# 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, 3^{rd}
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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