Barcha fanlardan online testlar

Matematika olimpiada Tuman 2019-2020 o'quv yili

11-sinf Matematika olimpiada №2

InfoMaster

Avgust 19, 2024

120 Ko'rishlar 3 izohlar

SaqlashSaqlanganOlib tashlandi 2

Tomonidan yaratilgan InfoMaster

11-sinf Matematika olimpiada №2

2019-yil tuman bosqichida tushgan savollar

1 / 25

1. Sonlarni kamayish tartibida joylashtiring:

A) b>c>a

B) c>a>b

C) c>b>a

D) a>b>c

2 / 25

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+1

B) y=-x²-2x

C) y=-x²+2x

D) y=x²-2x

3 / 25

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

A) 7sin5x+5sin7x+C

B) −7cos5x−5cos7x+c

C) 7cos5x−5cos7x+c

D) 7sin5x−5sin7x+c

4 / 25

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

A) 1

B) (0;3)

C) a=3

D) a>3, a=0

5 / 25

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

A) 61%

B) 70%

C) 60%

D) 71%

6 / 25

6. Tenglamani yeching:

A) πk; −arcctg4+πk; k∈Z

B) arccos0,8+2πk; k∈Z

C) π −arcctg4+πk; k∈Z

D) πk; π−arcctg4+πk; k∈Z

7 / 25

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

A) 24cos7xcos5x

B) 24sin5xcos7x

C) −24sin7xcos5x

D) 24sin7xsin5x

8 / 25

8. Ifodani soddalashtiring:

A) 1+√(a+1)

B) 1−√(a-1)

C) √(a²-1)

D) 0

9 / 25

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

A) 4√3-6

B) 1

C) 2√2−1

D) 6-2√3

10 / 25

10. 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) 27

B) 100

C) 45

D) 216

11 / 25

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

A) [−2;0]

B) [−2;∞)

C) (−∞;−2]

D) [2;∞)

12 / 25

12. 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

13 / 25

13. 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) 2

D) 15/7

14 / 25

14. 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

15 / 25

15. Tengsizlikni yeching.

A) (2/3;2)

B) (4/3;3)

C) (1/2;∞)

D) (5/3;2)

16 / 25

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

A) 13

B) 12

C) 10

D) 11

17 / 25

17. ni hisoblang.

A) -12

B) 12

C) -13

D) 13

18 / 25

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

A) (1−a)(1+b)

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

C) 3(1−a)

D) 1+b

19 / 25

19. funksiyaning aniqlanish sohasini toping.

A) (2/3;∞)

B) (-∞;2/3)∪(2/3;∞)

C) (-∞;4/3)

D) (-∞;4/3)∪(4/3;∞)

20 / 25

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) √10

B) 6

C) 12√30

D) √30

21 / 25

21. ifodani soddalshtiring

A) 1

B) 2cosα

C) 2sinα

D) cosα

22 / 25

22. 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

23 / 25

23. 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) 52

C) 50

D) 51

24 / 25

24. 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) 18

B) 20

C) 15

D) 10

25 / 25

25. 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