Microsoft Word Копия Test A. docx


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Test A

  1. a,b,c haqiqiy musbat sonlar:

a+3c + 4b − 8c ifodaning

a+2b+c a+b+2c a+b+3c eng kichik qiymatini toping?

(A)12 2−15 (B)2 2 (C)12 2−17

(D)15 2−19


  1. x, y haqiqiy sonlar uchun,

(x+5)2 +(y−12)2 =196 o'rinli bo'lsa x2 +y2 ni eng kichik qiymatini toping?

(A)2 (B)1 (C) 3 (D) 2


3. f(x) funksiya haqiqiy sonlar da quyidagi shartlarni bajaradi: f(1)=1,

f(x+5)≥ f(x)+5, f(x+1)≤ f(x)+1

g(x)= f(x)+1− x bo'lsa, g(2002) ni toping?

(A)1 (B)2 (C)−2 (D)−1


4. Agar log4(x+2y)+log4(x−2y)=1 bo'lsa x − y ning eng kichik qiymatini toping?

(A) 3 (B) 2 (C) 5 (D)1


  1. sin2 x+acosx+a2 ≥1+cosx ushbu

tengsizlik ihtiyoriy x∈R da o'rinli,bo'lsa a ning manfiy qiymatini toping?

(A)a≤−1(B)a≤−2 (C)a≥−2 (D)−1≤a≤1



  1. A(0;2) nuqta va y2 =x+4 parobolaga

tegishli B va C nuqtalar berilgan, bunda AB⊥BC bo'lsa C nuqtaning ordinatasi qanday qiymatlarni qabulqila oladi?

(A)y≥1 (B)y≥0 (C)y≤ 0, y≥ 4 (D)y≤4



  1. Agar x∈#%$−51π2 ;−π3&(' bo'lsa quyidagi funksiyaning eng katta qiymatini toping?

! 2π$ ! π$ ! π$

y =tg#x+ &−tg#x+ &+cos#x+ &

" 3 % " 6% " 6%



    1. 2 (B) 2 (C) 3 (D) 3



  1. x, y∈ (−2,2) va xy=−1 bo'lsa

4 2 9 2 ning eng kichik qiymatini

A= +

4−x 9−y toping?



    1. (B) (C) (D)



  1. ABCD tetrayedrda AB=1, CD= 3 , AB va CD chiziqlar orasidagi masofa va burchak mos ravishda 2 va ga teng. Bu tetrayedrni hajmini toping?



  1. Tengsizlikni yeching: x3 −2x2 −4x +3<0

(A)(−3,3)

(B)(−1,3)

" −1+ 5% " 5 −1 % (C)$−3,− '∪$ ,3'

# 2 & # 2 &

(D)!# 5 +1,3$&

" 2 %


  1. Agar A⊆B bo'lsa a∈R ni toping, bunda

A={x x2 −4x+3< 0, x∈R}

B={x 21−x +a≤ 0, x2 −2(a+7)x+5≤ 0, x∈R}

(A)−4≤a≤1(B)−3≤a (C)a≤1 (D)∅



  1. Agar a,b,c,d natural sonlar va loga b= 3 ,

2

logc d= , a−c=9 bo'lsa b−d ni toping?



    1. 95 (B)93 (C)97 (D)107

  1. Tengsizlikni yeching: 2 1 1 3

log x−1+ log x +2 > 0

2 2

(A)[2,3) (B)(2,3] (C)[2,4) (D)(2,4]


  1. O nuqta ΔABC ichida olingan va O!!A!"+2O!!B!"+3O!!C!"=0 o'rinli bo'lsa. SΔABC ni

SΔAOC

toping?

(A)2 (B)3 (C) (D)


  1. n=abc uch xonali son, a,b,c sonlardan teng yonli uch burchak qurish mumkun (muntazam uchburchak ham kiradi), bunda uch xonali sonlar nechta?

    1. 45 (B)81 (C)165 (D)216



  1. a0,a1,a2,...,an,... ketma-­‐ketlikda

(3−an+1)⋅(6+an)=18 va a0 =3 o'rinli bo'lsa

1 + 1 + 1 +...+ 1 ni hisoblang?

a0 a1 a2 a10

    1. 1361 (B)1362 (C)1364 (D)1365

  1. M(−1;2) va N(1;4) va P(x;0) nuqtalar koordinata tekisligida berilgan ∠MPN burchak eng katta qiymatga ega bo'ladigan P nuqtaning x apsisasini toping?

