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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. bo‘lsa, nimaga teng?

A) 3

B) 7

C) 5

D) 9

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2. 2, 3, 4, 5, 6, 7, 8, 9, 10 sonlariga bo‘lganda mos ravishda 1, 2, 3, 4, 5, 6, 7, 8, 9 qoldiqlar hosil bo‘ladigan eng kichik natural sonni toping

A) 1519

B) 2519

C) 5039

D) 1019

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

A) π/12+πk/2; k∈Z)

B) π/12+2πk; k∈Z

C) π/12+πk; k∈Z

D) π/6+πk; k∈Z

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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) 1

B) 4√3-6

C) 6-2√3

D) 2√2−1

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5. 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) 4√3+7

B) 7-4√3

C) (1+√3)/2

D) (√3-1)/2

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6. 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) 10

B) 15

C) 20

D) 18

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7. ifodani soddalshtiring

A) 1

B) 2sinα

C) 2cosα

D) cosα

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8. funksiyaning aniqlanish sohasini toping.

A) (-∞;4/3)

B) (-∞;2/3)∪(2/3;∞)

C) (2/3;∞)

D) (-∞;4/3)∪(4/3;∞)

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9. Tenglamani yeching:

A) πk; π−arcctg4+πk; k∈Z

B) π −arcctg4+πk; k∈Z

C) arccos0,8+2πk; k∈Z

D) πk; −arcctg4+πk; k∈Z

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10. 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) 72

D) 18

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

A) [2;∞)

B) (−∞;−2]

C) [−2;∞)

D) [−2;0]

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

A) π/4

B) π/2

C) π/3

D) 0

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

A) 7sin5x−5sin7x+c

B) −7cos5x−5cos7x+c

C) 7sin5x+5sin7x+C

D) 7cos5x−5cos7x+c

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

A) 12

B) 13

C) 10

D) 11

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

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

B) 3(1−a)

C) (1−a)(1+b)

D) 1+b

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16. 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) 52

D) 51

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17. Ifodani soddalashtiring:

A) √(a²-1)

B) 1−√(a-1)

C) 1+√(a+1)

D) 0

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18. funksiyaning boshlang`ich funksiyasini toping.

A) I

B) II

C) III

D) IV

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19. 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) 2

B) 25/12

C) 2√2

D) 15/7

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

A) 24cos7xcos5x

B) 24sin7xsin5x

C) −24sin7xcos5x

D) 24sin5xcos7x

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

A) 5 va 7

B) −7 va −5

C) −7 va 5

D) −5 va 7

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22. 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.