The CLEP: Precalculus 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; for this reason, many college-bound students take a CLEP exam in order to skip over introductory courses.

The content of the exam is broken down as follows: algebraic expressions, equations, and inequalities (20%); the concept, properties, and operations of functions (15%); the symbolic, graphical, and tabular representations of functions (30%); analytic geometry (10%); trigonometry and its applications (15%); and functions as models (10%). The algebraic expressions subsection covers the following topics: operations with algebraic expressions; equations and inequalities, including linear, quadratic, absolute value, polynomial, rational, radical, exponential, logarithmic, and trigonometric; and solving systems of linear and nonlinear equations. The functions subsection covers the following topics: the general properties of functions; function notation; the concept of a function; and symbolic operations with functions. The representations of functions subsection covers the following topics: operations and transformations of symbolic, graphical, and tabular functions; and the properties of common functions, including linear, quadratic, absolute value, square root, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, and piece-wise functions. The analytical geometry subsection includes questions on lines, circles, parabolas, ellipses, and hyperbolas. The trigonometry subsection covers the following topics: basic trigonometric functions, their inverses, and the application of basic trigonometric ratios and identities; and the application of trigonometry to various problem-solving contexts. Finally the functions as models subsection covers the interpretation and production of symbolic, graphical, tabular, and verbal representations of functions. The Precalculus exam consists of 48 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 Precalculus Practice Questions

## CLEP Precalculus Answer Key

1. B. The domain of a function is the set of input values that make the function true.

2. D. The quadratic formula is

3. A. Compute the exponent before multiplying by 500.

4. D. The cosecant is the reciprocal of the sine of an angle in a right triangle.

5. C. In a natural logarithm, the base is the irrational number e = 2.71828…

6. A. In calculus, *i* = √ -1, an imaginary number.

7. B. Remember that the logarithm of a number to a base is the power the base needs to be raised by in order to yield the number.

8. A. Asymptotes are those lines whose distance to a given curve approaches zero, without necessarily ever touching.

9. E. The change of base formula is used to convert elements in one basis to another, assuming that both bases describe the same elements.

10. C. Remember that the logarithm of a number to a base is the power the base needs to be raised by in order to yield the number.