(A)x=1 (B)x=−1 (C)x=−2 (D)x=0

  1. x−3+ 6−x≥k ushbu tengsislik

yechimga ega bo'ladigan k ning eng katta qiymatini toping?

(A) 6− 3 (B) 3 (C) 6+ 3 (D) 6


!!!"

19. Fazoda A,B,C,D nuqtalar berilgan, AB=3,

!!!" !!!" !!!"

BC=7 , CD=11 va DA=9 bo'lsa

!!!" !!!"



AC⋅BD ni qiymatini toping?

(A)0 (B)10 (C)115 (D)155 20. k2 −13k ∈N natural son bo'lsa k natural sonni nechta qiymati bor?

(A)1ta (B)2ta (C)0ta (C)5ta

21. ΔABC birlik aylanaga ichki chizilgan A burchagi bissikrisasi aylanani A1 da, B burchagi bissikrisasi aylanani B1 da, C burchagi bissikrisasi aylanani C1 da, kesib



A B C AA1cos +BB1cos +CC1cos

o'tadi. 2 2 2 ni

sinA+sinB+sinC toping?

(A)2 (B)4 (C)6 (D)8


  1. T={0,1,2,3,4,5,6} va

"a1 a22 a33 a44 i %

M =# + + + ;a ∈T,i =1,2,3,4&

$ 7 7 7 7 '

Mning barcha qiymatlari kamayish tartibda yozilgan, 2017-­‐o'rindagi qiymatini toping?


  1. f (x) funksiya (0,∞) oraliqda kamayuvchi, agar f (2a2 +a+1)< f (3a2 −4a+1) bo'lsa

a=?

! 1$


(A)(1,3) (B)#0, &∪(1,5) (C)(1,5) (D)(0,5)

" 3%


  1. Agar 0<α<β<γ<2π va ∀x∈R uchun cos(x+α)+cos(x+β)+cos(x+γ)=0 bo'lsa, γ−αni toping?



  1. DABC tetrayedrning hajmi ACB=45! ,

AC bo'lsa CD ni uzunligini

AD+BC+ =3

2

toping?


(A) 5 (B) 3 (C) 2 (D) 7


  1. Kvadratning bir tomoni y=2x−17 chiziqda, qolgan ikkita uchi y=x2 parobolada bo'lsa uning yuzining eng katta qiymatini toping?

(A)90 (B)100 (C)80 (D)98

  1. Raqamlari yig'indisi 7 bo'lgan harqanday natural son «omadli son» hisobladi. Bu sonlarni o'sish tartibida yozilgan a1,a2,...,an,... shu ko'rinishda. Agar an =2005 bo'lsa a5n ni toping? (A)45000 (B)50000 (C)52000 (C)54000

  2. f (x)= x3 +ax2 +bx+c uchta haqiqiy

x1, x2, x3 ildizlarga ega. a,b,c va h musbat

sonlar bunda x1−x2 =h va x3 >1(x1+x2) 2

o'rinli bo'lsa 2a3 +273c−9ab ni eng katta h

qiymatini toping?


(A) (B) (C) (D)


  1. Uchburchak tomonlari l,m,n. l>m>n va

!" 3l4$%=!"3m4$%=!"3k4$ o'rinli.

%

#10 & #10 & #10 &



{x}-­‐x ning kasir qismi. Ushbu uchburchak perimetrining eng kichik qiymatini toping?

    1. 2002 (B)3002 (C)3003 (D)5003



  1. f (x)= log (x2 −2x−3) ushbu funksiyaning o’sish oralig’ini toping?

