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# Algebra for Praxis II ParaPro Test Prep Study Guide

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Updated on Mar 16, 2011

The practice quiz for this study guide can be found at:

Math for Praxis II ParaPro Test Prep Practice Problems

There will likely not be too many questions about algebra on the ParaPro Assessment, but you will be expected to solve linear equations and identify how numbers make up a pattern.

### Linear Equations

A linear equation contains an unknown value, called a variable. The equals sign separates an equation into two sides. You will be asked to find the value of the variable using information in the equation.

The first step is to get all of the variable terms on one side and all of the numbers on the other side. This is accomplished by undoing the operations that are attaching numbers to the variable, thereby isolating the variable. The operations are always done in reverse PEMDAS order: start by adding/subtracting, then multiply/divide.

It is very important to remember that whenever an operation is performed on one side, the same operation must be performed on the other side.

Examples
Solve for k in the equation 3k = 33.
To get k by itself on the left side of the equation, both sides need to be divided by 3.
k = 11
The value of k is 11.
Solve for m in the equation 5m + 8 = 48.
Undo the addition of 8 by subtracting 8 from both sides of the equation. Then undo the multiplication by 5 by dividing by 5 on both sides of the equation.
–8 = –8
m = 8
The variable, m, is now isolated on the left side of the equation, and its value is 8.

### Checking Solutions to Equations

To check an equation, substitute the value of the variable into the original equation.

Example

To check the solution of the previous equation, substitute the number 8 for the variable m in 5m + 8 = 48.

5(8) + 8 = 48

40 + 8 = 48

48 = 48

Because this statement is true, the answer m = 8 must be correct.

### Patterns

The ability to detect patterns in numbers is a very important mathematical skill. Patterns exist everywhere in nature, business, and finance. When you are asked to find a pattern in a series of numbers, look to see if there is some common number you can add, subtract, multiply, or divide each number in the pattern by to give you the next number in the series.

For example, in the sequence 5, 8, 11, 14 … you can add 3 to each number in the sequence to get the next number in the sequence. The next number in the sequence is 17.

Examples

What is the next number in the sequence , 3, 12, 48?

Each number in the sequence can be multiplied by the number 4 to get the next number in the sequence: × 4 = 3, 3 × 4 = 12, 12 × 4 = 48, so the next number in the sequence is 48 × 4 = 192

Sometimes it is not that simple. You may need to look for a combination of multiplying and adding, dividing and subtracting, or some combination of other operations.

What is the next number in the sequence 0, 1, 2, 5, 26?

Keep trying various operations until you find one that works. In this case, the correct procedure is to square the term and add 1: 02 + 1 = 1, 12 + 1 = 2, 22 + 1 = 5, 52 + 1 = 26, so the next number in the sequence is 262 + 1 = 677.

The practice quiz for this study guide can be found at:

Math for Praxis II ParaPro Test Prep Practice Problems