10-sinf Matematika olimpiada №3

Tomonidan yaratilgan InfoMaster

2021-2022 o'quv yili viloyat bosqichida tushgan savollar.

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1. tenglama y ning qanday qiymatlarida o‘rinli.

A) 9

B) 3

C) 729

D) 343

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2. [2x-1]=x tenglamani butun yechimlar sonini toping. Bu yerda [a]− a sonining butun qismi.

A) 3 ta

B) 4 ta

C) 2 ta

D) 1 ta

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3. Tenglama nechta yechimga ega?

A) 4

B) 2

C) 3

D) 5

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

A) 5

B) 6

C) 7

D) 4

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5. Agar bo‘lsa, |xyz| ni toping.

A) 1000

B) 100

C) 800

D) 500

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6. 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) 1

D) 2

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7. 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) 5√3/12

B) 5√6/24

C) 5√2/5

D) 2/5

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8. ?(?) = ?⁵ − 7?⁴ + 3?³ − ? + 2 ko‘phadni ?² + ? ga bo‘lgandagi qoldiqni aniqlang.

A) 6? + 2

B) 10? + 2

C) 8? + 2

D) 4? + 2

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

A) −6? + 42

B) −6? + 6

C) 6? − 24

D) 6? − 30

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10. Agar

A) 0

B) 3π/2

C) π

D) π/2

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11. 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) 10

B) 15

C) 9

D) 8

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12. 10²⁰²² − 2²⁰²¹ ayirmani 24 ga bo‘lgandagi qoldiqni toping.

A) 16

B) 0

C) 12

D) 8

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

A) -24

B) -26

C) -25

D) -27

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

A) √21

B) 35

C) 2√21

D) 4√21

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

A) 16

B) 14

C) 17

D) 15

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16. ?(? − 1) = 2?(5? + 4) va ?(2? − 1) = 4? + 4 bo‘lsa, ?(?) ni toping

A) x+25

B) 20x+48

C) 20x+50

D) 0

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

A) -2

B) 1

C) 0

D) -1

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18. bo‘lsa ? ning qiymatini toping.

A) 12

B) 25

C) 37

D) 40

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19. englikni qanoatlantiradigan ? ning eng kichik qiymatini toping.

A) 0

B) 3

C) 1

D) -1

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

A) sin18°

B) 2cos² 9°

C) 1

D) tg9°

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21. Tenglamalar sistemasi nechta yechimga ega?

A) 10

B) 6

C) 12

D) 8

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

A) √2

B) 1

C) √3

D) 2√2

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

A) 36

B) 81

C) 72

D) 144

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24. (?² − 2? + 3)(?² + 6? + 12) = 6 bo‘lsa, ? + ? ni toping.

A) -2

B) 3

C) 2

D) -3

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25. 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) 7

C) 8

D) 6

Author: InfoMaster