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Matematika olimpiada Tuman 2022-2023 o'quv yili

10-sinf Matematika olimpiada №4

InfoMaster

Avgust 19, 2024

250 Ko'rishlar 200 izohlar

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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. a ning qanday qiymatlarida $4x^{2}-4(a-1)x+1=0$ kvadrat tenglamaning ildizlari yig‘indisi manfiy bo‘ladi?

A) 0<a<2

B) a<1

C) 0<a<1

D) a<0

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2. Agar x²(a²+b²+9)+2(a+b+3)x+3=0 tenglama haqiqiy yechimga ega bo`lsa, a+b ni toping.

A) 3

B) 2

C) 4

D) 6

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3. bo'lsa kasrning qiymatini hisoblang.

A) 2-√11

B) √11+1

C) √11-2

D) √11-1

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4. Uchburchak tomonlarining uzunliklari berilgan tenglamaning ildizlariga mos keladi. ?³ − 24?² + 183? − 440 = 0. Uchburchakning yuzini hisoblang.

A) 35

B) √21

C) 4√21

D) 2√21

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5. Agar ? > 0, ? + ?² = 7,25; ?² − ? = 2 va ?² = √(? − 1) ∙ √(2 − ?) bo‘lsa, ?(√(? − 1) + √(2 − ?)) ning qiymatini toping.

A) 7

B) 6

C) 5

D) 4

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6. Chizmada ABCD −parallelolgramm. DE ni ntoping.

A) 9

B) 6

C) 4

D) 5

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

A) 40

B) 54

C) 36

D) 48

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8. Soddalashtiring:

A) 2a

B) a+b

C) a-b

D) 2b

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9. Tenglamani yeching:

A) 4

B) 5

C) 3

D) 2

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

A) 2 va 3

B) 3

C) 3 va 10

D) 3 va 15

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

7 ∆ 1 operatsiya natijasini toping.

A) 86

B) 125

C) 32

D) 592

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12. ?³?³ = 1024 tenglikni qanoatlantiruvchi nechta (?; b) butun sonlar juftligi mavjud?

A) 3

B) 2

C) 4

D) 5

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

A) 20

B) 10

C) 5

D) 40

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

A) 5

B) 2

C) 4

D) 3

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

A) 2√45

B) √65

C) √25

D) 36

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16. tenglama nechta haqiqiy yechimga ega?

A) 3

B) 1

C) 4

D) 2

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

A) III

B) IV

C) II

D) I

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

A) y = x² − 8x − 2

B) y = x² − 8x + 14

C) y = x² + 8x + 2

D) y = x² + 8x − 14

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19. Soddalashtiring: bunda, |?| < 3

A) 9

B) 9-2?

C) 1-2?

D) 2? − 9

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

A) 2

B) 6

C) 5

D) 3

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21. ∠BAD= ∠ABD= 20∘, ∠DBC= 110∘, ∠BCD= 30∘ va AB= 2, CD=?

A) 2

B) 3

C) 1

D) 4

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22. 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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23. 1,2,3,4…..,2021,2022 sonlar orasidan nechtasi 3 ga ham, 7 ga ham bo‘linmaydi?

A) 1098

B) 1156

C) 1084

D) 1128

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24. Tenglamani yeching:

A) 15/17

B) -1

C) 8/17

D) 0

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

A) 21

B) 19

C) 20

D) 18

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26. Agar bo'lsa, ni toping.

A) 4.5

B) 3.5

C) 5

D) 4

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27. 4 ga karrali va o‘nli yozuvida 4, 5, 6, 8 raqamlari bo‘lmagan to‘rt xonali sonlar nechta?

A) 150

B) 210

C) 120

D) 180

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

A) 4

B) 53

C) 49

D) 51

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29. Agar ni toping.

A) 4

B) 0.16

C) 8

D) 0.8

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30. ABCD qavariq to‘rtburchakda ∠BAD= ∠CDA= 60∘, ∠BDA= ∠CAB, AB= 2 va CD= 9 bo‘lsa, AD ni toping.

A) 12

B) 6

C) 9

D) 11

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