Precalculus and Calculus 1 Placement Exam Objectives and Review

Calculus and Precalculus Placement Exam Objectives

Students registering for Precalculus are responsible for part I, "Algebra Basics," and part II,"Functions - Basics," objectives 1 and 2. Students enrolling in Calculus are responsible for all objectives.

Algebra Basics

Apply properties of simple interest.
Factor simple polynomials.
Simplify and evaluate algebraic expressions (including rational expressions)
- Distributive, Associative, and Commutative Properties
- Laws of Exponents (including negative and fractional exponents)
Solve equations (linear, quadratic, and systems).
Apply order of operations.
Multiply polynomials.
Compute distances in the plane.
Apply the Pythagorean Theorem.
Graph linear equations.
Determine linear equations (slope-intercept, point-slope, point-point)
Solving systems of equations

Functions - Basics

Definition of function
Domain and range
Composition of functions
Piecewise defined functions
Inverse functions

Families of functions

Students should be able to

Understand and apply basic properties;
Recognize graphical representations; and
Identify simple transformations (i.e. shifts, reflections, and stretches/compressions) for the following types of functions:
- Linear functions
- Quadratic functions
- Polynomial functions (degree> 2)
  - (especially roots and behavior)
- Rational functions
  - (especially domain, range and asymptotes)
- Exponential functions
  - (especially definition and laws of exponents)
- Logarithmic functions
  - (especially definition and laws of logarithms)
- Trigonometric functions
  - (especially basic definitions, special values of unit circle, degrees to and from radians, and Pythagorean Identities)

Sample Test

Sample exam for Precalc ⁄ Calc (save the file, then open)
Solution to sample exam for Precalc ⁄ Calc
Grading interpretation for Practice Exam

Sample Problems

You may read these in your web browser, or right-click and save the link target as a file. You will need a pdf reader (like Adobe Acrobat) to view the file.

Online Review

The following links give free online resources for reviewing prealgebra, algebra and precalculus skills:

ALEKS^® Course Review

If you would like to approach your review for Precalculus or Calculus more thoroughly, or if you know you have significant deficiencies in your background that you would like to correct, you may choose to use Bethel's ALEKS "Prep. for Precalculus" or "Prep. for Calculus 1" courses. These courses are online and self-paced. A 6-week access code for each course can be purchased for under $40. Each course begins with a diagnostic test, and then creates a personalized plan for working through various topics that need attention. To enroll in one of these courses please see: ALEKS enrollment instructions for Prep. for Precalculus or the ALEKS enrollment instructions for Prep. for Calculus.

ALEKS is a registered trademark of ALEKS Corporation.

Back to Math Pretest and Placement Exams