UW COLLEGES DEPARTMENT OF MATHEMATICS

                                                             COURSE GUIDELINES

Course Title: Pre-Calculus Mathematics

Course Number: MAT 124 Number of Credits: 5

Contact hrs/wk:            Lecture  5

Course Prerequisites: A grade of C or better in MAT 105 or placement based on placement test score..

Degree Designation: MS

Catalog description: Functions and graphs, including linear, polynomial, logarithmic and exponential functions: complex numbers and theory of equations; binomial theorem; mathematical induction; trigonometric functions, their basic properties and graphs; identities; inverse trigonometric functions; solving trigonometric equations; de Moivres theorem.  Students may not earn more than five credits of any combination of MAT 110, MAT 113, and MAT 124.

Course content (list of topics normally covered):

1. Functions

Graphing linear and quadratic functions.

Intercepts, zeros and symmetry.

Graphing polynomials and other functions.

Transformations.

Graphing rational functions and asymptotes.

Operations on functions.

Inverse functions.

2. Theory of Polynomial Equations

Synthetic division (optional).

Complex numbers and the Fundamental Theorem of Algebra.

Remainder and factor theorems.

DesCartes Rule of Signs (optional).

Rational zeros of polynomials (optional).

Approximation of zeros of polynomials (optional).

3. Exponential and Logarithmic Functions

Basic properties and graphs of exponential functions.

Basic properties and graphs of logarithmic functions.

Solving exponential and logarithmic equations.

Applications of exponential and logarithmic functions.

4. Angles and Angle Measurement.

Radian measure.

Arc length and angular velocity.

Standard position and special angles.

5. Trigonometric Functions

Unit circle and circular function definitions.

Graphs of trigonometric functions.

Coterminal and reference angles.

Amplitude, period, and phase shift of sine, cosine, and tangent.

Basic identities and proofs.

6. Right Triangle Trigonometry

Solving right triangles.

Applications of right triangles.

7. Trigonometric Formulas

Addition formulas.

Double and half-angle formulas.

Product-to-sum and sum-to-product formulas.

8. Oblique Triangles

Law of Sines

Law of Cosines

Area formulas

9. Inverse Trigonometric Functions

Definitions and graphs of inverse functions.

Solving trigonometric equations.

10. Complex Numbers in Trigonometric Form

Converting between standard and polar form.

Multiplication and division in trigonometric form.

DeMoirvres Theorem.

Roots of complex numbers.

11. Systems of Equations and Matrices

Solving systems of linear equations.

Matrix solutions of linear equations (optional).

Determinants and Cramers Rule (optional).

12. Mathematical Induction (optional)

Content-based department proficiencies:

Graph basic algebraic functions using intercepts and symmetry.

Graph polynomial and rational functions using roots and asymptotes.

Use function transformations.

Use function algebra and composition.

Understand inverse functions and notation.

Use the Factor Theorem for polynomials and the Fundamental Theorem of Algebra.

Apply the laws of exponents and laws of logarithms.

Solve exponential and logarithmic equations.

Use the basic concepts of circular functions.

Prove and use basic trigonometric identities.

Graph the trigonometric functions using amplitude, period and phase shift.

Understand the inverse trigonometric functions.

Solve right triangles and oblique triangles.

Solve trigonometric equations.

Colleges-wide proficiencies assigned to course:

Students should be able to demonstrate the following:

A. Analytical skills Performance Indicators: Students should be able to:

1. Interpret and synthesize information and ideas.

4. Select and apply scientific and other appropriate methodologies.

B. Quantitative skills Performance Indicators: Students should be able to:

1. Solve quantitative and mathematical problems.

2. Interpret graphs, tables, and diagrams.

Representative textbooks used for the course: (editions change over time)

Barnett, Ziegler, Byleen, Precalculus: A Graphing Approach, McGraw-Hill

Bittinger, Beecher, Ellenbogen, Penna, Algebra & Trigonometry, 2nd Ed. , Addison-Wesley             Longman

Holder - A Primer for Calculus, 6th Edition,

Larson, Hostetler,  Edwards - Precalculus:A Graphing Approach, Houghton-Mifflin

Stewart, Redlin, Watson - Precalculus, 3rd Edition, Brooks-Cole

Sullivan, Sullivan III, Precalculus Enhanced with Graphing Utilities 2nd.  Ed, Prentice-Hall

Approved April 22, 2006