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Qormaata galuumsa kutaa 12ffaa Herregaa, bara 2006 A.L.I (2014)

Gaaffilee dhugaa qormaata galuumsa yunivarsiitii kutaa 12 kan Herregaa, akkuma barattoonni bara 2006 A.L.I itti fudhatanitti. Tokkoon tokkoon gaaffii deebii sirrii fi ibsa qaba.

Bilisaan shaakaluu jalqabaaWaraqaa gaaffii

  • Damee lamaanuu

    Eenyutu fudhata

  • 2006 A.L.I (2014)

    Bara qormaataa

  • Gaaffilee 60 deebii waliin

    Kuusaa kana keessa

Gaaffilee qormaata kanaa yaalaa

Deebii banuun dura tokkoon tokkoon gaaffii ofii keessaniin deebisaa. Ibsi gara kutaa kitaaba barnootaa sirriitti waan qajeelchuuf, yeroo gaaffii dogoggortan fuula kam irra deebi'uu akka qabdan ni beektu.

Gaaffii 1

A water tank is a circular cylinder with base radius 2m and height 3m. If the tank is empty and water is pumped into it at rate of 2m32\mathrm{m}^3/min, how long does it take for the tank to be full?

  1. A.1.5 min
  2. B.3/2 π\pimin
  3. C.6π6\pi
  4. D.12 min
Deebii fi ibsa ilaalaa

Deebii: C 6π6\pi

Maaliif

The volume of the cylinder is V=πr2h=π(22)(3)=12π m3V = \pi r^2 h = \pi (2^2)(3) = 12\pi\text{ m}^3. At a rate of 2 m3/min2\text{ m}^3/\text{min}, the time required is 12π2=6π minutes\frac{12\pi}{2} = 6\pi\text{ minutes}.

Gaaffii 2

If A=(20−112000−1)A=\begin{pmatrix} 2 & 0 & -1 \\ 1 & 2 & 0 \\ 0 & 0 & -1 \end{pmatrix} and (2A+B)T=ATA(2A + B)^{T} = A^{T}A, then which one of the following is equal to B?

  1. A.(10−2200004)\begin{pmatrix} 1 & 0 & -2 \\ 2 & 0 & 0 \\ 0 & 0 & 4 \end{pmatrix}
  2. B.(000000000)\begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix}
  3. C.(80−448000−4)\begin{pmatrix} 8 & 0 & -4 \\ 4 & 8 & 0 \\ 0 & 0 & -4 \end{pmatrix}
  4. D.(120000−204)\begin{pmatrix} 1 & 2 & 0 \\ 0 & 0 & 0 \\ -2 & 0 & 4 \end{pmatrix}
Deebii fi ibsa ilaalaa

Deebii: D (120000−204)\begin{pmatrix} 1 & 2 & 0 \\ 0 & 0 & 0 \\ -2 & 0 & 4 \end{pmatrix}

Maaliif

Taking the transpose of both sides gives 2A+B=(ATA)T=ATA2A + B = (A^T A)^T = A^T A, so B=ATA−2AB = A^T A - 2A. Calculating ATA=(52−2240−202)A^T A = \begin{pmatrix} 5 & 2 & -2 \\ 2 & 4 & 0 \\ -2 & 0 & 2 \end{pmatrix} and subtracting 2A2A yields (120000−204)\begin{pmatrix} 1 & 2 & 0 \\ 0 & 0 & 0 \\ -2 & 0 & 4 \end{pmatrix}.

Gaaffii 3

Which one of the following represents a geometric sequence?

  1. A.3, 1, 1/3, 1/9, 1/27,?
  2. B.1/2, -1/3, 1/4, -1/5, 1/6,?
  3. C.1,3, 6, 10, 15,?
  4. D.-3, 6, -9, 12, -15,?
Deebii fi ibsa ilaalaa

Deebii: A 3, 1, 1/3, 1/9, 1/27,?

Maaliif

A sequence is geometric if the ratio between consecutive terms is constant. In A, each term is multiplied by a common ratio of r=1/3r = 1/3 (3,1,1/3,1/9,…3, 1, 1/3, 1/9, \dots).

Gaaffii 4

The sequence {(n−1)(2n+1)1−n2}n=1∞\left\{\frac{(n-1)(2n+1)}{1-n^{2}}\right\}_{n=1}^{\infty} converges to:

  1. A.−∞-\infty
  2. B.-2
  3. C.0
  4. D.1
Deebii fi ibsa ilaalaa

Deebii: B -2

Maaliif

Expanding the numerator gives 2n2−n−12n^2 - n - 1. Taking the limit as n→∞n \to \infty of 2n2−n−11−n2\frac{2n^2 - n - 1}{1 - n^2} yields the ratio of the leading coefficients, 2−1=−2\frac{2}{-1} = -2.

Gaaffii 5

If F(x) is an ant derivative of f(x)=1−2/x2f(x) = 1 - 2/x^{2} and F(1) = 0, then F(2) is equal to:

  1. A.0
  2. B.1/2
  3. C.-1/2
  4. D.3
Deebii fi ibsa ilaalaa

Deebii: A 0

Maaliif

The general antiderivative is F(x)=x+2x+CF(x) = x + \frac{2}{x} + C. Given F(1)=1+2+C=0F(1) = 1 + 2 + C = 0, we have C=−3C = -3, which gives F(2)=2+22−3=0F(2) = 2 + \frac{2}{2} - 3 = 0.

Gaaffii 6

Which one of the following expression is a polynomial expression?

  1. A.x2−3x+sin⁡xx^{2} - 3x + \sin x
  2. B.4x3+12x2−xπx2\frac{4x^{3}+12x^{2}-x}{\pi x^{2}}
  3. C.2+π1+π2\frac{2+\pi}{1+\pi^{2}}
  4. D.2−3x23+7x52+3x−12 - 3x^{\frac{2}{3}} + 7x^{\frac{5}{2}} + 3x^{-1}
Deebii fi ibsa ilaalaa

Deebii: C 2+π1+π2\frac{2+\pi}{1+\pi^{2}}

Maaliif

A polynomial consists of terms with non-negative integer powers of the variable. Any real constant, such as 2+π1+π2\frac{2+\pi}{1+\pi^2}, is a constant polynomial (degree 0).

Qormaata guutuu PDF dhaan buufadhaa

Gaaffilee 60 kuusaa kana keessa jiran hunda akka waraqaa qormaataa maxxanfameetti, furtuu deebii ibsa 49 waliin immoo akka faayilii lammaffaatti. Maxxansaa yookiin daataa malee dubbisaa.

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Qormaata kana taa'uu dura Herregaa qayyabadhu

Yaadannoon gabaabaan Herregaa kutaa 12 kaardii 33 qaba. Tokkoon tokkoon boqonnaa boqonnaadhaan kitaaba biyyaalessaa irraa qophaa'ee seericha, mallattoowwan isaa maal bakka akka bu'an fi dogoggora qabxii nama dhabsiisu ni ibsa.

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Kunneen gaaffilee dhugaa qormaata galuumsa Herregaa bara 2006 A.L.I ti?

Eeyyee. Qormaata galuumsa yunivarsiitii biyyaalessaa kan Herregaa barattoonni bara 2006 A.L.I (2014) fudhatan irraa fudhataman. Kuusaan keenya gaaffilee isaa 60 qaba; tokkoon tokkoon isaanii deebii fi ibsa gara kitaaba barnootaatti qajeelchu qabu.

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