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Matematika olimpiada Tuman 2022-2023 o'quv yili

10-sinf Matematika olimpiada №4

InfoMaster

Avgust 19, 2024

27 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. Sonlarni o‘sish tartibida joylashtiring: $a=sin,b=cos22,c=sin61^{0}$

A) c,b,a

B) b,a,c

C) b,c,a

D) a,c,b

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2. Agar f(x+1) =7+3x funksiya uchun f (a)=2 tenglik o`rinli bo`lsa, a ning qiymatini toping.

A) 10

B) -2/3

C) 12

D) 8

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3. Uchburchakning ikkita burchagi mos ravishda 38^o va 52^oga teng. Uchinchi burchagi uchidan tushirilgan bissektrisa va mediana orasidagi burchakni toping.

A) 14°

B) 7°

C) 10°

D) 17°

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

A) 4√21

B) 2√21

C) 35

D) √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) 6

B) 4

C) 7

D) 5

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

A) 6

B) 2

C) 3

D) 5

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

A) 36

B) 48

C) 54

D) 40

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

A) 51

B) 49

C) 53

D) 4

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9. ?³?³ = 1024 tenglikni qanoatlantiruvchi nechta (?; b) butun sonlar juftligi mavjud?

A) 4

B) 3

C) 2

D) 5

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

A) 10

B) 20

C) 5

D) 40

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12. Agar bo'lsa, ni toping.

A) 3.5

B) 4.5

C) 4

D) 5

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

A) 4

B) 49

C) 51

D) 53

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14. Tenglamani yeching:

A) 5

B) 3

C) 4

D) 2

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15. Chizmada ABCD −parallelolgramm. DE ni ntoping.

A) 6

B) 5

C) 9

D) 4

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16. 4 ga karrali va o‘nli yozuvida 4, 5, 6, 8 raqamlari bo‘lmagan to‘rt xonali sonlar nechta?

A) 120

B) 150

C) 210

D) 180

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

A) 2√45

B) 36

C) √25

D) √65

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18. Agar ni toping.

A) 0.16

B) 8

C) 0.8

D) 4

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

A) IV

B) II

C) I

D) III

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

A) 20

B) 19

C) 21

D) 18

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21. Soddalashtiring: bunda, |?| < 3

A) 9-2?

B) 9

C) 2? − 9

D) 1-2?

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

A) 56

B) 55

C) 54

D) 53

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

A) 6

B) 12

C) 9

D) 11

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24. Tenglamani yeching:

A) -1

B) 0

C) 8/17

D) 15/17

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25. 1,2,3,4…..,2021,2022 sonlar orasidan nechtasi 3 ga ham, 7 ga ham bo‘linmaydi?

A) 1156

B) 1084

C) 1128

D) 1098

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26. 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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27. Uchinchi raqami to‘rtinchi raqamidan 1 ga kichik bo‘lgan to‘rt xonali sonlar sonini toping

A) 900

B) 810

C) 720

D) 990

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28. tenglama nechta haqiqiy yechimga ega?

A) 3

B) 2

C) 1

D) 4

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

A) 3

B) 4

C) 5

D) 2

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

A) 3 va 15

B) 3 va 10

C) 2 va 3

D) 3

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10-sinf Matematika olimpiada №4

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