Barcha fanlardan online testlar

Matematika olimpiada Tuman 2022-2023 o'quv yili

11-sinf Matematika olimpiada №4

InfoMaster

Avgust 19, 2024

882 Ko'rishlar 2 izohlar

SaqlashSaqlanganOlib tashlandi 1

11-sinf Matematika olimpiada №4

2022-yil 12-oktyabr:

2022-2023 o'quv yilida tuman bosqichida tushgan savollar!

1 / 30

1. Agar va bo‘lsa, ni toping.

A) 11

B) 25

C) 31

D) 39

2 / 30

2. 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

3 / 30

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) 72

C) 288

D) 234

4 / 30

4. (?²+ 4? + 8)² + 3?³ + 14?² + 24? = 0 tenglamaning ildizlari yig’indisini toping.

A) -6

B) -7

C) -11

D) -5

5 / 30

5. Agar a = √5 + 1 va b = √5 − 1 bo‘lsa, 2a² − ab − a² ifodaning qiymatini toping.

A) 6√5 + 2

B) 3√5 + 6

C) √5 + 6

D) 6√5 + 1

6 / 30

6. Muntazam uchburchak 36 ta yuzi 1 ga teng bo‘lgan kichkina muntazam uchburchaklardan iborat (chizmaga qarang!). ABC uchburchak yuzini toping.

A) 12

B) 13

C) 10

D) 11

7 / 30

7. formula bilan berilgan sonli ketma-ketlikning dastlabki 20 ta hadining o‘rta arifmetigini toping.

A) 25/6

B) 20/3

C) 23/6

D) 22/3

8 / 30

8. bo’lsa, P(−1) ni toping.

A) 115

B) 100

C) 105

D) 120

9 / 30

9. Soddalashtiring:

A) -1

B) −сtg13°

C) −сtg²1°

D) −сtg1°

10 / 30

10. O‘tkir burchakli uchburchakning ikki tomon uzunliklari ayirmasi 8, bu tomonlarning uchinchi tomondagi proyeksiyalari mos ravishda 8 va 20 ga teng. Berilgan uchburchakka tashqi chizilgan aylana radiusini toping.

A) 85/6

B) 37/3

C) 83/6

D) 35/3

11 / 30

11. Tenglamani yeching:

A) 29/462

B) 0

C) 10/21

D) ∅

12 / 30

12. Soatning minut mili 144° ga burilganda, soatning soat mili qanday burchakka burilada?

A) 12°

B) 18°

C) 6°

D) 9°

13 / 30

13. Raqamlari yig‘indisi 10 dan kam bo‘lmagan, raqamlari ko‘paytmasi esa 10 dan katta bo‘lmagan uch xonali sonlar nechta?

A) 89

B) 106

C) 100

D) 96

14 / 30

14. Hisoblang:

A) D

B) C

C) B

D) A

15 / 30

15. a²b⁵ = 6²⁰ tenglikni qanoatlantiruvchi nechta (?; ?) butun sonlar juftligi mavjud?

A) 12

B) 10

C) 8

D) 14

16 / 30

16. Nargizada 2 ta olma va 3 ta nok bor. U 5 kun ketma-ket har kuni singliga bittadan meva beradi. Bu ishni necha usul bilan amalga oshirish mumkin?

A) 8

B) 6

C) 10

D) 12

17 / 30

17. Tengsizliklar sistemasinining butun yechimlari sonini toping.

A) 4

B) 7

C) 6

D) 5

18 / 30

18. Soddalashtiring:

A) A

B) B

C) D

D) C

19 / 30

19. Agar bo‘lsa sin²α ni toping.

A) B

B) A

C) C

D) D

20 / 30

20. ABCD - kvadrat, AC-diagonal. Agar AE=BE+CE ( a + b = c ) bo‘lsa, ∠AEB burchakni toping(chizmaga qarang!).

A) 45

B) 50

C) 60

D) 55

21 / 30

21. Uchlari A(2; −3), B(6; −1), C(6; 4) va D(2; 2) nuqtalarda bo‘lgan ABCD to‘rtburchak yuzini toping.

A) 15

B) 20

C) 16

D) 18

22 / 30

22. To‘g‘ri burchakli uchburchakning bir burchagi 60° ga teng. Bu burchakdan chiqarilgan bissektrisaning uzunligi 2 m. Uchburchakning gipotenuzasi uzunligini toping.

A) 2√3

B) √3

C) √5

D) √5 +1

23 / 30

23. Arifmetik progressiyada ?₂ = 12, ?₇ − ?₄ = 9 bo‘lsa, ?₁₉ni toping.

A) 54

B) 63

C) 61

D) 56

24 / 30

24. (3 − cos²x− 2sinx)(lg²y+ 2lgy+ 4) ≤ 3 bo‘lsa, sin²x+ 20y+ 1 ni toping.

A) 4

B) 5

C) 2

D) 3

25 / 30

25. ABC uchburchakda ctgA+ctgB= 3 va AB= 12 bo‘lsa, ABC uchburchak yuzini toping.

A) 521

B) 265

C) 123

D) 216

26 / 30

26. y = x² − 2x + 3 parabolaga y = 3 to‘g‘ri chiziqqa nisbatan simmetrik bo‘lgan parabola tenglamasini tuzing.

A) y = x² − 2x - 3

B) y =-x² + 2x + 3

C) y =-x² + 2x - 3

D) y = -x² − 2x + 3

27 / 30

27. Soddalashtiring: bunda, |?| < 1.

A) 2a+4

B) -2

C) 2-2a

D) 4-2a

28 / 30

28. Doskaga ?₁, ?₂, ?₃, . . . , ?₂₀₀ sonlari yozilgan. Ma’lumki, ?₁ = 3, ?₂ = 9. Agar ixtiyoriy n natural son uchun ?_n+2 = ?_n+1 − ?_n tenglik o‘rinli bo‘lsa, ?₂₀₀ ni toping.