Algebra Tests: Practice Problems for Tests and Quizzes

How Should My Child Prepare for an Algebra Test?

Depending where he or she is in the algebra curriculum, your child's algebra test might involve plotting linear equations and/or solving for variables. A linear equation, also called a straight-line equation, is an algebraic equation that, when plotted on a graph, will produce a straight line. You can help your child understand this concept by making sure he or she knows the components of a linear equation. For instance, in the equation y = mx + b, known as the slope-intercept form, 'm' represents the slope of a line, and 'b' represents the y-intercept.

If your son or daughter's test will involve solving for variables, you might want to walk him or her though the steps involved. For example, consider the problem 22 = 4x - 2. The first step is to isolate the variable by adding 2 to both sides of the equation (24 = 4x). Then, divide both sides by 4. The answer is x = 6.

Some teachers give students study guides, which can be a valuable resource for your child when preparing for an upcoming test. You should go over these guides with your child to make sure he or she understands them. You also might formulate some practice problems of your own, modeled after those below.

Practice Problems and Solutions

1. 33 = 12x + 15

Your child should begin by subtracting 15 from both sides. The resulting equation should look like this: 18 = 12x. He or she should then divide both sides by 12. The answer is x = 1.5.

2. 51 = 9x - 30

For this problem, your child should first add 50 to both sides (81 = 9x). Then, he or she should divide both sides by 9. The answer is x = 9.

Remind your child to check his or her answers by plugging the number (in this case, 9) back into the equation. For example 9(9) - 30 = 51.

3. Twice a number, x, minus 13 is 55. What number is x?

A word problem like this may be more challenging for your child because he or she must create the equation, in this case, 2x - 13 = 55. The solution is x = 34.

4. Identify the slope and y-intercept coordinate for this equation: y = 5x - 2.

The slope is 5, and the y-intercept coordinate is (0, -2).

5. Graph the equation y = -2x + 3.

The slope of the graph should be -2/1, which means it's a negative slope. The line should intercept the y-axis at (0, 3).

6. x^2 + 4 = 20

Some algebra problems include exponents. To solve, your child should isolate the variable by subtracting 4 from both sides so that x^2 = 16. Then, he or she should calculate the square root of 16. The answer is x = 4.