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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

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1. funksiyaning qiymatlar to‘plamini toping.

A) [-2;2]

B) [1;4]

C) [-1;3]

D) [1;3]

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2. 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) 27

B) 216

C) 100

D) 45

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3. 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) 433

B) 443

C) 444

D) 423

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

A) -4⁵

B) -2⁹

C) -2¹¹

D) -4⁴

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5. Hisoblang:

A) 0

B) 2

C) 1.5

D) 1

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6. 100 dan kichik musbat butun sonlar orasida 2 ga ham, 3 ga ham, 7 ga ham bo‘linmaydigan nechta son mavjud?

A) 29

B) 26

C) 28

D) 27

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

A) 120/17

B) 260/17

C) 60/7

D) 20/3

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

A) 14 sm

B) 7 sm

C) 12 sm

D) 18 sm

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

A) 90°

B) 30°

C) 120°

D) 60°

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10. Soddalashtiring:

A) I

B) IV

C) III

D) II

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

A) 12

B) 14

C) 16

D) 15

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12. 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) 3

C) 6

D) 4

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13. Soddalashtiring:

A) 3cosx

B) cosx

C) 3cos2x

D) 3sin2x

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14. Soddalashtiring:

A) 2

B) 2sinα

C) cosα

D) 1

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15. 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) 6

D) 12

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16. Hisoblang:

A) 81/109

B) 95/243

C) 85/104

D) 172/249

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

A) 1

B) 3

C) 2

D) 4

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18. (?²+ 4? + 8)² + 3?³ + 14?² + 24? = 0 tenglamaning ildizlari yig’indisini toping.

A) -11

B) -7

C) -6

D) -5

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19. 80 ni qanday musbat butun songa bo‘lganda, hosil bo‘ladigan qoldiq bo‘linmaning 25%iga teng bo‘ladi?

A) 19

B) 11

C) 10

D) 21

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

A) 1

B) 2

C) 4

D) √5

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21. bo‘lsa, ?² + ?² ni toping.

A) 65/21

B) 20.2

C) 61/20

D) 20

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22. Tenglamalar sistemasi nechta yechimga ega?

A) 8

B) 10

C) 12

D) 6

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

A) √5 + 6

B) 6√5 + 1

C) 3√5 + 6

D) 6√5 + 2

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24. 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) 73

C) 65

D) 55

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

A) 0.6

B) 0.5

C) 0.2

D) 0.8