(A)(−∞,−1) (B)(−∞,1) (C)(1,+∞) (D)(3,+∞)



  1. x2 = 4y, x2 =−4y, x=4 va x=-­‐4 ushbu chiziqlar bilan chegaralangan shakilni OY o'qi atrofida aylantirishdan hosil bo'lgan jisimning hajmi V1. x2 +y2 ≤16 ,

x2 +(y−2)2 ≥4 , x2 +(y+2)2 ≥4 bu chiziqlar

bilan chegaralangan shakilni OY o'qi atrofida aylantirishdan hosil bo'lgan jism hajmi V2 bo'lsa quyidagilardan qaysi biri

to'g'ri:

(A)V1 =1V2 (B)V1 =2V2 (C)V1 =V2

2 3

(D)V1 =2V2



  1. f (x)= x x − x ushbu funhsiya uchun qasi

1−2 2

tasdiq to'g'ri:



    1. juft (B)toq (C) na juft,na toq (D)juft va toq

  1. x+y=1 bu to'g'ri chiziq x2 +y2 =1 ushbu

4 3 16 9

ellipsni A va B nuqtalarda kesib o'tadi, P nuqta ellipisda olingan. SΔPBA =3 bo'lsa bunday P nuqtadan nechta mavjud?


(A)1 (B)2 (C)3 (C)4


  1. f (x)= x2 +bx+c(a,b,c ∈ R,a ≠ 0) ushbu funksiya uchun quyidagilar o'rinli: 1) x∈R , f(x−4)= f(2− x) va f (x)≥ x

    1. agar x∈ (0,2) bo'lsa f(x)≤"$x+1%'2

# 2 &

    1. f(x) ning ) x∈R da, eng kichik qiymati

0 m (m>1) ning eng katta qiymati toping bunda shunday t ∈ R borki f (x+t)≤ x o'rinli x∈[1,m] da.

(A)m=8 (B)m=9 (C)m=7 (D)m=10



  1. f(x)=2 x+1+ 2x−3+ 15−3x −2 19

"3 %da qiymatlarsohasini toping?

x∈$#2,5'&

(A)(−∞;0) (B)(−∞;0] (C)(−∞;−1] (D)(−∞;1)


36. {1,2,3,...}barcha natural sonlar qatoridan aniq kvadratlarini olib tashlab yangi sonlar ketma-­‐ketligi tuzildi. Yangi tuzilgan ketma-­ketlikning 2003-­‐hadini toping?

(A)2046 (B)2047 (C)2048 (D)2049

tenglama

hech bo'lmasa bitta yechimga ega. α ni toping?

(A) (B)π , 5π (C)π, 5π (D)

12 12 6 12



  1. O'tkir burchakli uchburchak ABC da CE va BD balantliklar H nuqtada kesishadi.DE ni diametr qilib chizilgan aylana AB va AC ni mos ravishda F va G da kesib o'tadi. FG va AH chiziqlar K nuqtada kesishadi. Agar BC=25, BD=20 va BE=7 bo'lsa, AK ni uzunligini toping?

(A)7,84 (B)8,44 (C)8,64 (D)6,84

  1. xOy tekislikda A!#0, 4$& , B(−1,0) va C(1,0)

" 3%

berilgan. Shunday P nuqtalar to'plamini toping, bunda P nuqtadan BC chiziqgacha bo'lgan masofa, P dan AC va AB tomonlarga bo'lgan masofalarning o'rta giometrigiga teng.

!#S(aylana):2x2+2y2+3y-2 =0

(A)" 2 2

#$ T(giperbola):8x - 17y +12y- 8 = 0

!#S(aylana):4x2+4y2+3y-2 =0

(B)" 2 2

#$ T(giperbola):7x - 18y +12y- 8 = 0

!#S(aylana):3x2+3y2+4y-2 =0

(C)" 2 2

#$ T(giperbola):9x - 18y +12y+8 = 0

!#S(aylana):5x2+5y2+4y-12 =0

(D)" 2 2

#$ T(giperbola):9x - 10y +12y+2 = 0



40. Quyidagi chizmalarda Po,P1,P3,....Pn,... shakillar berilgan P0 muntazam uchburchak yuzi 1ga teng. Keyingi shakilni hosil qilish uchun oldingi shakildani har bir tomonini o'rta kesmasiga muntazam uch burchak bo'rtib tashqi qurilgan va shu ish keyingi shakil uchu ham dovom ettirilgan:

Sn -­‐ Pn shakilning yuzi bo'lsa hisoblang:

limSn



n→∞

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