# College Mathematics

## Description of the Examination

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.

## Knowledge and Skills Required

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

- Solving routine, straightforward problems (about 50 percent of the examination)
- Solving nonroutine problems requiring an understanding of concepts and the application of skills and concepts (about 50 percent 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 is integrated into the exam software, and it is available to students during the entire testing time. Students are expected to know how and when to make appropriate use of the calculator. The scientific calculator **for the iBT versions** of the CLEP exams, together with a brief video tutorial, is available to students as a free download for a 30-day trial period. **Students and encouraged to download the calculator and become familiar with its functionality prior to taking the exam.**

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

Students will find the online scientific calculator helpful in performing calculations (e.g, arithmetic, exponents, roots, logarithms).

The scientific calculator for the eCBT versions of the CLEP exams is available on the **CLEP Sampler**.

The eCBT and iBT versions of the scientific calculators look different, but both calculators have the necessary capabilities that students will use to help them answer questions on the exams.

### 20%

Algebra and Functions^{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

### 10%

Counting and Probability

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

### 15%

Data Analysis and Statistics

- 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

### 20%

Financial Mathematics

- 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

### 10%

Geometry

- 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

### 15%

Logic and Sets

- 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

### 10%

Numbers

- 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.}

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