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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. ko‘phadning barcha koeffitsientlari va ozod hadining yig‘indisini toping.

A) 245

B) -238

C) 125

D) -247

2 / 30

2. Perimetri 4 ga o`tkir burchagi 30^oga va shu burchak qarshisidagi tomoni √3 ga teng bo`lgan uchburchakka ichki chizlgan aylana radiusini toping.

A) (1+√3)/2

B) 4√3+7

C) 7-4√3

D) (√3-1)/2

3 / 30

3. |x²+2x-8|=3a tenglama a ning qanday qiymatlarida 3 ta haqiqiy yechimga ega bo`ladi.

A) a>3, a=0

B) 1

C) (0;3)

D) a=3

4 / 30

4. Teng yonli АВС uchburchakda: АВ = ВС = 25 sm va АС = 14 sm. ВС tomonga AD balandlikning D asosida urinuvchi va АС tomon o‘rtasidan o‘tuvchi aylana radiusini toping.

A) 3

B) 175/48

C) 177/48

D) 211/47

5 / 30

5. Soddalashtiring:

A) cosx

B) 3sin2x

C) 3cos2x

D) 3cosx

6 / 30

6. ?(3) ∙ (? − 2) + ?(? − 1) = 3? bo‘lsa, ?(1) ni toping.

A) 3

B) 2

C) 4

D) 6

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7. 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) 85/6

B) 35/3

C) 83/6

D) 37/3

8 / 30

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

A) 45

B) 60

C) 50

D) 55

9 / 30

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

A) 89

B) 96

C) 100

D) 106

10 / 30

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

A) 5320

B) 6320

C) 6230

D) 6320

11 / 30

11. Agar ifodaning qiymatini toping.

A) 0.8

B) 20

C) 0.05

D) 4

12 / 30

12. 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) 2√3

D) √3

13 / 30

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

A) 13/3

B) 10/3

C) 8/3

D) 16/3

14 / 30

14. 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) 18

C) 15

D) 20

15 / 30

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

A) 521

B) 265

C) 123

D) 216

16 / 30

16. Agar bo‘lsa sin²α ni toping.

A) B

B) C

C) A

D) D

17 / 30

17. Hisoblang:

A) D

B) A

C) C

D) B

18 / 30

18. 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) 12

B) 6

C) 8

D) 10

19 / 30

19. Tengsizliklar sistemasinining butun yechimlari sonini toping.

A) 7

B) 5

C) 4

D) 6

20 / 30

20. 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) 91

B) 40

C) 81

D) 41

21 / 30

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

A) 12

B) 10

C) 14

D) 8

22 / 30

22. 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

23 / 30

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

A) 12

B) 10

C) 13

D) 11

24 / 30

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

A) 15

B) 17

C) 16

D) 19

25 / 30

25. bo’lsa, P(−1) ni toping.

A) 100

B) 105

C) 115

D) 120

26 / 30

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

A) 9°

B) 6°

C) 12°

D) 18°

27 / 30

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

A) 23/6

B) 22/3

C) 25/6

D) 20/3

28 / 30

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

A) 4-2a

B) 2-2a

C) -2

D) 2a+4

29 / 30

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

A) 40°

B) 20°

C) 50°

D) 30°

30 / 30

30. 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.