## Precalculus

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The Precalculus exam tests students' knowledge of specific properties of many types of functions.

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**2020 CLEP Official Study Guide**

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This study guide provides practice questions for all 34 CLEP exams. The ideal resource for taking more than one exam. Offered only by the College Board.

**CLEP® Precalculus Examination Guide**

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The Precalculus exam tests students' knowledge of specific properties of many types of functions.

# Precalculus

## Knowledge and Skills Required

Depending on your institution's policy, a passing score on the exam can:

- Show your college math professors that you're ready for a calculus class
- Allow you to opt out of a math proficiency core requirement
- Earn you three college credits

The Precalculus examination assesses student mastery of skills and concepts required for success in a first-semester calculus course. A large portion of the exam is devoted to testing a student's understanding of functions and their properties. Many of the questions test a student's knowledge of specific properties of the following types of functions: linear, quadratic, absolute value, square root, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, and piecewise-defined. Questions on the exam will present these types of functions symbolically, graphically, verbally, or in tabular form. A solid understanding of these types of functions is at the core of all precalculus courses, and it is a prerequisite for enrolling in calculus and other college-level mathematics courses.

The examination contains approximately 48 questions, in two sections, to be answered in 90 minutes. Any time candidates spend on tutorials and providing personal information is in addition to the actual testing time.

- Section 1: 25 questions, 50 minutes.

The use of an online graphing calculator (non-CAS) is allowed for this section. Only some of the questions will require the use of the calculator. - Section 2: 23 questions, 40 minutes.

No calculator is allowed for this section.

Although most of the questions on the exam are multiple-choice, there are some questions that require students to enter a numerical answer.

### Graphing Calculator

A graphing calculator, the TI-84 Plus CE, is integrated into the exam software, and available to students during **Section 1** of the exam. Only some of the questions actually require the graphing calculator.

Information about the graphing calculator, including opportunities to practice, is available __here__.

In order to answer some of the questions in the calculator section of the exam, students may be required to use the online graphing calculator in the following ways:

- Perform calculations (e.g., exponents, roots, trigonometric values, logarithms)
- Graph functions and analyze the graphs
- Find zeros of functions
- Find points of intersection of graphs of functions
- Find minima/maxima of functions
- Find numerical solutions to equations
- Generate a table of values for a function

Questions on the examination require candidates to demonstrate the following abilities:

- Recalling factual knowledge and/or performing routine mathematical manipulation
- Solving problems that demonstrate comprehension of mathematical ideas and/or concepts
- Solving nonroutine problems or problems that require insight, ingenuity, or higher mental processes

The subject matter of the Precalculus examination is drawn from the following topics. The percentages next to the topics indicate the approximate percentage of exam questions on that topic.

### Algebraic Expressions, Equations, and Inequalities (20%)

- Ability to perform operations on algebraic expressions
- Ability to solve equations and inequalities, including linear, quadratic, absolute value, polynomial, rational, radical, exponential, logarithmic, and trigonometric
- Ability to solve systems of equations, including linear and nonlinear

### Functions: Concept, Properties, and Operations (15%)

- Ability to demonstrate an understanding of the concept of a function, the general properties of functions (e.g., domain, range), function notation, and to perform symbolic operations with functions (e.g., evaluation, inverse functions)

### Representations of Functions: Symbolic, Graphical, and Tabular (30%)

- Ability to recognize and perform operations and transformations on functions presented symbolically, graphically, or in tabular form
- Ability to demonstrate an understanding of basic properties of functions and to recognize elementary functions (linear, quadratic, absolute value, square root, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, and piecewise-defined functions) that are presented symbolically, graphically, or in tabular form

### Analytic Geometry (10%)

- Ability to demonstrate an understanding of the analytic geometry of lines, circles, parabolas, ellipses, and hyperbolas

### Trigonometry and its Applications* (15%)

- Ability to demonstrate an understanding of the basic trigonometric functions and their inverses and to apply the basic trigonometric ratios and identities (in right triangles and on the unit circle)
- Ability to apply trigonometry in various problem-solving contexts

### Functions as Models (10%)

- Ability to interpret and construct functions as models and to translate ideas among symbolic, graphical, tabular, and verbal representations of functions

* Note that trigonometry permeates most of the major topics and accounts for more than 15% of the exam. The actual proportion of exam questions that requires knowledge of either right triangle trigonometry or the properties of the trigonometric functions is approximately 30%–40%.

