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Matematika attestatsiya №13

InfoMaster

Iyul 21, 2022

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OMAD YOR BO'LSIN!

Matematika fanidan attestatsiya savollari №13

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1. Kichchik diagonali tomoniga teng bo’lgan rombga , tomoni diametr qilib yarim doira va uning ichiga romb tomoniga hamda yarim doiraga urunuvchi aylana chizilgan . Agar romb tomoni 8 bo’lsa aylana markazidan diagonallar kesishish nuqtasigacha bo’lgan masofani toping.

A) 4

B) 3

C) 2

D) 1

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2. Arifmetik progressiyada a_n+1=a_n+2 va a₄=4 bo'lsa, uning dastlabki 12 ta hadini yig'indisini toping.

A) 126

B) 96

C) 114

D) 108

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3. AM||KL , ∠BCD=70°,∠CDE=40°, ∠DEF =45°,∠EFG=80°, ∠FGK=70°∠MBC=x ga teng bo`lsa x ni toping ?

A) 40°

B) 20°

C) 10°

D) 30°

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4. x>0 bo‘lsa, 128x+1/x² yig‘indining eng kichik qiymatini toping.

A) 64

B) 48

C) 32

D) 16

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5. Ifodaning qiymatini quyidagi sonlardan qaysi biriga teng.

3¹⁹·2⁵
3¹⁶·2⁸
3¹³·2⁸
32⁹·2⁸

A) 3

B) 1

C) 2

D) 4

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6. ABC uchburchak o‘tkir burchaklarining bissektrisalari D nuqtada kesishadi. Bunda ∠A = 90° , BD = 8 , CD = 6 bo‘lsa, BCD uchburchak yuzini toping.

A) 12

B) 6√2

C) 12√2

D) 8√2

7 / 40

7. x va y natural sonlar uchun 20∙x! = y! bo‘lsa, y ning qabul qiladigan qiymatlari yig‘indisini toping.

A) 25

B) 23

C) 26

D) 20

8 / 40

8. Kubning diagonalidan ushbu diagonal bilan kesishmaydigan qirrasigacha bo‘lgan masofa 4 ga teng. Kubning hajmini toping.

A) 180√2

B) 144√2

C) 128√2

D) 240√2

9 / 40

9. Bir nechta natural sonlardan tuzilgan S to‘plam berilgan. Bu sonlarning o‘rta
arifmetigi eng kattasini hisobga olmaganda 32 ga, eng kichigini hisobga olmaganda 40 ga, eng kattasini ham eng kichigini ham hisobga olmaganda esa 35 ga teng. Agar eng katta son eng kichigidan 72 ga ortiq bo‘lsa, u holda S to‘plamdagi barcha sonlarning o‘rta arifmetigini toping.

A) 36,8

B) 36,2

C) 36,6

D) 36,4

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10. BCD-A markazli aylananing yoyi, ED // BA, DE⟘EF, EC=ED=7 va BF=1 boʻlsa, AF ning qiymatini toping.

A) 15

B) 15

C) 12

D) 13

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11. (0!+1!+ 2022!)¹²⁵ sonning birlar xonasida qaysi raqam turadi?

A) 2

B) 6

C) 4

D) 3

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12. Tengsizlikni yeching.

A) x∈(10;1000)

B) x∈(0;1000)

C) x∈[0;1000]

D) x∈(1;1000]

13 / 40

13. Konus o’q kesimi yuzi 4√3 ga teng muntazam uchburchakdan iborat. Konus to’la sirtini toping?

A) 12π

B) 6π

C) 18π

D) 24π

14 / 40

14. k va l ning qanday qiymatlarida y=k/x giperbola va y=kx+l to’g’ri chiziq M( -1;1) nuqtalardan o’tadi.

A) -1;-2

B) -1; 2

C) 1;0

D) -1; 0

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15. Agar tg(x+y)=3 va tg(x-y)=2 bo’lsa tg2x+5 ning yarmini toping

A) -1

B) 5

C) 1

D) 2

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16. sin(2arctg0,75) ni hisoblang

A) 12/15

B) 11/15

C) 22/25

D) 24/25

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17. Uchburchakning b va c ga teng tomonlari orasidagi burchagi 30⁰ ga teng. Uchburchakning uchunchi tomoni 12 ga teng bo'lsa hamda uning tomonlari c² = b² + 12b + 144 shartni qanoatlantirsa, c ning qiymatini toping.

