Algebra for Nursing School Entrance Exam Study Guide

Positive and Negative Numbers

Positive and negative numbers, also known as signed numbers, are best shown as points along the number line:

Numbers to the left of (smaller than) 0 are negative and those to the right are positive. Zero is neither negative nor positive. If a number is written without a sign, it is assumed to be positive. Notice that when you are on the negative side of the number line, bigger numbers have smaller values. For example, –5 is less than –2.You come into contact with negative numbers more often than you might think; for example, very cold temperatures are recorded as negative numbers.

As you move to the right along the number line, the numbers get larger. Mathematically, to indicate that one number, say 4, is greater than another number, say –2, the greater than sign (>) is used:

4 > –2

On the other hand, to say that –2 is less than 4, we use the less than sign (<):

–2 < 4

Arithmetic with Positive and Negative Numbers

The table on the next page illustrates the rules for doing arithmetic with signed numbers. Notice that when a negative number follows an operation, it is often enclosed in parentheses to avoid confusion.

When more than one arithmetic operation appears, you must know the correct sequence in which to perform the operations. For example, do you know what to do first when calculating 2 + 3 × 4? You're right if you said, "Multiply first." The correct answer is 14. If you add first, you'll get the wrong answer of 20! The correct sequence of operations is:

Even when signed numbers appear in an equation, the step-by-step process works exactly as it does for positive numbers. You just have to remember the arithmetic rules for negative numbers. For example, let's solve –14x + 2 = –5.

Algebraic Expressions

An algebraic expression is a group of numbers, unknowns, and arithmetic operations, like 3x – 2y. This one may be translated as "3 times some number minus 2 times another number." To evaluate an algebraic expression, replace each variable with its value. For example, if x = 5 and y = 4, we would evaluate 3x – 2y as follows:

3(5) – 2(4) = 15 – 8 = 7

Squares and Square Roots

It's not uncommon to see squares and square roots on standardized math tests, especially on questions that involve right triangles.

To find the square of a number, multiply that number by itself. For example, the square of 4 is 16, because 4 × 4 = 16.Mathematically, this is expressed as:

4² = 16

4 squared equals 16.

To find the square root of a number, ask yourself, "What number times itself equals the given number?" For example, the square root of 16 is 4 because 4 × 4 = 16.Mathematically, this is expressed as:

The square root of 16 is 4.

Because certain squares and square roots tend to appear more often than others on standardized tests, the best course is to memorize the most common ones.

How to Solve an Equation

Example: 5 – 2(3x + 1) = 7x – 8

1. Remove parentheses by distributing the value outside to both values within:
   5 – 6x – 2 = 7x – 8
2. If there are like terms on the same side of the equal sign, combine them:
   3 – 6x = 7x – 8
3. Decide where you want all of the x terms. Put all the x terms on one side by addition and subtraction:
   
4. Get all the constants on the other side by addition and subtraction:
   
5. Isolate the x by performing the opposite operation:
   

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

Mathematics for Nursing School Entrance Exam Practice Problems