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Matematika olimpiada Tuman 2019-2020 o'quv yili

11-sinf Matematika olimpiada №2

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Avgust 19, 2024

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11-sinf Matematika olimpiada №2

2019-yil tuman bosqichida tushgan savollar

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1. Beshyulduzning uchidagi burchaklarining yig‘indisini toping.

A) 90°

B) 240°

C) 270°

D) 180°

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2. va a,b>0 bo‘lsa, ifodaning eng kichik qiymatini toping.

A) 2

B) 4

C) 3

D) 1

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3. 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) 18

B) 234

C) 72

D) 288

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4. Radiusi 6 ga teng bo`lgan uchta aylana o`zaro tashqi urinishidan hosil bo`lgan egri chiziqli uchburchakka ichki chizilgan aylana radiusini toping.

A) 2√2−1

B) 6-2√3

C) 4√3-6

D) 1

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5. 3cos2x-3 sin2x=0 trigonometrik tenglamani yeching.

A) π/6+πk; k∈Z

B) π/12+πk; k∈Z

C) π/12+2πk; k∈Z

D) π/12+πk/2; k∈Z)

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6. f(x)=70cosxcos6x uchun boshlang`ich funksiya toping.

A) 7cos5x−5cos7x+c

B) 7sin5x+5sin7x+C

C) −7cos5x−5cos7x+c

D) 7sin5x−5sin7x+c

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

A) a=3

B) 1

C) a>3, a=0

D) (0;3)

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8. Tenglamani yeching: |x²-3x-2|=x²+3|x+2|+4

A) [−2;0]

B) [2;∞)

C) (−∞;−2]

D) [−2;∞)

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9. f(x)=x³/3-x²-35x+2 funksiya uchun f `(x)=0 bo`lsa x ni toping.

A) −7 va −5

B) −7 va 5

C) −5 va 7

D) 5 va 7

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

A) 24sin7xsin5x

B) 24sin5xcos7x

C) −24sin7xcos5x

D) 24cos7xcos5x

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11. a+b=−1 a+c=6 va b+c=1 bo`lsa, a² (3b+3c+2a)+b² (3a+3c+2b)+c² (3a+3b+2c) ning son qiymatini toping.

A) 45

B) 100

C) 27

D) 216

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12. Ifodani soddalashtiring:

A) 1+√(a+1)

B) 1−√(a-1)

C) √(a²-1)

D) 0

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13. Agar lg5=a va lg3=b bo`lsa, log₃₀⁡8 ni toping.

A) 1+b

B) 3(1−a)

C) (1−a)(1+b)

D) (3(1-a))/(1+b)

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14. ifodani soddalshtiring

A) 2sinα

B) 2cosα

C) cosα

D) 1

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15. Agar f(g(x))= − x+13 bo`lsa, f(x) va g(x) to`g`ri chiziqlar orasidagi burchakni toping .

A) π/2

B) π/3

C) π/4

D) 0

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16. 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) 7-4√3

B) (1+√3)/2

C) (√3-1)/2

D) 4√3+7

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17. Tenglamani yeching:

A) π −arcctg4+πk; k∈Z

B) arccos0,8+2πk; k∈Z

C) πk; π−arcctg4+πk; k∈Z

D) πk; −arcctg4+πk; k∈Z

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18. Asosi ga teng bo`lgan muntazam to`rtburchakli piramidaning uchidan o`tkazilgan kesma asos tomonini 2:4 nisbatda bo`ladi va asos tekisligi bilan 60^o li burchakhosilqiladi. Piramidahajmini toping.

A) 12√30

B) √30

C) 6

D) √10

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19. Bitta tekislikda yotuvchi n ta turli tog`ri chiziq o`tkazilgan. Ularning ixtiyoriy ikkitasi parallel emas va ixtiyoriy uchtasi bitta nuqtadan o`tmaydi ,ya`ni bitta nuqtada kesishmaydi. Bu to`g`ri chiziqlar tekislikni 1276 qismga ajratadi. n ni aniqlang?

A) 49

B) 50

C) 51

D) 52

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20. Bir savdogar 1 mеtrini 1200 tiyindan olgan matosini yuvib, kuritgandan so`ng 1800 tiyindan sotyapti. Mato yuvilib kuritilganidan so`ng 20 foizi qisqardi. Bularga ko`ra savdogar nеcha foiz foyda ko`radi?

A) 15

B) 18

C) 20

D) 10

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21. Poyezd 3 minutda 7 kilometrmasofani , motosikl 5 minutda 7 kilometrmasofanibosibo`tdi. Mototsikltezligipoyezdtezliginingnecha % initashkilqiladi?

A) 70%

B) 60%

C) 71%

D) 61%

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22. Tengsizlikni yeching.

A) (1/2;∞)

B) (4/3;3)

C) (2/3;2)

D) (5/3;2)

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

A) 10

B) 13

C) 11

D) 12

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24. funksiyaning boshlang`ich funksiyasini toping.

A) II

B) I

C) IV

D) III

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25. ABCD tetraedrning D uchidagi barcha yassi burchaklari to`g`ri. Shu tetraedrda kub shunday ichki chizilganki, kubning bitta uchi D nuqtada, unga qarama−qarshi uchi esa ABC yoqda yotibdi. Agar DA=5, DB=6 va DC=10 bo`lsa, kub qirrasining uzunligini toping.

A) 15/7

B) 2√2

C) 25/12

D) 2