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Matematika olimpiada Viloyat 2021-2022 o'quv yili

9-sinf Matematika olimpiada №3.1

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Avgust 19, 2024

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9-sinf Matematika olimpiada №3.1

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

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1. P(x) ko‘phadni x-a ga bo‘lgandagi qoldiqni toping.

A) 0

B) P(a)

C) P(x)

D) P(x-a)

2 / 25

2. Agar f(x) = (a + b − 4)x³+ 2x²+ (b − 3)x +6 juftfunksiyaberilganbo’lsa, f(b) ningqiymatini toping.

A) 20

B) 27

C) 24

D) 7

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3. ABC uchburchakda AL bissektrisa o’tkazildi. AB va BL kesmalarda E va D nuqtalar mos ravishda shunday olinganki, DL=LC, ED∥ AC. Agar
AE=15, AC=12 ekani ma’lum bo’lsa, ED kesma uzunligini toping.

A) 5

B) 3

C) 4

D) 2

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4. Kenguru oldinga 1 metrga yoki 3 metrga sakraydi. U 10 metr masofani bosib o‘tishni xohlaydi. U bu ishni necha usulda amalga oshira oladi?

A) 55

B) 36

C) 28

D) 30

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5. Tenglama ildizlari yig‘indisini toping. (? − |?|)² + ? + |?| = 100 .

A) 45

B) 55

C) 50

D) 40

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6. Ucburchakning tomonlari 13; 14; 15 ga teng. Ichki chizilgan aylana radiusini toping.

A) 3.5

B) 4.5

C) 4.8

D) 4

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7. ?(?) = 6/(?−1) va ?(?) = 2? − 1. ?(?(2)) + ?(?(3)) + ?(?(2)) + ?(?(3)) ni toping.

A) 9.8

B) 18.2

C) 12.6

D) 11.4

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8. bo‘lsa, ? + ? ni toping.

A) 16

B) 12

C) 13

D) 11

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9. to‘g‘ri chiziqlar orasidagi burchakni toping.

A) 30°

B) 15°

C) 45°

D) 5°

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10. Agar ? + ? + ? = 0 bo‘lsa, ni soddalashtiring.

A) 1.2

B) 0

C) 1

D) 1.8

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11. Uchburchakning to‘g‘ri burchagidan chiquvchi bissektrisa gipotenizani 15 va 20 ga teng qismlarga ajratadi. Uchburchak yuzini toping.

A) 264

B) 268

C) 294

D) 288

12 / 25

12. tengsizlikning butun yechimlari yig‘indisini toping.

A) 21

B) 12

C) 18

D) 20

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13. ?₁ va ?₂ sonlari 2?² − 3? − 2 = 0 tenglamaning ildizlari, |?₁ − ?₂| ni toping.

A) 2

B) 3

C) 2.5

D) 3.5

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14. f(x) kvadrat funksiyaga nisbatan ma’lumki, f(0) + f(1) = 0, f(2) + f(3) = 0. f(x) = 2022 tenglamaning ildizlari yig‘indisi nimaga teng? (bunda, f(x) = 2022 tenglama 2 ta turli yechimga ega).

A) 5

B) 4

C) 6

D) 3

15 / 25

15. Dastlab tarvuzning 99% i suv edi, quritilgandan so‘ng esa 98% suv bo‘ldi. Tarvuzning massasi necha marta kamaydi?

A) 2

B) 1.5

C) 2.5

D) 4

16 / 25

16. Soddalashtiring:

A) IV

B) I

C) II

D) III

17 / 25

17. Tenglamalar sistemasi nechta yechimga ega?

A) 12

B) 8

C) 10

D) 6

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18. Tenglamani yeching: (71² + 81²)(7² + 8²) = 1135² + ?²

A) 159

B) 161

C) 151

D) 169

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19. Beshta musbat son berilgan. Birinchi va beshinchi sonlar yig‘indisi 13 ga teng. Berilgan barcha sonlar yig‘indisidan ikkinchi son 3 marta, uchinchi son 4 marta, to‘rtinchi son esa 5 marta kichik. Berilgan sonlardan eng kattasini toping.

A) 22

B) 20

C) 15

D) 12

20 / 25

20. ABC uchburchak berilgan ∠B = 90°. AC va BC tomonlarida mos ravishda E va D nuqtalar shunday olinganki, bunda AE = EC, ∠ADB = ∠EDC. U holda CD: BD ni toping.

A) 3

B) 4

C) 2

D) 5

21 / 25

21. 4 ga bo‘lganda 3, 3 ga bo‘lganda esa 2 qoldiq hosil bo‘ladigan barcha ikki xonali sonlar
yig‘indisini toping.

A) 376

B) 384

C) 420

D) 424

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22. Aylanaga ichki chizilgan trapetsiyaning diagonallari o‘zaro perpendikulyar. Trapetsiya asoslari 1:7 nisbatda va perimetri 18 ga teng bo‘lsa, trapetsiya yuzini toping.

A) 16

B) 22

C) 13

D) 18

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23. Tenglama butun sonlarda nechta yechimga ega? (? − 2021)² − ?² + 2? = 14

A) 6

B) 4

C) 5

D) 3

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24. 1 dan 100 gacha bo‘lgan natural sonlar orasidagi ? sonlar shundayki, ? ning natural bo‘luvchilari ko‘paytmasi(1 va ? ham inobatga olinganda) ?³ ga teng. Shunday ? natural sonlar nechta?

A) 12

B) 16

C) 10

D) 18

25 / 25

25. Chizmadagi 14 ta kvadratning perimetrlar yig‘indisi 400 sm ga teng. Ushbu kvadratlarning yuzlari yig‘indisi necha kv.sm ni tashkil qiladi?