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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. va a,b>0 bo‘lsa, ifodaning eng kichik qiymatini toping.

A) 4

B) 2

C) 3

D) 1

2 / 25

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 / 25

3. Quyidagi sonlar orasidan musbat sonni aniqlang.

A) A

B) C

C) B

D) D

4 / 25

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

A) -2¹¹

B) -2⁹

C) -4⁴

D) -4⁵

5 / 25

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

A) 14 sm

B) 12 sm

C) 18 sm

D) 7 sm

6 / 25

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

A) 6√5 + 2

B) √5 + 6

C) 3√5 + 6

D) 6√5 + 1

7 / 25

7. Agar ? + 4/√?= 17 bo‘lsa, ? + 4√? ni toping.

A) 1

B) 2

C) 4

D) 3

8 / 25

8. 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) 5

B) 4

C) 6

D) 3

9 / 25

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

A) 15

B) 14

C) 16

D) 12

10 / 25

10. 100 dan kichik musbat butun sonlar orasida 2 ga ham, 3 ga ham, 7 ga ham bo‘linmaydigan nechta son mavjud?

A) 28

B) 29

C) 27

D) 26

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11. Hisoblang: 1 + 2 ∙ 2 + 3 ∙ 2² + 4 ∙ 2³+. … + 100 ∙ 2⁹⁹

A) D

B) C

C) A

D) B

12 / 25

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

A) 1

B) √5

C) 4

D) 2

13 / 25

13. Teng yonli АВС uchburchakda: АВ = ВС = 25 sm va АС = 14 sm. ВС tomonga AD balandlikning D asosida urinuvchi va АС tomon o‘rtasidan o‘tuvchi aylana radiusini toping.

A) 177/48

B) 175/48

C) 211/47

D) 3

14 / 25

14. 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) 65

B) 73

C) 53

D) 55

15 / 25

15. Soddalashtiring:

A) I

B) II

C) III

D) IV

16 / 25

16. bo‘lsa, ?² + ?² ni toping.

A) 20.2

B) 20

C) 61/20

D) 65/21

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

A) 3

B) 0

C) 1

D) 2

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

A) 0.8

B) 0.5

C) 0.6

D) 0.2

19 / 25

19. Soddalashtiring:

A) 3cosx

B) 3cos2x

C) 3sin2x

D) cosx

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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. Hisoblang:

A) 81/109

B) 95/243

C) 85/104

D) 172/249

22 / 25

22. Hisoblang:

A) 2

B) 0

C) 1.5

D) 1

23 / 25

23. Tenglamalar sistemasi nechta yechimga ega?

A) 6

B) 10

C) 12

D) 8

24 / 25

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

A) 10

B) 8

C) 12

D) 6

25 / 25

25. 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) 444

D) 433