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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.

The examination places little emphasis on arithmetic calculations, and it does not contain any questions that require the use of a calculator. However, an online scientific calculator (nongraphing) is available to candidates during the examination as part of the testing software.

It is assumed that candidates are familiar with currently taught mathematics vocabulary, symbols, and notation.

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.

10%

Sets

  • Union and intersection
  • Subsets, disjoint sets, equivalent sets
  • Venn diagrams
  • Cartesian product
10%

Logic

  • Truth tables
  • Conjunctions, disjunctions, implications, and negations
  • Conditional statements
  • Necessary and sufficient conditions
  • Converse, inverse, and contrapositive
  • Hypotheses, conclusions, and counterexamples
20%

Real Number System

  • Prime and composite numbers
  • Odd and even numbers
  • Factors and divisibility
  • Rational and irrational numbers
  • Absolute value and order
  • Open and closed intervals
20%

Functions and Their Graphs

  • Properties and graphs of functions
  • Domain and range
  • Composition of functions and inverse functions
  • Simple transformations of functions: translations, reflections, symmetry
25%

Probability and Statistics

  • Counting problems, including permutations and combinations
  • Computation of probabilities of simple and compound events
  • Simple conditional probability
  • Mean, median, mode, and range
  • Concept of standard deviation
  • Data interpretation and representation: tables, bar graphs, line graphs, circle graphs, pie charts, scatterplots, histograms
15%

Additional Topics from Algebra and Geometry

  • Complex numbers
  • Logarithms and exponents
  • Applications from algebra and geometry
  • Perimeter and area of plane figures
  • Properties of triangles, circles, and rectangles
  • The Pythagorean theorem
  • Parallel and perpendicular lines
  • Algebraic equations, systems of linear equations, and inequalities
  • Fundamental Theorem of Algebra, Remainder Theorem, Factor Theorem