Mary Jane Sterling teaches mathematics at Bradley University in Peoria, Illinois. She has been teaching mathematics for over 30 years.
Introduction.Terminology and Notation.
Order of Operations.
Graphing and the Coordinate Plane.
Simplifying Fractions.
Common Errors.
Pretest.
Pretest Questions.
Key to Pretest Questions.
Chapter 1: The Basics.
Rules for Exponents.
Laws for Using Exponents.
Adding and Subtracting Polynomials.
Multiplying Polynomials.
The FOIL Method.
Special Products.
Special Product #1.
Special Product #2.
Special Product #3.
Special Product #4.
Dividing Polynomials.
Divisors with One Term.
Long Division.
Synthetic Division.
Chapter Problems and Solutions.
Problems.
Answers and Solutions.
Supplemental Chapter Problems.
Problems.
Answers.
Chapter 2: Factoring and Solving Equations.
Greatest Common Factors and Factoring Binomials.
Greatest Common Factor.
Factoring Binomials.
Factoring Trinomials.
Factoring Other Polynomials.
Quadratic-Like Expressions.
Factoring by Grouping.
Solving Quadratic Equations.
Solving Quadratic Equations by Factoring.
Solving Quadratic Equations with the Quadratic Formula.
Solving Quadratic Equations Using Completing the Square.
Solving Quadratic-Like Equations.
Quadratic and Other Inequalities.
Radical Equations with Quadratics.
Chapter Problems and Solutions.
Problems.
Answers and Solutions.
Supplemental Chapter Problems.
Problems.
Answers.
Chapter 3: Function Operations and Transformations.
Functions and Function Notation.
Domain and Range.
Function Notation.
Function Operations.
Addition, Subtraction, Multiplication, and Division.
Composition of Functions.
Difference Quotient.
Inverse Functions.
Showing That Two Functions Are Inverses of One Another.
Solving for the Inverse of a Function.
Function Transformations.
Slides.
Flips.
Warps.
Chapter Problems and Solutions.
Problems.
Answers and Solutions.
Supplemental Chapter Problems.
Answers.
Chapter 4: Polynomials.
Remainder Theorem.
Rational Root Theorem and Descartes’ Rule of Sign.
Rational Root Theorem.
Descartes’ Rule of Sign.
Upper and Lower Bounds.
Using a Graphing Calculator to Graph Lines and Polynomials.
Solving Equations and Inequalities Using Graphing.
Chapter Problems and Solutions.
Problems.
Answers and Solutions.
Supplemental Chapter Problems.
Problems.
Answers.
Chapter 5: Exponential and Logarithmic Functions.
Exponential Functions.
Form y = a^{x}.
Form y = a^{-x}.
The Constant “e”.
Compound Interest.
Logarithmic Functions.
Laws of Logarithms.
Applications of Logarithms.
Solving Exponential and Logarithmic Equations.
Chapter Problems and Solutions.
Problems.
Answers and Solutions.
Supplemental Chapter Problems.
Problems.
Answers.
Chapter 6: Graphing.
Graphing Polynomials.
Graphing Rational Functions.
Graphing Radical Functions.
Graphing Absolute Value and Logarithmic Functions.
Graphing Functions Using Transformations.
Chapter Problems and Solutions.
Problems.
Answers and Solutions.
Supplemental Chapter Problems.
Problems.
Answers.
Chapter 7: Other Equations.
Radical Equations and Conjugates.
Rationalizing a Denominator.
Radical Equations—Squaring More Than Once.
Complex Numbers.
Operations Involving Complex Numbers.
Quadratic Formula and Complex Numbers.
Rational Equations.
Variation.
Chapter Problems and Solutions.
Problems.
Answers and Solutions.
Supplemental Chapter Problems.
Problems.
Answers.
Chapter 8: Conic Sections.
Circle.
Area and Circumference.
Standard Form.
Changing to the Standard Form Using Completing the Square.
Ellipse.
Parabola.
Hyperbola.
Graphing Conics.
Writing Equations of Circles.
Chapter Problems and Solutions.
Problems.
Answers and Solutions.
Supplemental Chapter Problems and Answers.
Problems.
Answers.
Chapter 9: Systems of Equations and Inequalities.
Solving Linear Systems Using the Addition Method.
Solving Linear Equations Using Substitution.
Solving Linear Equations Using Cramer’s Rule.
Systems of Non-Linear Equations.
Story Problems Using Systems of Equations.
Systems of Inequalities.
Chapter Problems and Solutions.
Problems.
Answers and Solutions.
Supplemental Chapter Problems.
Problems.
Answers.
Chapter 10: Systems of Linear Equations with Three or More Variables.
Addition Method.
Solving Linear Systems Using Matrices.
Operations on Matrices.
Addition and Subtraction of Matrices.
Scalar Multiplication.
Matrix Multiplication.
Inverse of a 2 x 2 Matrix.
Applications of Systems of Linear Equations.
Chapter Problems and Solutions.
Problems.
Answers and Solutions.
Supplemental Chapter Problems.
Problems.
Answers.
Customized Full-Length Exam.
Index.