College Placement Test Math Practice

The book contains pre-algebra, algebra, and college-level math problems.

For each of the problems, we provide an illustrated step-by-step mathematical solution, which shows you the formulas and all of the mathematical steps needed to solve each problem.

Each problem also includes a narrative explanation, which gives tips and exam strategies on how to solve similar problems on your college placement exam.

The book covers the following topics:

Pre-algebra:
Computations with Integers
Working with Fractions
- Multiplying Fractions
- Dividing Fractions
- Finding the Lowest Common Denominator
- Simplifying Fractions
Mixed Numbers
Percentages and Decimals
Solving Word Problems
Proportions
Rates and Ratios
Setting Up Equations
Working with Averages

Algebra:
Evaluating and Simplifying Numerical Expressions
Polynomials
- The FOIL Method and Working with Polynomials
- Multiplying Polynomials Using the FOIL Method
- Dividing Polynomials Using Long Division
- Evaluating Polynomial Expressions
- Substituting Values in Polynomial Expressions
- Operations on Polynomials that Have More than Two Terms
Factoring
- Factoring - Advanced Problems
- Factoring to Find Possible Values of a Variable
- Fractions that Contain Fractions
- Fractions that Contain Radicals
- Fractions that Contain Rational Expressions
- Working with Quadratics
Rational Expressions
- Adding and Subtracting Fractions that Contain Rational Expressions
- Multiplying Fractions that Contain Rational Expressions
- Dividing Fractions that Contain Rational Expressions
Functions
Imaginary and Complex Numbers
Inequalities
Laws of Exponents
- Adding and Subtracting Exponents
- Fractions as Exponents
- Positive and Negative Exponents
- Zero Exponent
Logarithmic Functions
Matrices
Multiple Solutions
Scientific Notation
Sequences and Series
Sigma Notation
Solving by Elimination
Solving for an Unknown Variable
Special Operations
Square Roots, Cube Roots, and Other Radicals
- Factoring Radicals
- Multiplication of Radicals
- Rationalizing Radicals
Systems of Equations

College-level math:
Angles and the Pythagorean Theorem
Circles and Arcs
Squares and Rectangles
Linear Equations and Graphs
Midpoints
Slope and Slope-Intercept
x and y intercepts
Basic trigonometry