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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. funksiyaning grafigi qaysi choraklardan o‘tadi?

A) I,II,III,IV

B) II,III

C) I,II

D) III,IV

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2. Koordinata boshidan o‘tuvchi, simmetriya o‘qi ordinata o‘qiga parallel, cho‘qqisi y=x va y+x-2=0 to‘g‘ri chiziqlar kesishgan nuqtada bo‘lgan parabolaning tenglamasini toping.

A) y=-x²-2x

B) y=-x²+2x

C) y=-x²+1

D) y=x²-2x

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

A) (0;3)

B) a=3

C) a>3, a=0

D) 1

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

A) 24cos7xcos5x

B) 24sin5xcos7x

C) −24sin7xcos5x

D) 24sin7xsin5x

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5. Tenglamani yeching:

A) πk; −arcctg4+πk; k∈Z

B) arccos0,8+2πk; k∈Z

C) πk; π−arcctg4+πk; k∈Z

D) π −arcctg4+πk; k∈Z

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6. 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) 5 va 7

D) −7 va 5

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

A) 1+b

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

C) (1−a)(1+b)

D) 3(1−a)

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

A) (−∞;−2]

B) [2;∞)

C) [−2;∞)

D) [−2;0]

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9. funksiyaning aniqlanish sohasini toping.

A) (-∞;4/3)∪(4/3;∞)

B) (2/3;∞)

C) (-∞;4/3)

D) (-∞;2/3)∪(2/3;∞)

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10. ni hisoblang.

A) 13

B) -13

C) 12

D) -12

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

A) 7sin5x−5sin7x+c

B) 7sin5x+5sin7x+C

C) −7cos5x−5cos7x+c

D) 7cos5x−5cos7x+c

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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/3

B) 0

C) π/2

D) π/4

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

A) 70%

B) 61%

C) 71%

D) 60%

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14. 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) (√3-1)/2

C) (1+√3)/2

D) 4√3+7

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15. 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) 51

B) 50

C) 52

D) 49

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16. Tengsizlikni yeching.

A) (5/3;2)

B) (1/2;∞)

C) (2/3;2)

D) (4/3;3)

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17. ifodani soddalshtiring

A) 2sinα

B) 2cosα

C) 1

D) cosα

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18. 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√2

B) 25/12

C) 15/7

D) 2

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19. 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) 216

B) 45

C) 100

D) 27

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20. 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) √30

B) √10

C) 12√30

D) 6

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21. 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) 10

C) 18

D) 20

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22. funksiyaning boshlang`ich funksiyasini toping.