Pre-Calculus

DESCRIPTION

This course is both a review of algebra courses you may have completed and the introduction and practice of new concepts designed to prepare you for calculus. The course begins with a treatment of the real number system, then reviews solving equations. Functions and their properties are covered next followed by related theorems. The lesson on the complex number system allows for a more in-depth discussion of mathematics. Also covered are identities, solving triangles and matrices.

OBJECTIVES

After completing the course, students will be able to:

• Perform operations within the real and complex number systems.
• Solve equations in one, two or three variables, using several methods, including matrices.
• Identify, graph and name the integral parts of all types of functions.
• Derive, prove and solve identities.
• Solve all types of triangles.

Course Outline

1. EQUATIONS AND GRAPHS
   
   
   1. Topics from Algebra and Geometry
   2. Solving Equations
   3. Setting Up Equations: Applications
   4. Inequalities
   5. Rectangular Coordinates; Graphs; Circles
   6. Lines
   7. Linear Curve Fitting
      
      
2. FUNCTIONS AND THEIR GRAPHS
   
   
   1. Functions
   2. More about Functions
   3. Graphing Techniques: Transformations
   4. Operations on Functions; Composite Functions
   5. Mathematical Models: Constructing Functions
      
      
3. POLYNOMIAL AND RATIONAL FUNCTIONS
   
   
   1. Quadratic Functions; Curve Fitting
   2. Polynomial Functions
   3. Rational Functions
   4. Synthetic Division
   5. The Real Zeros of a Polynomial Function
   6. Complex Numbers; Quadratic Equations with a Negative Discriminant
   7. Complex Zeros; Fundamental Theorem of Algebra

Course Outline Second Semester

4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS
   
   
   1. One-to-one Functions; Inverse Functions
   2. Exponential Functions
   3. Logarithmic Functions
   4. Properties of Logarithms; Curve Fitting
   5. Logarithmic and Exponential Equations
   6. Compound Interest
   7. Growth and Decay
   8. Logarithmic Scales
      
      
5. TRIGONOMETRIC FUNCTIONS
   
   
   1. Angles and Their Measure
   2. Trigonometric Functions: Unit Circle Approach
   3. Properties of the Trigonometric Functions
   4. Right Triangle Trigonometry
   5. Graphs of the Trigonometric Functions
   6. Sinusoidal Graphs: Sinusoidal Curve Fitting
      
      
6. ANALYTIC TRIGONOMETRY
   
   
   1. Trigonometric Identities
   2. Sum and Difference Formulas
   3. Double-angle and Half-angle Formulas
   4. Product-to-Sum and Sum-to-Product Formulas
   5. The Inverse Trigonometric Functions
   6. Trigonometric Equations
      
      
7. APPLICATIONS OF TRIGONOMETRIC FUNCTIONS
   
   
   1. Solving Right Triangles
   2. The Law of Sines
   3. The Law of Cosines
   4. The Area of a Triangle
   5. Simple Harmonic Motion; Damped Motion
      
      
8. POLAR COORDINATES; VECTORS
   
   
   1. Polar Coordinates
   2. Polar Equations and Graphs
   3. The Complex Plane; De Moivre's Theorem
   4. Vectors
   5. The Dot Product
   6. Vectors in Space
      
      
9. ANALYTIC GEOMETRY
   
   
   1. Conics
   2. The Parabola
   3. The Ellipse
   4. The Hyperbola
   5. Rotation of Axes; General Form of a Conic
   6. Polar Equations of Conics
   7. Plane Curves and Parametric Equations

TEXTBOOK: Precalculus 5th Edition, Michael Sullivan, 1999