 30

17. (3 − cos²x− 2sinx)(lg²y+ 2lgy+ 4) ≤ 3 bo‘lsa, sin²x+ 20y+ 1 ni toping.

A) 5

B) 4

C) 3

D) 2

18 / 30

18. Agar bo‘lsa sin²α ni toping.

A) A

B) C

C) D

D) B

19 / 30

19. Tenglamani yeching:

A) 0

B) ∅

C) 29/462

D) 10/21

20 / 30

20. Uchlari A(2; −3), B(6; −1), C(6; 4) va D(2; 2) nuqtalarda bo‘lgan ABCD to‘rtburchak yuzini toping.

A) 16

B) 15

C) 18

D) 20

21 / 30

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

A) √5 +1

B) √3

C) 2√3

D) √5

22 / 30

22. Agar ifodaning qiymatini toping.

A) 0.8

B) 0.05

C) 20

D) 4

23 / 30

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

A) 6320

B) 5320

C) 6320

D) 6230

24 / 30

24. ? soniga teskari bo‘lgan son ? ning 9% ini tashkil qiladi. ? ni toping. (?u yerda, ? > 0)

A) 16/3

B) 8/3

C) 13/3

D) 10/3

25 / 30

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

A) 30°

B) 40°

C) 50°

D) 20°

26 / 30

26. Soddalashtiring:

A) A

B) C

C) B

D) D

27 / 30

27. a²b⁵ = 6²⁰ tenglikni qanoatlantiruvchi nechta (?; ?) butun sonlar juftligi mavjud?

A) 12

B) 10

C) 8

D) 14

28 / 30

28. 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) 85/6

D) 35/3

29 / 30

29. ?(3) ∙ (? − 2) + ?(? − 1) = 3? bo‘lsa, ?(1) ni toping.

A) 4

B) 3

C) 2

D) 6

30 / 30

30. bo’lsa, P(−1) ni toping.