College Algebra Practice Test

About This College Algebra Practice Test

This test is designed for a typical college algebra review rather than an introductory algebra drill. It emphasizes function notation and structure, polynomial and rational behavior, exponential and logarithmic equations, sequences, transformations, and analytic geometry.

The questions require recognition of domain restrictions, composition order, inverse operations, the Remainder Theorem, discriminants, asymptotes, logarithm laws, geometric-series formulas, and standard conic forms.

College Algebra Topics Covered

The test includes domains of rational and radical functions, compositions and inverses, polynomial zeros and remainders, quadratic roots, rational-function asymptotes, exponential equations, logarithmic equations and identities, arithmetic and geometric series, function transformations, circles, and polynomial construction from zeros.

How to Approach the Questions

1. State domain restrictions before simplifying a function.
2. Use function composition from the inside outward.
3. Match a problem to the correct theorem, such as the Remainder Theorem or discriminant test.
4. Check logarithmic and rational solutions against their original domains.

Common Mistakes to Avoid

Common errors include confusing inverse functions with reciprocals, reversing composition order, overlooking excluded denominator values, using numerator zeros as vertical asymptotes, treating exponential equations as linear, and applying logarithm rules to sums.

Practice Format

Use this free 20-question test for college placement preparation, course review, tutoring, or independent study. Each answer includes immediate worked feedback.