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Matematika olimpiada Viloyat 2021-2022 o'quv yili

10-sinf Matematika olimpiada №3

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Avgust 19, 2024

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10-sinf Matematika olimpiada №3

2021-2022 o'quv yili viloyat 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) a<0

B) a<1

C) 0<a<2

D) 0<a<1

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2. Agar f(g(x))=x²-6x+6 va f(x)=x−3 funksiyalar berilgan bo`lsa, g(x) funksiya ko`rinishini aniqlang.

A) (x-3)²

B) (x+3)²

C) x²-12-3

D) x²+12x+3

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3. ABCD to‘rtburchakda А va В burchaklar- to‘g‘ri, tg∠D = 3/4 va ВС = AD/2 = АВ + 2 bo‘lsa, АС ni toping.

A) 9

B) 10

C) 15

D) 8

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4. Soddalashtiring: (4cos² 9° −3)(4cos² 27° −3)·ctg9°

A) 1

B) tg9°

C) 2cos² 9°

D) sin18°

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

A) 5

B) 6

C) 4

D) 7

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6. Tenglamalar sistemasi nechta yechimga ega?

A) 8

B) 12

C) 6

D) 10

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7. englikni qanoatlantiradigan ? ning eng kichik qiymatini toping.

A) 3

B) 1

C) -1

D) 0

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8. 10²⁰²² − 2²⁰²¹ ayirmani 24 ga bo‘lgandagi qoldiqni toping.

A) 8

B) 16

C) 0

D) 12

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9. ?(?) = ?⁵ − 7?⁴ + 3?³ − ? + 2 ko‘phadni ?² + ? ga bo‘lgandagi qoldiqni aniqlang.

A) 10? + 2

B) 6? + 2

C) 4? + 2

D) 8? + 2

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10. Agar bo‘lsa, ?(0) − ?(5) ayirmani toping.

A) -25

B) -27

C) -26

D) -24

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11. bo‘lsa ? ning qiymatini toping.

A) 37

B) 12

C) 25

D) 40

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12. Agar ?₁ = 6? − 6 va у₂//?₁ hamda у₂ to‘g‘ri chiziq ?(6; 6) nuqtadan o‘tsa, ?₂ ni toping.

A) 6? − 24

B) −6? + 6

C) 6? − 30

D) −6? + 42

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13. ABCD to‘rtburchakda АВ = CD = 9 va bu to‘rtburchakka radiusi 4 ga teng aylana ichki chizilgan. ABCD to‘rtburchak yuzini toping.

A) 72

B) 144

C) 81

D) 36

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14. Agar ni toping.

A) 0.81

B) 0.96

C) 0.9

D) 0.8

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15. (?² − 2? + 3)(?² + 6? + 12) = 6 bo‘lsa, ? + ? ni toping.

A) 2

B) -2

C) 3

D) -3

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16. Tenglamani yeching: 3^x+3 + 8·3^x+2 = 33

A) 0

B) -1

C) -2

D) 1

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17. Ayirmasi noldan farqli bo‘lgan arifmetik progressiyaning 4-hadidan boshlab 14- hadigacha bo‘lgan hadlar yig‘indisi 77 ga teng. Progressiyaning 7 ga teng bo‘lgan had nomerini toping.

A) 10

B) 8

C) 9

D) 11

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18. ?(? − 1) = 2?(5? + 4) va ?(2? − 1) = 4? + 4 bo‘lsa, ?(?) ni toping

A) 20x+48

B) 0

C) x+25

D) 20x+50

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19. a,b,c−ABC uchburchakning tomonlari. Agar a⁴ + b⁴ + c⁴ + 32 = 2(a²b² + b²c² + a²c²) bo‘lsa, ABC uchburchak yuzini toping.

A) √3

B) 2√2

C) √2

D) 1

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20. Agar bo‘lsa, |xyz| ni toping.

A) 100

B) 500

C) 1000

D) 800

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

A) 4√21

B) √21

C) 35

D) 2√21

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22. Agar cos ∠A = 1/5 va sin∠B = 1/2 bo‘lsa, АВС uchburchakning mos ravishda А va В uchlaridan tushirilgan balandliklar nisbatini toping.

A) 2/5

B) 5√6/24

C) 5√2/5

D) 5√3/12

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

A) 17

B) 16

C) 15

D) 14

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24. Qavariq to‘rtburchakning diagonallari 3 va 4 ga teng. Agar qarama qarshi tomonlarining o‘rtalarini tutashtirishdan hosil bo‘lgan kesmalar uzunliklari o‘zaro teng bo‘lsa, qavariq to‘rtburchakning yuzini toping.

A) 5

B) 6

C) 8

D) 7

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25. x, y sonlari (x² + 1)(y² + 1) + 2(x − y)(1 − xy) = 4(1 + xy) tenglikni qanoatlantiradi |1 + x| ∙ |1 − y| ni toping.

A) 9

B) 3

C) 2

D) 1