# Precalculus

### Why Should You Take CLEP Precalculus?

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

### Description of the Examination

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 is integrated into the exam software, and it is available to students during **Section 1** of the exam.

Only some of the questions actually require the graphing calculator. Students are expected to know how and when to make appropriate use of the calculator. The graphing calculator, together with brief video tutorials, is available to students as a free download for a 30-day trial period. **Students are expected to download the calculator and become familiar with its functionality prior to taking the exam.**

Get more information about the calculator and download a trial version.

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

### Knowledge and Skills Required

Questions on the examination require candidates to demonstrate the following abilities in the approximate proportions indicated.

- 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.

### 20%

Algebraic Expressions, Equations, and Inequalities

- 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

### 15%

Functions: Concept, Properties, and Operations

- 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)

### 30%

Representations of Functions: Symbolic, Graphical, and Tabular

- 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

### 10%

Analytic Geometry

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

### 15%

Trigonometry and its Applications*

- 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

### 10%

Functions as Models

- 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 percent 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 percent.

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