Pre Calculus Syllabus

1.1 The Distance and Midpoint Formulas;Introduction to Graphing Equations

1.2 Intercepts;Symmetry

1.3 Solving Equations Using a Graphing Utility

1.4 Lines

1.5 Circles

2.1 Functions

2.2 The Graph of a Function

2.3 Properties of Functions

2.4 Library of Functions;Piecewise-defined Functions

2.5 Graphing Techniques:Transformations

2.6 Mathematical Models:Building Functions

3.1 Linear Functions and Their Properties

3.2 Linear Models:Building Linear Functions from Data

3.3 Quadratic Functions and Their Properties

3.4 Build Quadratic Models from Verbal Descriptions and from Data

3.5 Inequalities Involving Quadratic Functions

4.1 Polynomial Functions and Models

4.2 The Real Zeros of a Polynomial Function

4.3 Complex Zeros;Fundamental Theorem of Algebra

4.4 Properties of Rational Functions

4.5 The Graph of a Rational Function

4.6 Polynomial and Rational Inequalities

5.1 Composite Functions

5.2 One-to-One Functions; Inverse Functions

5.3 Exponential Functions

5.4 Logarithmic Functions

5.5 Properties of Logarithms

5.6 Logarithmic and Exponential Equations

5.7 Financial Models

5.8 Exponential Growth and Decay Models; Newton's Law; Logistic Growth and Decay Models

5.9 Building Exponential, Logarithmic, and Logistic Models from Data

6.1Angles and Their Measure

6.2 Trigonometric Functions: Unit Circle Approach

6.3Properties of the Trigonometric Functions

6.4 Graphs of the Sine and Cosine Functions

6.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions

6.6 Phase Shift; Sinusoidal Curve Fitting

7.1 The Inverse Sine, Cosine, and Tangent Functions

7.2 The Inverse Trigonometric Functions(Continued)

7.3 Trigonometric Equations

7.4 Trigonometric Identities

7.5 Sum and Difference Formulas

7.6 Double-angle and Half-angle Formulas

7.7 Product-to-Sum and Sum-to-Product Formulas

8.1 Right Triangle Trigonometry;Applications

8.2 The Law of Sines

8.3 The Law of Cosines

8.4 Area of a Triangle

8.5 Simple Harmonic Motion;Damped Motion; Combining Waves

9.1Polar Coordinates

9.2 Polar Equations and Graphs

9.3 The Complex Plane; De Moivre's Theorem

9.4 Vectors

9.5 The Dot Product

9.6 Vectors in Space

9.7 The Cross Product 

10.1 Conics

10.2 The Parabola

10.3 The Ellipse

10.4 The Hyperbola

10.5 Rotation of Axes;General Form of a Conic

10.6 Polar Equations of Conics

10.7 Plane Curves and Parametric Equations

11.1 Systems of Linear Equations:Substitution and Elimination

11.2 Systems of Linear Equations:Matrices

11.3 Systems of Linear Equations:Determinants

11.4 Matrix Algebra

11.5 Partial Fraction Decomposition

11.6 Systems of Nonlinear Equations

11.7 Systems of Inequalities

11.8 Linear Programming

12.1 Sequences

12.2 Arithmetic Sequences

12.3 Geometric Sequences;Geometric Series

12.4 Mathematical Induction

12.5 The Binomial Theorem

13.1 Counting

13.2 Permutations and Combinations

13.3 Probability

14.1 Finding Limits Using Tables and Graphs

14.2 Algebra Techniques for Finding Limits

14.3 One-sided Limits; Continuous Functions

14.4 The Tangent Problem; The Derivative

14.5 The Area Problem; The Integral