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Matematika olimpiada Viloyat 2021-2022 o'quv yili

11-sinf Matematika olimpiada №3

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Avgust 19, 2024

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11-sinf Matematika olimpiada №3

2021-2022 o'quv yilida viloyat bosqichida tushgan savollar

1 / 25

1. To‘g‘ri burchakli uchburchakda AC=3, BC=4, CD-balandlik va CE-bissektrisa. DE ni toping.

A) 23/35

B) 15/31

C) 21

D) 12/35

2 / 25

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

A) −7 va −5

B) −5 va 7

C) −7 va 5

D) 5 va 7

3 / 25

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

A) 6√5 + 1

B) 3√5 + 6

C) √5 + 6

D) 6√5 + 2

4 / 25

4. To‘g‘ri burchakli uchburchakka ichki va tashqi chizilgan aylana radiuslari nisbati 2 : 5 bo‘lsa, uchburchakning katta o‘tkir burchagining kosinusini toping.

A) 0.2

B) 0.5

C) 0.6

D) 0.8

5 / 25

5. Hisoblang:

A) 1

B) 2

C) 1.5

D) 0

6 / 25

6. bo‘lsa, ?² + ?² ni toping.

A) 20.2

B) 65/21

C) 20

D) 61/20

7 / 25

7. (?²+ 4? + 8)² + 3?³ + 14?² + 24? = 0 tenglamaning ildizlari yig’indisini toping.

A) -11

B) -6

C) -5

D) -7

8 / 25

8. 80 ni qanday musbat butun songa bo‘lganda, hosil bo‘ladigan qoldiq bo‘linmaning 25%iga teng bo‘ladi?

A) 21

B) 10

C) 19

D) 11

9 / 25

9. Uchburchakning tomonlari 10, 24 va 26. Aylananing markazi uchburchakning katta tomonida yotadi va ikki kichik tomonlari bu aylanaga urinadi. Aylana radiusini toping.

A) 60/7

B) 120/17

C) 20/3

D) 260/17

10 / 25

10. АВCDE beshburchak berilgan, М, N, Р va Q nuqtalar —АВ, ВС, CD va DE tomonlarning o‘rtalari. Agar U va V — МP? va NQ ning o‘rtasi bo‘lsa, АЕ: UV nisbatni toping.

A) 6

B) 5

C) 3

D) 4

11 / 25

11. Berilgan natural son 400 dan katta va 500 dan kichik. Uning raqamlari yig‘indisi 9 va u berilgan sonning raqamlari teskari tartibda yozilgan sonning 47/36 qismiga teng. Berilgan sonni toping.

A) 443

B) 423

C) 433

D) 444

12 / 25

12. Agar ?(?) = ?²⁰²¹ + 3?²⁰²⁰ + 3?²⁰¹⁹ − ?²⁰¹⁸ + 1 bo‘lsa, ni toping.

A) 3

B) 0

C) 1

D) 2

13 / 25

13. Tenglama nechta yechimga ega? Bunda, x ∈ (1; 47)

A) 14

B) 16

C) 15

D) 12

14 / 25

14. Soddalashtiring:

A) 2

B) cosα

C) 1

D) 2sinα

15 / 25

15. Soddalashtiring:

A) IV

B) III

C) I

D) II

16 / 25

16. Ikki xonali sonni qandaydir natural songa bo‘lganda bo‘linmada 3 va qoldiqda 8 hosil bo‘ladi. Agar bo‘linuvchining raqamlari o‘rni almashtirilsa va bo‘luvchi son o‘zgarishsiz qoldirilsa, u holda bo‘linmada 2 va qoldiqda 5 hosil bo‘ladi. Bo‘linuvchning dastlabki qiymatini toping.

A) 53

B) 55

C) 65

D) 73

17 / 25

17. Soddalashtiring:

A) 3sin2x

B) 3cosx

C) 3cos2x

D) cosx

18 / 25

18. Funksiyaning eng kichik qiymatini toping. ?(?) = (2? + 6)⁵ − 4(2? + 6)⁴, bunda |? + 3| ≤ 2.

A) -2¹¹

B) -4⁵

C) -2⁹

D) -4⁴

19 / 25

19. Hisoblang:

A) 81/109

B) 172/249

C) 95/243

D) 85/104

20 / 25

20. ABC uchburchakning AC tomonida shunday D nuqta olinganki, bunda ∠ABC=∠BDC, 5AB=4BD. Agar BC=10 bo‘lsa, ACni toping.

A) 6

B) 12

C) 10

D) 8

21 / 25

21. Sektor perimetri 28 sm ga teng, uning yuzi esa 49 sm2. Sektor yoyining uzunligini toping.

A) 7 sm

B) 18 sm

C) 12 sm

D) 14 sm

22 / 25

22. Tenglamalar sistemasi nechta yechimga ega?

A) 12

B) 6

C) 10

D) 8

23 / 25

23. Aylanaga АВС uchburchak ichki chizilgan. Uchburchakning СС1medianasining davomi aylanani ? nuqtada kesib o‘tadi. ni toping.

A) 4

B) 2

C) √5

D) 1

24 / 25

24. Quyidagi sonlar orasidan musbat sonni aniqlang.

A) D

B) C

C) A

D) B

25 / 25

25. To‘g‘ri burchakli uchburchak o‘tkir burchaklari yarimlarining tangenslari ko‘paytmasi 1/6 ga teng bo‘lsa, uchburchak o‘tkir burchaklarining kosinuslari yig‘indisini toping.

A) 1.4

B) 4/3

C) √6/2

D) √5/2