# College Mathematics

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

## Overview

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

The exam contains approximately 60 questions to be answered in 90 minutes. Some of these are pretest questions that will not be scored.

## Knowledge and Skills Required

Questions on the College Mathematics exam require candidates to demonstrate the following abilities in the approximate proportions indicated:

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

### 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.

To use the calculator during the exam, students need to select the **Calculator** icon. Information about how to use the calculator is available in the **Help** icon under the **Calculator** tab. Students are expected to know how and when to make appropriate use of the calculator.

Visit ETS to learn more and to practice using the scientific calculator.. The subject matter of the College Mathematics exam is drawn from the following topics. The percentages next to the main topics indicate the approximate percentage of exam questions on that topic.

### 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 and 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, and 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.

## Score Information

### ACE Recommendation for College Mathematics

Credit-granting Score | 50 |

Semester Hours | 3 |

**Note:** Each institution reserves the right to set its own credit-granting policy, which may differ from the American Council on Education (ACE). Contact your college to find out the score required for credit and the number of credit hours granted.