# College Algebra Placement Test Study Guide

The student may use any calculator he or she wishes but may not use a computer. (The student
must furnish the calculator.)

The time limit for the test is three hours. The test consists of 26 questions. About half the points
come from 17 multiple-choice problems, while the other half come from 9 open-ended and
graphing problems .

The problems on the test are of average difficulty. They are at the level of difficulty generally
found in the regular exercises in any College Algebra textbook .

The current course textbook is College Algebra: A Graphing Approach, 3rd Edition; Larson,
Hostetler, and Edwards; however, any College Algebra textbook should provide sufficient
information.

To pass this placement test, a student should have a working knowledge of the following topical
areas:

Functions:
The student should be able to:
• Apply the definition of a function.
• Perform operations on a function (add, subtract , multiply, divide).
• Evaluate a composite function.
• Determine the domain and the range of a function.
• Find the inverse of a function or indicate there is no inverse.
• Graph a function.
• Determine the zeros of a polynomial function (number, type, value).
• Distinguish between odd and even functions.
• Translate a function on a graph and then determine the corresponding change in the
equation of the function .
• Recognize the graphs of elementary families of functions ( linear , square root , greatest
integer, absolute value, quadratic , cubic, rational exponential, logarithmic).

Logarithms:
The student should be able to:
• Translate back and forth between a logarithmic equation and the corresponding
exponential equation .
• Define and use common and natural logarithms.
• Graph exponential and logarithmic functions.
• Use the properties of logarithms to simplify expressions.
• Use the properties of logarithms to solve logarithmic equations and basic exponential
equations.

Graphs:
The student should be able to:
• Write the equation of a parabola , circle, hyperbola, or ellipse based on its graph.
• Graph a parabola, circle, hyperbola , or ellipse based on its equation.
• Graph absolute value, exponential, logarithmic, or rational functions.
• Graph the solution of a system of inequalities ( linear and non -linear), identifying the
coordinates of the vertices.

General:
Besides the topics specifically listed above, the placement test assumes that the student has
acquired knowledge of the fundamental concepts of algebra. The student should be able to:
• Solve equations and inequalities.
• Apply the properties of exponents.
Simplify radicals .
Simplify algebraic expressions .
• Work with complex numbers .

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