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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.

1 / 25

1. Hisoblang:

A) 3

B) 2

C) 4

D) 1

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2. 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) 60%

B) 70%

C) 50%

D) 65%

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3. Tenglama nechta yechimga ega?

A) 3

B) 5

C) 2

D) 4

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

A) -26

B) -24

C) -25

D) -27

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5. Agar bo‘lsa, |xyz| ni toping.

A) 500

B) 1000

C) 800

D) 100

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

A) 6? − 30

B) −6? + 42

C) 6? − 24

D) −6? + 6

7 / 25

7. englikni qanoatlantiradigan ? ning eng kichik qiymatini toping.

A) -1

B) 3

C) 1

D) 0

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8. Agar ni toping.

A) 0.8

B) 0.81

C) 0.9

D) 0.96

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9. ?(? − 1) = 2?(5? + 4) va ?(2? − 1) = 4? + 4 bo‘lsa, ?(?) ni toping

A) 20x+48

B) x+25

C) 20x+50

D) 0

10 / 25

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

A) 1

B) 9

C) 3

D) 2

11 / 25

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

A) 1

B) tg9°

C) 2cos² 9°

D) sin18°

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12. bo‘lsa ? ning qiymatini toping.

A) 25

B) 40

C) 12

D) 37

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

A) 4

B) 7

C) 6

D) 5

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

A) 144

B) 81

C) 72

D) 36

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15. ?(?) = ?⁵ − 7?⁴ + 3?³ − ? + 2 ko‘phadni ?² + ? ga bo‘lgandagi qoldiqni aniqlang.

A) 8? + 2

B) 4? + 2

C) 6? + 2

D) 10? + 2

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16. ?² + |? − 3| ≤ |?2 + ?| − 3 tengsizlikni yeching.

A) x>3

B) x<0

C) x ≤ 3

D) 3 ≤ x

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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) 8

B) 9

C) 10

D) 11

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

A) √21

B) 2√21

C) 4√21

D) 35

19 / 25

19. 10²⁰²² − 2²⁰²¹ ayirmani 24 ga bo‘lgandagi qoldiqni toping.

A) 12

B) 16

C) 8

D) 0

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20. 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) 2/5

C) 5√6/24

D) 5√2/5

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21. 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) 8

C) 15

D) 10

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22. 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) 8

B) 6

C) 5

D) 7

23 / 25

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

A) -2

B) 1

C) 0

D) -1

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24. Agar