Barcha fanlardan online testlar

Matematika olimpiada Viloyat 2021-2022 o'quv yili

11-sinf Matematika olimpiada №3

InfoMaster

Avgust 19, 2024

66 Ko'rishlar 1 izoh

SaqlashSaqlanganOlib tashlandi 0

11-sinf Matematika olimpiada №3

2021-2022 o'quv yilida viloyat bosqichida tushgan savollar

1 / 25

1. Koordinata boshidan o‘tuvchi, simmetriya o‘qi ordinata o‘qiga parallel, cho‘qqisi y=x va y+x-2=0 to‘g‘ri chiziqlar kesishgan nuqtada bo‘lgan parabolaning tenglamasini toping.

A) y=-x²+1

B) y=x²-2x

C) y=-x²-2x

D) y=-x²+2x

2 / 25

2. 3cos2x-3 sin2x=0 trigonometrik tenglamani yeching.

A) π/12+πk/2; k∈Z)

B) π/12+2πk; k∈Z

C) π/6+πk; k∈Z

D) π/12+πk; k∈Z

3 / 25

3. bo‘lsa, ?² + ?² ni toping.

A) 61/20

B) 65/21

C) 20.2

D) 20

4 / 25

4. Tenglamalar sistemasi nechta yechimga ega?

A) 6

B) 8

C) 10

D) 12

5 / 25

5. Hisoblang:

A) 2

B) 1

C) 0

D) 1.5

6 / 25

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) 27

D) 28

7 / 25

7. 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

8 / 25

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

A) -7

B) -11

C) -5

D) -6

9 / 25

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

A) 4

B) 2

C) 3

D) 1

10 / 25

10. Soddalashtiring:

A) 1

B) 2

C) 2sinα

D) cosα

11 / 25

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

A) -4⁴

B) -4⁵

C) -2⁹

D) -2¹¹

12 / 25

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

A) B

B) D

C) C

D) A

13 / 25

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

A) 6√5 + 1

B) 6√5 + 2

C) √5 + 6

D) 3√5 + 6

14 / 25

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

A) 30°

B) 60°

C) 90°

D) 120°

15 / 25

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

A) B

B) C

C) A

D) D

16 / 25

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

A) 4

B) 2

C) 3

D) 1

17 / 25

17. 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) 0.6

C) 0.2

D) 0.5

18 / 25

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

A) 16

B) 12

C) 15

D) 14

19 / 25

19. 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) 211/47

B) 175/48

C) 3

D) 177/48

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) √6/2

B) 4/3

C) 1.4

D) √5/2

21 / 25

21. 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) 444

C) 433

D) 423

22 / 25

22. Soddalashtiring:

A) II

B) I

C) III

D) IV

23 / 25

23. Hisoblang:

A) 85/104

B) 95/243

C) 172/249

D) 81/109

24 / 25

24. 80 ni qanday musbat butun songa bo‘lganda, hosil bo‘ladigan qoldiq bo‘linmaning 25%iga teng bo‘ladi?

A) 11

B) 19

C) 10

D) 21

25 / 25

25. 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) 20/3

C) 120/17

D) 260/17