Barcha fanlardan online testlar

Matematika olimpiada Viloyat 2021-2022 o'quv yili

11-sinf Matematika olimpiada №3

InfoMaster

Avgust 19, 2024

13 Ko'rishlar 1 izoh

SaqlashSaqlanganOlib tashlandi 0

11-sinf Matematika olimpiada №3

2021-2022 o'quv yilida viloyat bosqichida tushgan savollar

1 / 25

1. tenglama nechta natural yechimga ega?

A) 1

B) 4

C) 2

D) 3

2 / 25

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

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

B) (1−a)(1+b)

C) 3(1−a)

D) 1+b

3 / 25

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

A) 2

B) 1

C) 3

D) 0

4 / 25

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

A) 8

B) 6

C) 10

D) 12

5 / 25

5. Quyidagi sonlar orasidan musbat sonni aniqlang.

A) B

B) D

C) A

D) C

6 / 25

6. Tenglamalar sistemasi nechta yechimga ega?

A) 10

B) 6

C) 12

D) 8

7 / 25

7. Soddalashtiring:

A) 2

B) 1

C) 2sinα

D) cosα

8 / 25

8. АВС uchburchak ∠C=60° burchagining bissektrisasi 5√3 ga teng. Agar АС : ВС = 5 :2 bo‘lsa, ВС ni toping.

A) A

B) D

C) C

D) B

9 / 25

9. Soddalashtiring:

A) 3sin2x

B) 3cosx

C) cosx

D) 3cos2x

10 / 25

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

A) -2¹¹

B) -4⁵

C) -2⁹

D) -4⁴

11 / 25

11. 100 dan kichik musbat butun sonlar orasida 2 ga ham, 3 ga ham, 7 ga ham bo‘linmaydigan nechta son mavjud?

A) 28

B) 27

C) 29

D) 26

12 / 25

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

A) 20/3

B) 60/7

C) 260/17

D) 120/17

13 / 25

13. 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) 444

B) 433

C) 423

D) 443

14 / 25

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

A) 16

B) 15

C) 12

D) 14

15 / 25

15. Aylananing ОА, ОВ, ОС radiuslari o‘tkazilgan. Agar bo‘lsa, АОВ burchakni toping.

A) 30°

B) 90°

C) 60°

D) 120°

16 / 25

16. 80 ni qanday musbat butun songa bo‘lganda, hosil bo‘ladigan qoldiq bo‘linmaning 25%iga teng bo‘ladi?

A) 21

B) 11

C) 10

D) 19

17 / 25

17. (?²+ 4? + 8)² + 3?³ + 14?² + 24? = 0 tenglamaning ildizlari yig’indisini toping.

A) -7

B) -5

C) -6

D) -11

18 / 25

18. 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) 6√5 + 2

D) √5 + 6

19 / 25

19. Soddalashtiring:

A) II

B) IV

C) I

D) III

20 / 25

20. 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) 4/3

B) √5/2

C) √6/2

D) 1.4

21 / 25

21. 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) 73

D) 65

22 / 25

22. Hisoblang:

A) 1.5

B) 2

C) 0

D) 1

23 / 25

23. 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) 3

B) 4

C) 5

D) 6

24 / 25

24. Hisoblang: (1 − tg5°)(1 − tg20°)2 + 2(2tg20° + tg5°)

A) 1

B) 2

C) 4

D) 3

25 / 25

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