Pre-Calculus Syllabus

Semester 1

Functions and Graphs

1. Real Numbers and the Coordinate Plane

2. Graphing Utilities and Complete Graphs

3. Functions

4. Linear Functions and Inequalities

5. Quadratic Functions and Geometric Transformations

6. Operations on Functions and Composition of Functions

 

Functions and Their Zeros

1. Zeros of Polynomial Functions

2. Applications and finding Complete Graphs of Problem Situations

3. Solving Linear and Quadratic Equations Algebraically

4. Solving Linear Inequalities

5. Solving Higher-order Inequalities Algebraically and Graphically

6. Realtions and Parametric Equations

7. Inverse Functions

 

Polynomial Functions

1. Graphs of Polynomial Functions

2. Continuity, the Intermediate Value Property, and End Behavior

3. Real Zeros of Polynomials:  The Factor Theorem

 

Rational Functions and Functions Involving Radicals

1. Rational Functions and Asymptotes

2. Rational Functions and Their Graphs

3. Equations and Inequalities with Rational Functions

4. Radical Functions

 

Exponential and Logrithmic Functions

1. Exponential Functions

2. Simple and Compound Interest

3. Effective Rate and Annuities

4. Logarithmic Functions and Their Properties

5. Graphs of Logarithmic Functions

6. Equations, Inequalities, and Extreme value Problems

 

Semester 2

The Trigonometric Functions

1. Angles and Their Measure

2. The Trigonometric Functions and the Unit Circle

3. Graphs of sin x and cos x

4. Graphs of other Trig Functions

5. Trigonometric Functions of an Acute Angle

6. Applying Trig Functions

 

Analytic Trigonometry

1. Transformations and Trigonometric Graphs

2. Inverse Trigonometric Functions

3. Solving Trigonometric Equations and Inequalities Graphically

4. Trigonometric Identities

5. Sum and Difference Identites

6. Solving Trigonometric Equations and Inequalities Analytically

 

More Applications of Trigonometry

1. Law of Sines

2. Law of Cosines

3. Trigonometric Form of Complex Numbers

4. Vectors

 

Parametric Equations and Polar Coordinates

1. Parametric Equations and Graphs

2. Polar Coordinates and Graphs

3. Motion Problems and Parametric Equations

4. Conic Sections

 

Sequences, Series, and Three-Dimensional Geometry

1. Sequences

2. Finite and Infinite Series

3. Binomial Theorem

4. Counting, Permutations, and Combinations