The CLEP: Mathematics examination was developed by the College Board as a way for individuals to demonstrate undergraduate-level knowledge and skills in this subject. Almost three thousand American colleges give credit to students who pass a CLEP exam.

The content of the exam is broken down as follows: sets (10%); logic (10%); real number systems (20%); functions and their graphs (20%); probability and statistics (25%); and additional topics from algebra and geometry (15%). The sets subsection covers the following topics: union and intersection; subsets; Venn diagrams; and the Cartesian product. The logic subsection covers the following topics: truth tables; conjunctions, disjunctions, implications, and negations; conditional statements; necessary and sufficient conditions; converse, inverse, and contrapositive; and hypotheses, conclusions, and counterexamples. The real number system subsection covers the following topics: prime and composite numbers; odd and even numbers; factors and divisibility; rational and irrational numbers; absolute value and order; and open and closed intervals. The functions subsection covers the following topics: the properties and graphs of functions; domain and range; and the composition of functions and inverse functions. The probability and statistics subsection covers the following topics: counting problems; the computation of probabilities of simple and compound events; simple conditional probability; mean, median, mode, and range; and standard deviation. Finally, the additional topics subsection covers the following: complex numbers; logarithms and exponents; applications from algebra and geometry; perimeter and area of plane figures; the properties of triangles, circles, and rectangles; the Pythagorean theorem; parallel and perpendicular lines; and algebraic equations and inequalities. The College Mathematics exam consists of 60 multiple-choice questions and must be completed within 90 minutes.

After the exam is complete, an unofficial score report will be made available. This score report will include the total score on a scale of 20 to 80; the American Council on Education recommends that students get credit if they score 50 or above. The total score is the raw score (number of correct answers) adjusted according to the difficulty of the exam version. The College Board does not distinguish between unanswered questions and questions answered incorrectly, so test-takers are encouraged to respond to every question. Some of the questions on the exam are pre-test questions, which are used to develop future versions of the exam and do not contribute to the raw score. It is impossible for test-takers to determine which questions are pre-test questions. The CLEP exams are administered in both computer and paper formats at over a thousand locations throughout the world. To register for an exam, visit the College Board website.

## CLEP College Mathematics Practice Questions

## CLEP College Mathematics Answer Key

1. B. The negative signs have been converted by calculating them as inverses.

2. C. Remember that coefficients can only be combined when they have like variables.

3. C. To determine the mean (also called the average), add the members of the set together and divide by the number of members.

4. E. The two equations listed do not eliminate any possible values for x and y.

5. A. The mode of a data set is the value that appears most frequently.

6. E. The rule is found by combining the right sides of the two functions.

7. D. The range of a set of data is the difference between the greatest value and the least.

8. C. The inverse is found by setting three as a denominator for both terms in the expression.

9. E. Complementary angles often share a side.

10. A. This problem can be solved by setting up the following equation: