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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

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

Functions - Basics

1. Definition of function
2. Domain and range
3. Composition of functions
4. Piecewise defined functions
5. Inverse functions

Families of functions

Students should be able to

1. Understand and apply basic properties;
2. Recognize graphical representations; and
3. 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)

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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.

• Basic Algebra (Precalculus and Calculus)
• Exponential and Logarithmic Functions (Precalculus and Calculus)
• Trigonometry (Calculus)

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Online Review

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

• http://www.purplemath.com/
• http://www.wtamu.edu/academic/anns/mps/math/mathlab/index.htm
• http://www.sosmath.com/
• http://www.sparknotes.com/math
• http://www.free-ed.net/free-ed/Math/default.asp

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