# Page 1 College-Level Mathematics Study Guide for the ACCUPLACER® test

## How to Prepare for the ACCUPLACER College Level Math Test

### General Information

The ACCUPLACER College-Level Mathematics section is slightly longer than the Arithmetic section at 20 questions. It is composed of questions in five areas of college level mathematics. These sections include: Algebraic Operations, Solutions of Equations and Inequalities, Coordinate Geometry, Applications, and Functions/Trigonometry. Each section requires you to complete questions related to the topic at hand, or make an educated guess as to what the answer is. Remember that the test is computer adaptive, so be sure to try your best on each question before moving on. The next question level will be based on how well you answer the current question.

### Algebraic Operations

The algebraic operations questions on the test evaluate your knowledge regarding algebra and its functions. Algebraic operations covered include:

#### Simplifying Rational Algebraic Expressions

Fractions consisting of a polynomial in either the numerator or denominator are termed rational expressions:

$\frac{x^2 + 2}{3x}$, $\frac{1}{2x}$, and $\frac{x^3 - 4x}{2x^4}$

are all rational expressions. In cases where the numerator and denominator share a factor, the expression can be reduced:

$\frac{3x^2}{6x}$ simplifies to $\frac{x}{2}$, for example.

When simplifying a rational expression, always look first for any greatest common factor among the terms of the polynomial. If the expression is quadratic, factor if possible. After the expressions are factored, eliminate those that occur in both the numerator and denominator.

Notice that all factorization can be verified by redistributing the factored values to return to the original expression.

Get in the habit of verifying your factoring as you work through a problem in order to avoid arithmetic errors. Also, the numerator in this case should be recognized as a difference of squares: $x^2 - 1^2 = (x+1) \cdot (x-1)$, and a quick FOILing confirms the factoring of the denominator.

Occasionally, a rational expression involves a fraction divided by a fraction. When encountering these fractions, rearrange them so that they are in the standard form of a fraction, with 1 expression in the numerator and 1 expression in the denominator: