## College Mathematics

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The College Mathematics exam covers material generally taught in a college course for nonmathematics majors.

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**2019 CLEP Official Study Guide**

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This study guide provides practice questions for all 33 CLEP® exams. The ideal resource for taking more than one exam. Offered only by the College Board.

**CLEP® College Mathematics Examination Guide**

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The College Mathematics exam covers material generally taught in a college course for nonmathematics majors.

# College Mathematics

## Knowledge and Skills Required

The College Mathematics examination covers material generally taught in a college course for nonmathematics majors and majors in fields not requiring knowledge of advanced mathematics.

The examination contains approximately 60 questions to be answered in 90 minutes. Some of these are pretest questions that will not be scored. Any time candidates spend on tutorials and providing personal information is in addition to the actual testing time.

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

- Solving routine, straightforward problems (about 50% of the examination)
- Solving nonroutine problems requiring an understanding of concepts and the application of skills and concepts (about 50% of the examination)

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

### Scientific Calculator

A scientific (nongraphing) calculator, the TI-30XS MultiView™, is integrated into the exam software and available to students during the entire testing time. Students are expected to know how and when to make appropriate use of the calculator.

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

### Algebra and Functions (20%)^{1}

- Solving equations, linear inequalities, and systems of linear equations by analytic and graphical methods
- Interpretation, representation, and evaluation of functions: numerical, graphical, symbolic, and descriptive methods
- Graphs of functions: translations, horizontal and vertical reflections, and symmetry about the x-axis, the y-axis, and the origin
- Linear and exponential growth
- Applications

### Counting and Probability (10%)

- Counting problems: the multiplication rule, combinations, and permutations
- Probability: union, intersection, independent events, mutually exclusive events, complementary events, conditional probabilities, and expected value
- Applications

### Data Analysis and Statistics (15%)

- Data interpretation and representation: tables, bar graphs, line graphs, circle graphs, pie charts, scatterplots, and histograms
- Numerical summaries of data: mean (average), median, mode, and range
- Standard deviation, normal distribution (conceptual questions only)
- Applications

### Financial Mathematics (20%)

- Percents, percent change, markups, discounts, taxes, profit, and loss
- Interest: simple, compound, continuous interest, effective interest rate, effective annual yield or annual percentage rate (APR)
- Present value and future value
- Applications

### Geometry (10%)

- Properties of triangles and quadrilaterals: perimeter, area, similarity, and the Pythagorean theorem
- Parallel and perpendicular lines
- Properties of circles: circumference, area, central angles, inscribed angles, and sectors
- Applications

### Logic and Sets (15%)

- Logical operations and statements: conditional statements, conjunctions, disjunctions, negations, hypotheses, logical conclusions, converses, inverses, counterexamples, contrapositives, logical equivalence
- Set relationships, subsets, disjoint sets, equality of sets, and Venn diagrams
- Operations on sets: union, intersection, and complement
- Applications

### Numbers (10%)

- Properties of numbers and their operations: integers and rational, irrational, and real numbers (including recognizing rational and irrational numbers)
- Elementary number theory: factors and divisibility, primes and composites, odd and even integers, and the fundamental theorem of arithmetic
- Measurement: unit conversion, scientific notation, and numerical precision
- Absolute value
- Applications

1. Types of functions that will be considered are linear, polynomial, radical, exponential, logarithmic, and piecewise defined.

## Study Resources

Most textbooks used in college-level mathematics courses cover the topics in the outline given earlier, but the approaches to certain topics and the emphasis given to them may differ. To prepare for the College Mathematics exam, it is advisable to study one or more introductory college-level mathematics textbooks, which can be found in most college bookstores or online. Elementary algebra textbooks also cover many of the topics on the College Mathematics exam. 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.*

- Angel, Abbott, and Runde,
*A Survey of Mathematics with Applications*(Pearson) - Aufmann, Lockwood, Nation, and Clegg,
*Mathematical Excursions*(Cengage) - Bello, Britton, and Kaul,
*Topics in Contemporary Mathematics*(Cengage) - Bennett and Briggs,
*Using and Understanding Mathematics*(Addison Wesley) - Blitzer,
*Thinking Mathematically*(Pearson) - Bluman,
*Mathematics in Our World*(McGraw-Hill) - Burger and Starbird,
*The Heart of Mathematics*(Wiley) - Consortium for Mathematics and Its Applications,
*For All Practical Purposes: An Introduction to Contemporary Mathematics*(COMAP) - Johnson and Mowry,
*Mathematics: A Practical Odyssey*(Cengage) - Miller, Heeren, and Hornsby,
*Mathematical Ideas*(Pearson) - Pirnot,
*Mathematics All Around*(Pearson) - Setek and Gallo,
*Fundamentals of Mathematics*(Prentice Hall) - Smith,
*The Nature of Mathematics*(Cengage) - Tannenbaum,
*Excursions in Modern Mathematics*(Pearson)

## 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.*

## Score Information

**Passing Score for College Mathematics**

ACE Recommended Score*: 50

Semester Hours: 6

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.