# ALEKS Math FREE Sample Practice Questions

Preparing for the ALEKS Math test? To do your best on the ALEKS Math test, you need to review and practice real ALEKS Math questions. There’s nothing like working on ALEKS Math sample questions to hone your math skills and put you more at ease when taking the ALEKS Math test. The sample math questions you’ll find here are brief samples designed to give you the insights you need to be as prepared as possible for your ALEKS Math test.

Check out our sample ALEKS Math practice questions to find out what areas you need to practice more before taking the ALEKS Math test!

Start preparing for the 2022 ALEKS Math test with our free sample practice questions. Also, make sure to follow some of the related links at the bottom of this post to get a better idea of what kind of mathematics questions you need to practice.

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**10 Sample ALEKS Math Practice Questions**

1- If \(f(x) = 5 + x\) and \( g(x) = \ – x^2 – 1 – 2x \), then find \((g – f)(x)\)?

2- Simplify the following inequality.

\( \frac{|3+x|}{7 }≤ 5 \)

3- \( tan (– \frac{π}{6}) = ? \)

4- \( \frac{\sqrt{32a^5 b^3}}{\sqrt{2ab^2} } = ? \)

5- The cost, in thousands of dollars, of producing \(x\) thousands of textbooks is

\( C (x) = x^2 + 10x + 30 \). The revenue, also in thousands of dollars, is \(R(x) = 4x\). Find the profit or loss if 3,000 textbooks are produced. (profit \(=\) revenue\( –\) cost)

6- Suppose a triangle has the dimensions indicated below:

Then Sin B =?

7- Find the slope-intercept form of the graph \(6x – 7y = – 12\)

8- What are the zeros of the function:\( f(x)=x^3+5x^2+6x?\)

9- What is the solution of the following system of equations?

\( \begin{cases}5x+y=9\\10x-7y=-18\end{cases} \)

10- Find the Radius of the graph \( (x – 3)^2 + (y + 6)^2 = 16 \)

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## Answers:

1- **\(– x^2 – 3x – 6\)**

\((g – f)(x) = g(x) – f(x) = (– x^2 – 1 – 2x) – (5 + x) – x^2 – 1 – 2x – 5 – x = \ – x^2 – 3x – 6\)

2- **\(-38≤x≤32\)**

\(\frac{|3+x|}{7}≤5⇒|3+x|≤35⇒-35≤3+x≤35⇒-35-3≤x≤35-3⇒ -38≤x≤32 \)

3-** \(–\frac {\sqrt{3}}{3} \)**

\( tan (– \frac{π}{6}) = \ –\frac {\sqrt{3}}{3} \)

4- **\(4a^2\sqrt{b} \)**

\( \frac{\sqrt{32a^5 b^3}}{\sqrt{2ab^2} } = \frac{4a^2 \sqrt{2ab}}{b\sqrt{2a} } = 4a^2\sqrt{b} \)

5- **57,000 loss**

\(c(3)=(3)^2+10(3)+30=9+30+30=69 4×3=12⇒12-69=-57⇒57,000\) loss

6- **\(\frac{4}{5}\)**

sinB\(=\frac{Opposite Side}{Hypotenuse}=\frac{4}{5}\)

7- **\(y=\frac{6}{7} x+\frac{12}{7}\)**

\(-7y=-6x-12⇒y=\frac{-6}{-7} x-\frac{12}{-7}⇒y=\frac{6}{7} x+\frac{12}{7}\)

8- **\(0, -2, -3\)**

Frist factor the function:

\(x (x+2)(x+3)\)

To find the zeros, \(f(x)\) should be zero.

\(f(x)=x (x+2)(x+3)=0\)

Therefore, the zeros are:

\(x=0\)

\((x+2)=0 ⇒ x= -2\)

\((x+3)=0 ⇒ x= -3\)

9- **\((1,4)\)**

\(\begin{cases}5x+y=9\\10x-7y=-18\end{cases}\)⇒ Multiply the first equation by \(-2 ⇒ \begin{cases}-10x-2y=-18\\10x-7y=-18\end{cases}\) Add two equations \(⇒ –9y = –36 ⇒ y = 4\) then: \(x = 1\)

10- **4**

\((x – h)^2 + (y – k)^2 = r^2 ⇒\) center: (h,k) and radius: r

\((x – 3)^2 + (y + 6)^2 = 12 ⇒\) center: \((3,-6)\) and radius: \(\sqrt{16}=4\)

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