Description of the Examination
The College Algebra examination covers material that is usually taught in a one-semester college course in algebra. Nearly half of the test is made up of routine problems requiring basic algebraic skills; the remainder involves solving nonroutine problems in which candidates must demonstrate their understanding of concepts. The test includes questions on basic algebraic operations; linear and quadratic equations, inequalities, and graphs; algebraic, exponential, and logarithmic functions; and miscellaneous other topics.
It is assumed that candidates are familiar with currently taught algebraic vocabulary, symbols, and notation. The test places little emphasis on arithmetic calculations. However, an online scientific calculator (nongraphing) will be available during the examination.
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 Algebra 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 Algebra examination is drawn from the following topics. The percentages next to the main topics indicate the approximate percentage of exam questions on that topic.
- Factoring and expanding polynomials
- Operations with algebraic expressions
- Operations with exponents
- Properties of logarithms
Equations and inequalities
- Linear equations and inequalities
- Quadratic equations and inequalities
- Absolute value equations and inequalities
- Systems of equations and inequalities
- Exponential and logarithmic equations
Functions and their properties*
- Definition and interpretation
- Representation/modeling (graphical, numerical, symbolic, and verbal representations of functions)
- Domain and range
- Algebra of functions
- Graphs and their properties (including intercepts, symmetry, and transformations)
- Inverse functions
Number systems and operations
- Real numbers
- Complex numbers
- Sequences and series
- Factorials and Binomial Theorem
- Determinants of 2-by-2 matrices
*Each test may contain a variety of functions, including linear, polynomial (degree ≤ 5), rational, absolute value, power, exponential, logarithmic, and piecewise-defined.
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