Easy Pre-Calculus Step-by-Step, Second Edition

Carolyn Wheater taught math and computer technology for more than 40 years to students from elementary school through college. She continues to write about mathematics and test preparation and is a member of the National Council of Teachers of Mathematics.

1 Graphs and the Graphing Calculator
Step 1. Review Linear Equations
Step 2. Meet the Parents
Step 3. Master the Fundamentals of Graphing
Step 4. Transform the Graphs
Step 5. Master Basic Calculator Skills
2 Functions
Step 1. Analyze Relations and Functions
Step 2. Perform Arithmetic of Functions
Step 3. Compose Functions
Step 4. Find Inverse Functions
3 Quadratic Functions
Step 1. Solve Quadratic Functions
Step 2. Explore Complex Numbers
Step 3. Graph Parabolas
Step 4. Apply What You’ve Learned
4 Polynomial Functions
Step 1. Factor Polynomials
Step 2. Use Synthetic Division to Find Zeros
Step 3. Use Long Division to Factor Polynomials
Step 4. Find the Zeros of Polynomial Functions
Step 5. Graph Polynomial Functions
5 Rational Functions
Step 1. Operate with Rational Expressions
Step 2. Deal with Discontinuities
Step 3. Examine End Behavior
Step 4. Find Intercepts
Step 5. Graph Rational Functions
6 Conic Sections
Step 1. Analyze and Graph Parabolas
Step 2. Analyze and Graph Ellipses
Step 3. Analyze and Graph Circles
Step 4. Analyze and Graph Hyperbolas
Step 5. Graph and Solve Quadratic Systems
7 Exponential and Logarithmic Functions
Step 1. Get to Know the Exponential Function
Step 2. Define the Logarithmic Function
Step 3. Learn to Use Properties of Logarithms
Step 4. Solve Exponential and Logarithmic Equations
Step 5. Explore Exponential Growth and Decay
8 Radical Functions
Step 1. Review Rules for Exponents
Step 2. Simplify Radicals and Rationalize Denominators
Step 3. Explore the Square Root and Cube Root Functions
9 Systems of Equations
Step 1. Review Two-Variable Linear Systems
Step 2. Solve Systems of Linear Equations in Three Variables
Step 3. Solve Nonlinear Systems
10 Matrices and Determinants
Step 1. Master Matrix Arithmetic
Step 2. Find Determinants
Step 3. Apply Cramer’s Rule
Step 4. Find Inverse Matrices
Step 5. Solve Systems by Inverse Matrices
11 Triangle Trigonometry
Step 1. Review Right Triangle Trigonometry
Step 2. Use Trigonometry to Find Areas
Step 3. Use the Law of Cosines to Extend to Nonright Triangles
Step 4. Apply the Law of Sines
12 Trigonometric Functions
Step 1. Expand Your Concept of Angles
Step 2. Learn the Unit Circle
Step 3. Define Trigonometric Functions
Step 4. Explore Inverse Trigonometric Functions
Step 5. Verify Identities
Step 6. Use Identities
Step 7. Solve Trigonometric Equations
13 Polar and Parametric Equations
Step 1. Plot Points in the Polar Coordinate System
Step 2. Convert Coordinates Between Systems
Step 3. Graph Polar Equations
Step 4. Convert Equations Between Polar and Rectangular Forms
Step 5. Convert Equations Between Parametric and Function Forms
Step 6. Graph Parametric Equations
14 Transformations
Step 1. Understand the Geometry of Reflections
Step 2. Translate by Reflecting
Step 3. Rotate by Reflecting
Step 4. Dilate Geometrically
Step 5. Use Matrices for Transformations
15 Rotating Conics
Step 1. Create the Equation that Rotates a Conic
Step 2. Recognize Rotation in Equations
Step 3. Graph a Rotated Conic
Step 4: Classify Rotated Conics without Graphing
16 Complex Numbers
Step 1. Change Between Forms
Step 2. Add and Subtract Complex Numbers
Step 3. Multiply and Divide Complex Numbers
Step 4. Raise a Complex Number to a Power
Step 5. Find the Roots of a Complex Number
17 Limits
Step 1. Evaluate Limits
Step 2. Deal with Problems
Step 3. Use Properties of Limits
Step 4. Evaluate Infinite Limits and Limits at Infinity
18 Sequences and Series
Step 1. Find Terms of Sequences
Step 2. Find Limits of Sequences
Step 3. Find Sums of Series
Step 4. Find Sums of Infinite Series
Answer Key
Index