Preparing for Pre-Algebra test? The best way to prepare for your Pre-Algebra test is to work through as many Pre-Algebra practice questions as possible. Here are the top 10 Pre-Algebra practice questions to help you review the most important Pre-Algebra concepts. These Pre-Algebra practice questions are designed to cover mathematics concepts and topics that are found on the actual test. The questions have been fully updated to reflect the latest 2021 Pre-Algebra guidelines. Answers and full explanations are provided at the end of the post.

Start your Pre-Algebra test prep journey right now with these sample Pre-Algebra questions.

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## Pre-Algebra Practice Questions

1- What is the value of the expression \((5(x-2y)+(2-x))^2 \) when\(x=3\) and \(y=-2\) ?

☐A. 20

☐B. 50

☐C. 1156

☐D. 36

2- What is the slope of a line that is perpendicular to the line

\(4x-2y=12\) ?

☐A. -2

☐B. 4

☐C. 2

☐D.\(-\frac{1}{2}\)

3- Which of the following is equal to the expression below?

\((2x+2y)(2x-y)\)

☐A. \(4x^2- 2y^2\)

☐B. \(2x^2+6xy-2y^2\)

☐C. \(24x^2+2xy-2y^2\)

☐D. \(4x^2+2xy-2y^2\)

4- What is the product of all possible values of x in the following equation?

\(|x-10| = 3\)

☐A. 3

☐B. 7

☐C. 13

☐D. 91

5- \( [6 \times (- 24) + 8] – (-4) + [4 \times 5] \div 2 = ? \)

☐A. 111

☐B. \(-112\)

☐C. \(-122\)

☐D. \(-144\)

6- What is the value of x in the following system of equations?

\(2x+5y=11\)

\(4x-2y=-14\)

☐A. \(-1\)

☐B. 1

☐C. 4

☐D. \(-2\)

7- What is the median of these numbers? 2, 27, 28, 19, 67, 44, 35

☐A. 19

☐B. 28

☐C. 44

☐D. 35

8- A swimming pool holds 2,000 cubic feet of water. The swimming pool is 25 feet long and 10 feet wide. How deep is the swimming pool?_______

9- The area of a circle is \(64 π\). Which of the following is the circumference of the circle?

☐A. 8\(\pi\)

☐B. 12\(\pi\)

☐C. 16\(\pi\)

☐D. 64\(\pi\)

10- What is the value of \(3^6 \) ?______

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## Answers:

1- **D**

Plug in the value of \(x\) and \(y\).

\(x=3\) and \(y=-2\)

\((5(x-2y)+(2-x))^2=(5(3-2(-2))+(2-3))^2=(5(3+4)+(-1))^2 = (34)^2=36\)

2- **D**

The equation of a line in slope intercept form is: \(y=mx+b\)

Solve for \(y\).

\(4x-2y=12 {\Rightarrow} -2y=12-4x {\Rightarrow} y=(12-4x){\div}(-2) {\Rightarrow} y=2x-6\)

The slope of this line is 2.

The product of the slopes of two perpendicular lines is -1.

Therefore, the slope of a line that is perpendicular to this line is:

\(m_{1} {\times} m_{2} = -1 {\Rightarrow} 2 {\times} m_{2} = -1 {\Rightarrow} m_{2} = \frac{-1}{2}\)

3- **D**

Use FOIL method.

\((2x+2y)(2x-y) = 4x^2-2xy+4xy-2y^2=4x^2+2xy-2y^2\)

4- **D**

To solve absolute values equations, write two equations.

\(x-10\) could be positive 3, or negative 3. Therefore,

\(x-10=3 \Rightarrow x=13\)

\(x-10=-3 \Rightarrow x=7\)

Find the product of solutions: \(7 \times 13 = 91\)

5- **C**

Use PEMDAS (order of operation):

\([6 {\times} (- 24) + 8] – (- 4) + [4 × 5] {\div} 2 \)

\( [- 144 + 8] – (- 4) + [20] {\div} 2 =

[- 144 + 8] – (- 4) + 10 \)

\([- 136] – (- 4) + 10 = [- 136] + 4 + 10 = – 122\)

6- **D**

Solving Systems of Equations by Elimination

Multiply the first equation by (-2), then add it to the second equation.

\({-2(2x+5y= 11) \ 4x-2y=-14} {\Rightarrow} {-4x-10y= -22 \ 4x-2y=-14} {\Rightarrow} {-12y= -36} {\Rightarrow} {y= 3}\)

Plug in the value of y into one of the equations and solve for x.

\(2x+5(3)= 11 {\Rightarrow} 2x+15= 11 {\Rightarrow} 2x= -4 {\Rightarrow} x= -2\)

7- **B**

Write the numbers in order:

2, 19, 27, 28, 35, 44, 67

Median is the number in the middle. So, the median is 28

8- **8**

Use formula of rectangle prism volume.

\(V = (length) (width) (height) {\Rightarrow} 2000 = (25) (10) (height) {\Rightarrow} height = 2000 {\div} 250 = 8\)

9- **C**

Area of the circle is \(16 π\). Use the formula of areas of circles.

\(Area = πr^2 ⇒ 64 π> πr^2⇒ 64 > r^2⇒ r < 8\)

Radius of the circle is 8. Let’s put 8 for the radius. Now, use the circumference formula:

\(Circumference =2πr=2π (8)=16π\)

10- **729**

\((3^6 ) = 3 × 3 × 3 × 3 × 3 × 3 = 729\)

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