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Matematika olimpiada Tuman 2022-2023 o'quv yili

10-sinf Matematika olimpiada №4

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Avgust 19, 2024

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10-sinf Matematika olimpiada №4

2022-yil 12-oktabr:

2022-2023 o'quv yili tuman bosqichida tushgan savollar!

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1. Ninachi va chivin to‘g‘ri chiziq bo‘ylab harakatlanmoqda. Ninachi chivinni quvib yetmoqchi. Ninachining tezligi 1,2 m/s va chivinniki 30 sm/s. Necha sekunddan so‘ng ular orasidagi masofa 6,5 m dan 20 sm gacha qisqaradi?

A) 8 s

B) 6 s

C) 7 s

D) 5 s

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2. 2x²-2ax+1=0 kvadrat tenglama ildizlari uchun

tengliko`rinlibo`lsa, a ni toping.

A) 1

B) -3

C) 7

D) -1

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3. Ta`lim muassasida barcha o`quvchilar kamida bitta ingliz yoki nemis tilida so`zlashа oladilar. Ayrimlari ikkala tilni ham biladilar. O`quvchilarning 85%i ingliz tilini, 75%i nemis tilini biladilar. Ikkala tilni ham biladigan o`quvchilar barcha o`quvchilarning necha % ini tashkil etadi.

A) 50%

B) 60%

C) 70%

D) 65%

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4. tenglama nechta yechimga ega, agar x ∈ (0; 50)?

A) 16

B) 17

C) 14

D) 15

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5. ABC – gipotenuzasi AB bo‘lgan to‘g‘ri burchakli uchburchak. Gipotenuzaning ikki tomon davomida AB to‘g‘ri chiziqda AK = AC va BM = BC shartlar bilan kesmalar ajratilgan. KCM burchakni toping.

A) 90°

B) 120°

C) 150°

D) 135°

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6. Raqamlari yig‘indisi 3 ga teng bo‘lgan o‘n xonali natural sonlar nechta?

A) 55

B) 56

C) 54

D) 53

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7. y = x²− 2 parabolaga y = 2 to‘g‘ri chiziqqa nisbatan simmetrik bo‘lgan parabola tenglamasini tuzing.

A) y = x² − 8x + 14

B) y = x² − 8x − 2

C) y = x² + 8x − 14

D) y = x² + 8x + 2

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8. bo’lsa, (2? − 3)² ifodaning qiymatini toping.

A) 6

B) 5

C) 3

D) 2

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9. ?₁ va ?₂ sonlari ?² − 7? − 1 = 0 tenglama ildizlari bo‘lsa, ?²₁ + ?²₂ni toping.

A) 51

B) 53

C) 4

D) 49

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10. Agar ni toping.

A) 0.8

B) 0.16

C) 8

D) 4

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11. k parametrning qanday musbat qiymatida 20x²+ ?x + 5 = 0 tenglama bitta ildizga ega?

A) 20

B) 40

C) 5

D) 10

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12. bo‘lsa, f (5 − f (1− f (1− f (0)))) ni toping.

A) 21

B) 18

C) 19

D) 20

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13. Chizmada ABCD −parallelolgramm. DE ni ntoping.

A) 6

B) 9

C) 4

D) 5

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14. tenglama nechta haqiqiy yechimga ega?

A) 4

B) 1

C) 2

D) 3

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15. ? parametrning qanday musbat qiymatlarida ?² − (? + 3)? + 3? + 11 = 0 tenglamaning barcha ildizlari butun sonlardan iborat bo‘ladi?

A) 3 va 15

B) 3

C) 2 va 3

D) 3 va 10

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16. f(x) = ax² + b funksiya grafigi A(-1;5) va B(2;-1) nuqtalardan o‘tadi. f(5 − f(1)) ning qiymatini toping.

A) 2

B) 6

C) 7

D) 5

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17. 1,2,3,4…..,2021,2022 sonlar orasidan nechtasi 3 ga ham, 7 ga ham bo‘linmaydi?

A) 1156

B) 1084

C) 1098

D) 1128

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18. Soddalashtiring:

A) a-b

B) 2a

C) 2b

D) a+b

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19. Tenglamani yeching:

A) 0

B) 15/17

C) 8/17

D) -1

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20. Ikki son o’rtasidagi ∆ operatsiyasiga ko‘ra quyidagi natijalar olindi:

7 ∆ 1 operatsiya natijasini toping.

A) 86

B) 592

C) 32

D) 125

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21. Soddalashtiring: bunda, |?| < 3

A) 2? − 9

B) 1-2?

C) 9

D) 9-2?

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22. ?³?³ = 1024 tenglikni qanoatlantiruvchi nechta (?; b) butun sonlar juftligi mavjud?

A) 5

B) 4

C) 3

D) 2

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23. y = 4x² − 3x − 5 parabolaga x(0; 0) nuqtaga nisbatan simmetrik bo‘lgan parabola tenglamasini ko‘rsating.

A) y= 4x² + 3x - 5

B) y= -4x² − 3x - 5

C) y= 4x² − 3x + 5

D) y=-4x² − 3x+ 5

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24. tenglama bilan berilgan aylananing markazi koordinata tekisligining qaysi choragida yotadi?

A) II

B) IV

C) III

D) I

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25. ?₁ va ?₂ sonlari ?² − 7? − 1 = 0 tenglama ildizlari bo‘lsa, ?²₁ + ?²₂ni toping.

A) 51

B) 53

C) 49

D) 4

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26. ABCD qavariq to‘rtburchakka aylana ichki chizilgan. Agar АВ = 7, BC= 11 bo‘lsa, CD − AD ni toping.

A) 4

B) 5

C) 2

D) 3

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27. Chizmada AE = 2, BE= 6, DE= 3. Aylana diametrini toping.

A) √25

B) √65

C) 36

D) 2√45

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28. Qavariq o‘n ikki burchakning diagonallar sonini toping.

A) 36

B) 40

C) 48

D) 54

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29. Supermarketda reklama aksiyasi o‘tkazilmoqda: 3 ta shokolad sotib olgan xaridorga 4-shokolad sovg‘a tariqasida qo‘shib beriladi. Bitta shokolad narxi 28000 so‘m. Xaridor 300 000 so‘m evaziga eng ko‘pi bilan nechta shokolad xarid qila oladi?

A) 13

B) 14

C) 11

D) 12

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30. Tenglamani yeching: