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Qormaata fakkeenyaa kutaa 12ffaa Herregaa, bara 2016 A.L.I (2024)

Qormaata fakkeenyaa Herregaa bara 2016 A.L.I kenname, barattoota kutaa 12ffaa qormaata galuumsaatiif qopheessuuf, haala walfakkaatuun. Shaakala; qormaata galuumsaa mataa isaa miti. Tokkoon tokkoon gaaffii deebii sirrii fi ibsa qaba.

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Fakkeenyaa, bara 2016 A.L.I
Bara qormaataa
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Kan qopheesse
Gaaffilee 62 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

If $x$ and $y$ are composite natural numbers and $z$ is a prime number, then which one of the following is never true?

A. $x + y = z$
B. $x + y = 2z$
C. $xz = y$
D. $xy = z^2$

Deebii fi ibsa ilaalaa

Deebii: D $xy = z^2$

Maaliif

Since

z

is a prime number, the only factors of

z^2

are

1, z, z^2

. If

xy = z^2

where

x

and

y

are composite, they must both be greater than 1, so the only possibility is

x=z

and

y=z

, which contradicts the assumption that

z

is prime and

x,y

are composite.

Gaaffii 2

The simplified form of the expression $(\frac{5}{4})^3 (\frac{\sqrt{5}}{2})^{-4} \div (\frac{\sqrt[3]{5}}{\sqrt{2}})^6$ is:

A. $\frac{5}{2}$
B. $\frac{2}{5}$
C. $\frac{1}{5}$
D.5

Deebii fi ibsa ilaalaa

Deebii: B $\frac{2}{5}$

Maaliif

Simplifying each term:

(\frac{5}{4})^3 = \frac{125}{64}

,

(\frac{\sqrt{5}}{2})^{-4} = (\frac{2}{\sqrt{5}})^4 = \frac{16}{25}

, and

(\frac{\sqrt[3]{5}}{\sqrt{2}})^6 = \frac{25}{8}

. Multiplying the first two terms gives

\frac{125}{64} \times \frac{16}{25} = \frac{5}{4}

, and dividing by the third term gives

\frac{5}{4} \div \frac{25}{8} = \frac{5}{4} \times \frac{8}{25} = \frac{2}{5}

.

Gaaffii 3

To rationalize the denominator $\frac{3+\sqrt{2}}{4-\sqrt{3}}$ which one of the following expression is used as the rationalizing factor?

A. $\frac{3-\sqrt{2}}{3-\sqrt{2}}$
B. $\frac{3-\sqrt{2}}{4+\sqrt{3}}$
C. $\frac{4+\sqrt{3}}{4+\sqrt{3}}$
D. $\frac{1}{4+\sqrt{3}}$

Deebii fi ibsa ilaalaa

Deebii: C $\frac{4+\sqrt{3}}{4+\sqrt{3}}$

Maaliif

To rationalize the denominator of a fraction of the form

\frac{a}{b-\sqrt{c}}

, we multiply both the numerator and the denominator by the conjugate of the denominator, which is

b+\sqrt{c}

. Thus, the rationalizing factor is

\frac{4+\sqrt{3}}{4+\sqrt{3}}

.

Gaaffii 4

What is the value of $x$ for $2\left(\frac{243}{32}\right)^{2x} = 3\left(\frac{8}{27}\right)^{\frac{2}{3}x-1}$ ?

A. $\frac{1}{3}$
B. $\frac{4}{3}$
C. $\frac{2}{5}$
D. $\frac{1}{4}$

Deebii fi ibsa ilaalaa

Deebii: A $\frac{1}{3}$

Maaliif

Expressing the bases in terms of

\frac{3}{2}

, the equation becomes

2\left((\frac{3}{2})^5\right)^{2x} = 3\left((\frac{3}{2})^{-3}\right)^{\frac{2}{3}x - 1}

, which simplifies to

2(\frac{3}{2})^{10x} = 3(\frac{3}{2})^{-2x + 3}

. Dividing both sides yields

(\frac{3}{2})^{12x - 3} = \frac{3}{2}

, so

12x - 3 = 1

, giving

x = \frac{1}{3}

.

Gaaffii 5

Which one of the following systems of linear equation has infinitely many solutions?

