Barcha fanlardan online testlar

Matematika olimpiada Tuman 2019-2020 o'quv yili

11-sinf Matematika olimpiada №2

InfoMaster

Avgust 19, 2024

109 Ko'rishlar 3 izohlar

SaqlashSaqlanganOlib tashlandi 2

Tomonidan yaratilgan InfoMaster

11-sinf Matematika olimpiada №2

2019-yil tuman bosqichida tushgan savollar

1 / 25

1. Beshyulduzning uchidagi burchaklarining yig‘indisini toping.

A) 270°

B) 180°

C) 240°

D) 90°

2 / 25

2. 3²⁰¹⁷ sonning oxirgi ikkita raqamini toping.

A) 83

B) 13

C) 03

D) 63

3 / 25

3. 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) 100

B) 27

C) 216

D) 45

4 / 25

4. 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) 288

C) 72

D) 234

5 / 25

5. ifodani soddalshtiring

A) 2cosα

B) cosα

C) 1

D) 2sinα

6 / 25

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

A) 70%

B) 61%

C) 60%

D) 71%

7 / 25

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

A) 13

B) 11

C) 12

D) 10

8 / 25

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

A) [−2;0]

B) [2;∞)

C) (−∞;−2]

D) [−2;∞)

9 / 25

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

A) 3(1−a)

B) (1−a)(1+b)

C) 1+b

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

10 / 25

10. funksiyaning boshlang`ich funksiyasini toping.

A) II

B) IV

C) III

D) I

11 / 25

11. 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) 52

B) 51

C) 50

D) 49

12 / 25

12. ni hisoblang.

A) 12

B) -13

C) 13

D) -12

13 / 25

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

A) 24sin7xsin5x

B) 24sin5xcos7x

C) −24sin7xcos5x

D) 24cos7xcos5x

14 / 25

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

A) −7cos5x−5cos7x+c

B) 7sin5x−5sin7x+c

C) 7sin5x+5sin7x+C

D) 7cos5x−5cos7x+c

15 / 25

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

A) 5 va 7

B) −5 va 7

C) −7 va −5

D) −7 va 5

16 / 25

16. 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) 25/12

B) 15/7

C) 2√2

D) 2

17 / 25

17. 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) (√3-1)/2

B) 4√3+7

C) 7-4√3

D) (1+√3)/2

18 / 25

18. 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

19 / 25

19. 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) 10

C) 15

D) 20

20 / 25

20. |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

21 / 25

21. 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) 2√2−1

C) 6-2√3

D) 4√3-6

22 / 25

22. Tenglamani yeching: