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7-sinf Matematika olimpiada №1

InfoMaster

Aprel 29, 2022

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7-sinflar Matematika olimpiada №1

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1. A, B va C nuqtalar bir to`g`ri chiziqda yotadi. Agar AB=14 sm, BC=16,5 sm bo`lsa, AC ni toping.

A) 30,5 sm

B) 2,5 sm

C) 3,5 sm va 29,5 sm

D) 2,5 sm va 30,5 sm

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2. 1, 2, 3, 4, 5, 6 va 7 raqamlaridan, ularni takrorlamasdan nechta 4 xonali son tuzish mumkin?

A) 35 ta

B) 36 ta

C) 33 ta

D) 34 ta

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3. O’lchovlari 8 va 20 ga teng bo’lgan to’g’ri to’rt burchaklardan eng kamida nechtasini birlashtirib, kvadrat hosil qilish mumkin?

A) 11

B) 9

C) 10

D) 15

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4. Bir ishni 10 kishi 8 kunda bajara oladi. 2 kundan so`ng, uchinchi kuni ularga yordam berish uchun bir necha kishi qo`shildi va qolgan ishni 4 kunda bajarishdi. Necha kishi kelib qo`shilgan?

A) 3

B) 4

C) 5

D) 6

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5. Ikkita parallel to`g`ri chiziqlarni to`g`ri chiziq bilan kesishishidan hosil bo`lgan mos burchaklarning yig`indisi 210⁰ ga teng.Bu burchaklarni toping.

A) 105°; 105°

B) 110°; 100°

C) 80°; 130°

D) 115°; 95°

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6. Ifodani ko`paytuvchilarga ajrating: 9b²-(a-3b)²

A) (6b-a)(6b+a)

B) a²

C) (6b-a)a

D) 18b²-a²+6ab

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7. Ko’paytuvchilarga ajrating: x⁴+x²+1

A) III

B) IV

C) II

D) I

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8. Agar qo`shni burchaklardan biri ikkinchisidan 45⁰katta bo`lsa,ularni toping .

A) 112°30'; 67°30'

B) 111°30'; 68°30'

C) 113°;67°

D) 135°;45°

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9. Ifodaning qiymatini toping:

A) 195

B) 125

C) 25

D) 15

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10. Hisoblang:

A) IV

B) II

C) III

D) I

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11. Uchburchakning ikki bissektrissasining kesishishidan hosil bo`lgan burchak 128⁰ ga teng. Uchburchakning uchinchi burchagini toping.

A) 67

B) 64

C) 65

D) 66

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12. Soddalashtiring: 5b-(6b-a)-(a-6b)

A) 5b

B) 17b-2a

C) 5b-2a

D) 5b+2a

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13. Tenglamani yeching. 4,5-1,6∙(5x-3)=1,2∙(4x-1)-15,1

A) 1

B) 2

C) 3

D) 0

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14. Gazlamaning narxi 20 Ma’lum vaqtdan so’ng, yangi narx ham 25 ortdi. Gazlamaning narxi jami necha foiz ortdi?

A) 50 %

B) 70 %

C) 60 %

D) 55 %

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15. Sonni standart ko`rinishda yozing: 1247800000

A) II

B) III

C) I

D) IV

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16. Asosi BC bo`lgan teng yonli ABC uchburchakning perimetri 40 sm va teng tomonli BCD uchburchakning perimetri 45 sm ga teng. AB va BC tomonlarni toping.

A) AB =12 sm; BC =16 sm;

B) AB =12,5 sm; BC =15 sm;

C) AB =16 sm; BC =12 sm;

D) AB =15 sm; BC =12,5 sm;

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17. Qo`shni burchaklar 145⁰va 35⁰ga teng. Bu qo`shni burchaklar bissektrisalari tashkil qilgan burchakni toping.

A) 80°

B) 86°

C) 70°

D) 90°

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18. Algebraik kasrni qisqartiring:

A) IV

B) III

C) I

D) II

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19. Ifodani soddalashtiring: 125a³-225a² b+135ab²-27b³

A) (3a-5b)³

B) (3a+5b)³

C) (5a)³-(3b)³

D) (5a-3b)³

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20. M ni shunday birhad bilan almashtiringki, natijada noma’lumning barcha qiymatlarida to`g`ri tenglik hosil bo`lsin:

A) II

B) IV

C) III

D) I

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21. To`g`ri burchakli uchburchakning gipotenuzasiga tushirilgan medianasi 8 sm. Uchburchakning burchaklaridan biri 60⁰bo`lsa, bu burchakka yopishgan tomonlarini toping (sm).

A) 7

B) 8

C) 5

D) 9

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22. Uchburchakning ikkita uchidagi tashqi burchaklari o`zaro teng va perimetri 74 sm, uning bir tomoni 16 sm ga teng. Ikkita qolgan tomonlarini toping.

A) 29, 29

B) 29, 30

C) 31, 29

D) 27, 32

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23. Umumiy AB asosga ega bo`lgan ACB va ADB uchburchaklar berilgan. CD va AB lar O nuqtada kesishadi. Agar ∠DAB= ∠CBA, ∠CAB= ∠DBA, DB=24 sm bo`lsa, CA ni toping.

A) 48 sm

B) 12 sm

C) 24 sm

D) 30 sm

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24. To`g`ri burchakli parallelepipedning asosi tomoni c sm ga teng bo`lgan kvadratdan iborat bo`lib,balandligi d Bu parallelepipeddan qirrasi c sm bo`lgan kub qirqib olindi. Qolgan qismining hajmi V (sm³)ni hisoblash formulasini tuzing. Agar c=2,5 sm, d=4 sm bo`lsa, V ni toping.

A) 75/8

B) 81/8

C) 9

D) 1/8

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25. ABC uchburchakning AD medianasi BC tomondan keyin DE= AD bo`lgan kesmaga davom ettirilib, E nuqta B nuqta bilan tutashtirildi.Agar ∠ACD=45⁰, ∠ABD=35⁰ bo`lsa, ∠ABE ni toping.

A) 70°

B) 75°

C) 80°

D) 10°