A) 12√3

B) 24√3

C) 6√3

D) 12

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18. Hisoblang: sin10° •sin50° •sin70°

A) 0,5

B) 0

C) 0,125

D) 0,25

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19. Aniqmas integralni hisoblang.

A) lnx+c

B) ln(lnx)

C) ln(lnx)+c

D) xlnx-x+c

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20. f(2x-1)=4x-5 bo’lsa, f^-1(x)=?

A) (x-7)/2

B) (x-2)/3

C) (x+3)/2

D) (x-3)/3

21 / 40

21. f(x+10)=f(x)·f(x-10)-x f(0)=1/2 va f(10)=30 bo’lsa, f(20)=?

A) 2

B) 30

C) 6

D) 5

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22. x ning qanday qiymatida lg2; lg(2^x-1); lg(2^x+3) arfimetik progressiyani tashkil qiladi?

A) log₂5

B) 3

C) 2

D) log₅2

23 / 40

23. 2^a = 5 va 20^b = 125 bo’lsa, a ni b orqali ifodalang.

A) 2b/(3-b)

B) 3b/(2+b)

C) b/(3-b)

D) (3-b)/2b

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24. sin²α+ sin²β= 1 tenglamada 0<α<π/2 va 0<β<π/2 bo’lsa, α²+π²/2+β²+2αβ ni hisoblang.

A) 2π²

B) α²

C) 3π²/4

D) π²/4

25 / 40

25. Ikki natural sonning kvadratlarining o'rta arifmetigi 34 ga, o'rta geometrigi esa 8 ga teng. Shu sonlarning yig'indisini yarmini toping toping.

A) 9

B) 7

C) 14

D) 6

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26. Silindr yon sirtining yoyilmasi tomoni b ga teng kvadratdan iborat. Silindir to’la sirtini toping.

A) b²+b²/2π

B) b²/2π

C) b²-2π

D) b²-b²/2π

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27. 1,2,3,4,2,3,1,4,5,3,2,12,3,4,2,1,3,2,1,4,3,2,1,2,3,4,2,1,2,3. Chastotasi eng kata bo’lgan songa 3 ni qo’shsak achiqsa. a²= ?

A) 36

B) 25

C) 16

D) 49

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28. Meshdagi suv Sarvarning o'ziga 20 kunga, Behruzga esa 60 kunga yetadi. Meshdagi suv ikkalasiga necha kunga yetadi?

A) 14

B) 16

C) 12

D) 15

29 / 40

29. f(x)=2·tgx funksiyaning x₀=π nuqtadagi hosilasini toping.

A) 0

B) -2

C) 2

D) 1

30 / 40

30. Agar ln(ab)=2x ba ln(a/b)=2y bo'lsa, a=?

A) IV

B) I

C) II

D) III

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31. To’g’ri burchakli uchburchakning katetlari 5 sm va 12 sm. Uchburchakka ichki chizilgan aylananing radiusini toping.

A) 2 m;

B) 3 sm;

C) 2 sm;

D) 4 sm;

32 / 40

32. funksiyaga teskari funksiyani toping.

A) IV

B) I

C) II

D) III

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33. Teng yonli uchburchakning asosi yon tomonidan 15 ga ortiq uchburchakning asosiga tushirilgan balandligi 15 ga teng bo’lsa , uning asosini toping.

A) 40

B) 20

C) 42

D) 36

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34. y=6x+18 to’g’ri chiziq bilan chegaralangan soha yuzini toping.

A) 48

B) 12

C) 18

D) 27

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35. Agar f(x)=x³─5x²+2x+a va f "(2)=f(2) bo’lsa, a ning qiymatini toping.

A) 6

B) 12

C) 5

D) 10

36 / 40

36. y₁ va y₂ y² + my + n = 0 tenglamaning ildizlari, y₁ va y₂ ning har birini 4 taga orttirib, ildizlari hosil bo'lgan sonlarga teng kvadrat tenglama tuzildi. Agar uning ozod hadi n -24 (n dastlabki tenglamaning ozod hadi) ga teng bo'lsa, m nechaga teng?

A) 10

B) 11

C) 9

D) 12

37 / 40

37. sin (2arccos1/3) ni hisoblang.

A) 2/9

B) 4√4/9

C) 4√2/9

D) 2/3

38 / 40

38. ifoda x ning nechta qiymatida ma’noga ega emas?