A. $\begin{cases} 3x + y = -1 \ -x - \frac{1}{3}y = \frac{1}{3} \end{cases}$
B. $\begin{cases} x + y = 6 \ 2x - 5y = 0 \end{cases}$
C. $\begin{cases} x + 3y = 2 \ 2x - 4y = 1 \end{cases}$
D. $\begin{cases} x - 2y = 5 \ -3x + 6y = 1 \end{cases}$

Deebii fi ibsa ilaalaa

Deebii: A $\begin{cases} 3x + y = -1 \ -x - \frac{1}{3}y = \frac{1}{3} \end{cases}$

Maaliif

Multiplying the second equation in Option A,

-x - \frac{1}{3}y = \frac{1}{3}

, by

-3

gives

3x + y = -1

. This is identical to the first equation, meaning they represent the same line and therefore have infinitely many solutions.

Gaaffii 6

What is the solution set of the inequality $|3x + 6| - 2 \ge 4$ ?

A. $(-\infty, -4) \cup (0, \infty)$
B. $[-4, 0]$
C. $(-\infty, -4] \cup [0, \infty)$
D. $(-4, 0)$

Deebii fi ibsa ilaalaa

Deebii: C $(-\infty, -4] \cup [0, \infty)$

Maaliif

The inequality

|3x + 6| - 2 \ge 4

simplifies to

|3x + 6| \ge 6

, which implies

|x + 2| \ge 2

. This means

x + 2 \ge 2

(giving

x \ge 0

) or

x + 2 \le -2

(giving

x \le -4

), which in interval notation is

(-\infty, -4] \cup [0, \infty)

.

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Gaaffilee 62 kuusaa kana keessa jiran hunda akka waraqaa qormaataa maxxanfameetti, furtuu deebii ibsa 62 waliin immoo akka faayilii lammaffaatti. Maxxansaa yookiin daataa malee dubbisaa.

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Qormaatilee Herregaa kutaa 12ffaa hunda Qormaatilee bara 2016 A.L.I hunda Gosa barnootaa fi bara hunda

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Yaadannoon gabaabaan Herregaa kutaa 12 kaardii 32 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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Qormaata fakkeenyaa kutaa 12ffaa Herregaa, bara 2016 A.L.I (2024)

Gaaffilee qormaata kanaa yaalaa

If xxx and yyy are composite natural numbers and zzz is a prime number, then which one of the following is never true?

The simplified form of the expression (54)3(52)−4÷(532)6(\frac{5}{4})^3 (\frac{\sqrt{5}}{2})^{-4} \div (\frac{\sqrt[3]{5}}{\sqrt{2}})^6(45​)3(25​​)−4÷(2​35​​)6 is:

To rationalize the denominator 3+24−3\frac{3+\sqrt{2}}{4-\sqrt{3}}4−3​3+2​​ which one of the following expression is used as the rationalizing factor?

What is the value of xxx for 2(24332)2x=3(827)23x−12\left(\frac{243}{32}\right)^{2x} = 3\left(\frac{8}{27}\right)^{\frac{2}{3}x-1}2(32243​)2x=3(278​)32​x−1?

Which one of the following systems of linear equation has infinitely many solutions?

What is the solution set of the inequality ∣3x+6∣−2≥4|3x + 6| - 2 \ge 4∣3x+6∣−2≥4?

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Qormaatilee Herregaa biroo bara 2016 A.L.I

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Qormaatilee kana fakkaatan dabalataa

Qormaata kana taa'uu dura Herregaa qayyabadhu

If $x$ and $y$ are composite natural numbers and $z$ is a prime number, then which one of the following is never true?

The simplified form of the expression $(\frac{5}{4})^3 (\frac{\sqrt{5}}{2})^{-4} \div (\frac{\sqrt[3]{5}}{\sqrt{2}})^6$ is:

To rationalize the denominator $\frac{3+\sqrt{2}}{4-\sqrt{3}}$ which one of the following expression is used as the rationalizing factor?

What is the value of $x$ for $2\left(\frac{243}{32}\right)^{2x} = 3\left(\frac{8}{27}\right)^{\frac{2}{3}x-1}$ ?

What is the solution set of the inequality $|3x + 6| - 2 \ge 4$ ?