## Study Resources

Most textbooks used in college-level precalculus courses cover the topics in the outline given earlier, but the approaches to certain topics and the emphases given to them may differ. To prepare for the Precalculus exam, it is advisable to study one or more college textbooks, which can be found in most college bookstores. When selecting a textbook, check the table of contents against the knowledge and skills required for this test.

### Textbooks

*A survey conducted by CLEP found that the following textbooks are among those used by college faculty who teach the equivalent course. You might purchase one or more of these online or at your local college bookstore.*

- Axler,
*Precalculus: A Prelude to Calculus*(Wiley) - Barnett et al.,
*Precalculus: Functions and Graphs*(McGraw-Hill) - Bittinger et al.,
*Precalculus: Graphs & Models*(Addison-Wesley) - Blitzer,
*Precalculus*(Prentice Hall) - Connally et al.,
*Functions Modeling Change*(Wiley) - Dugopolski,
*Precalculus: Functions and Graphs*(Addison-Wesley) - Hungerford and Shaw,
*Contemporary Precalculus*(Brooks/Cole) - Larson and Hostetler,
*Precalculus: A Concise Course*(Brooks/Cole) - Narasimhan,
*Precalculus: Building Concepts and Connections*(Brooks/Cole) - Faires and DeFranza,
*Precalculus*(Brooks/Cole) - Ratti and McWaters,
*Precalculus*(Addison-Wesley) - Safier,
*Schaum's Outline of Precalculus*(McGraw-Hill) - Slavin and Crisonino,
*Precalculus: A Self-Teaching Guide*(Wiley) - Stewart, Redlin, and Watson,
*Precalculus: Mathematics for Calculus*(Brooks/Cole) - Sullivan,
*Precalculus*(Pearson/Prentice Hall) - Swokowski and Cole,
*Precalculus: Functions & Graphs*(Brooks/Cole) - Zill and Dewar,
*Precalculus with Calculus Previews*(Jones & Bartlett)

### Online Resources

*These resources, compiled by the CLEP test development committee and staff members, may help you study for your exam. However, none of these sources are designed specifically to provide preparation for a CLEP exam. The College Board has no control over their content and cannot vouch for accuracy.*

- Drexel University: Math Tools
- North Carolina State University: Math 107 Lectures
- Temple University: Calculus on the Web—Precalculus Book
- Discover Precalculus: A Creative and Connected Approach
- Khan Academy: Precalculus
- Dr. Husch’s U. of Tennessee Virtual Calculus and Precalculus Site
- Brief precalculus review at Harvey Mudd College
- Free online CLEP Precalculus course offered by Modern States Education Alliance

## Score Information

**Passing Score for Introductory Precalculus**

ACE Recommended Score*: 50

Semester Hours: 3

Each institution reserves the right to set its own credit-granting policy, which may differ from that of ACE. Contact your college as soon as possible to find out the score it requires to grant credit, the number of credit hours granted, and the course(s) that can be bypassed with a satisfactory score.

*The American Council on Education’s College Credit Recommendation Service (ACE CREDIT) has evaluated CLEP processes and procedures for developing, administering, and scoring the exams. The score listed above is equivalent to a grade of C in the corresponding course. The American Council on Education, the major coordinating body for all the nation’s higher education institutions, seeks to provide leadership and a unifying voice on key higher education issues and to influence public policy through advocacy, research, and program initiatives. Visit the ACE CREDIT website for more information.