Precalculus with MathZone Book

PreCalculus

Concepts, Connections and Applications

Chapter 1: Equations and Inequalities

1.1 Linear Equations, Formulas and Problem Solving

1.2 Linear Inequalities in One Variable with Applications

1.3 Solving Polynomial and Other Equations

1.4 Complex Numbers

1.5 Solving Non-Factorable Quadratic Equations

Chapter 2: Functions and Graphs

2.1 Rectangular Coordinates and the Graph of a Line

2.2 Relations, Functions and Graphs

2.3 Linear Functions and Rates of Change

2.4 Quadratic and Other Toolbox Functions

2.5 Functions and Inequalities -- A Graphical View

2.6 Regression, Technology and Data Analysis

Chapter 3: Operations on Functions and Analyzing Graphs

3.1 The Algebra and Composition of Functions

3.2 One-to-One and Inverse Functions

3.3 Toolbox Functions and Transformations

3.4 Graphing General Quadratic Functions

3.5 Asymptotes and Simple Rational Functions

3.6 Toolbox Applicaitons: Direct and Inverse Variation

3.7 Piecewise-Defined Functions

3.8 Analyzing the Graph of a Function

Chapter 4: Polynomial and Rational Functions

4.1 Polynomial Long Division and Synthetic Division

4.2 The Remainder and Factor Theorems

4.3 Zeroes of Polynomial Functions

4.4 Graphing Polynomial Functions

4.5 Graphing Rational Functions

4.6 Additional Insights into Rational Functions

4.7 Polynomial and Rational Inequalities - Analytical View

Chapter 5: Exponential and Logarithmic Functions

5.1 ExponentialFunctions

5.2 Logarithms and Logarithmic Functions

5.3 The Natural Logarithmic Function and Properties of Logarithms

5.4 Exponential/Logarithmic Equations and Applications

5.5 Applications from Investment, Finance and Physical Science

5.6 Exponential, Logarithmic and Logistic Regression Models

Chapter 6: An Introduction to Trigonometric Functions

6.0 An Introduction to Cycles and Periodic Functions (on the Web)

6.1 Radian Measure and the Trigonometric Functions
6.3 Graphs of the Sine and Cosine Functions

6.4 Graphs of the Tangent and Cotangent Functions

6.5 Transformations and Applicaitons of Trigonometric Graphs

6.6 Angle Measure, Special Triangles and Special Angles

6.7 The Trigonmetry of Right Triangles

6.8 Trigonometry and the Coordinate Plane

Chapter 7: Trigonometric Identities, Inverses and Equations

7.1 Fundamental Identities and Families of Identities

7.2 Constructing and Verifying Identities

7.3 The Sum and Difference Identities

7.4 Double Angle, Half Angle and Product-to-Sum Identities

7.5 The Inverse Trig Functions and their Application

7.6 Solving Basic Trig Equations

7.7 General Trig Equations and Applications

7.8 Trigonometric Models and Sinusoidal Regression

Chapter 8: Applications of Trigonometry

8.1 Oblique Triangles and the Law of Sines
8.2 Law of Sines and the Ambiguous Case

8.3 the Law of Cosines

8.4 Vectors and Vector Diagrams

8.5 Vectors Applications and the Dot Product

8.6 Complex Numbers in Trigonometric Form; Products and Quotients

8.7 Demoivre's Theorem and the Nth Roots Theorem

Chapter 9: Systems of Equations and Inequalities

9.1 Linear Systems in Two Variables with Applications

9.2 Linear Systems in Three Variables with Applications

9.3 Systems of Linear Inequalities and Linear Programming

9.4 Systems and Absolute Value Equations and Inequalities

9.5 Solving Linear Systems using Matrices and Row Operations

9.6 The Algebra of Matrices

9.7 Solving Linear Systems using Matrix Equations

9.8 Matrix Applications: Cramer's Rule, Partial Fractions and More

Chapter 10: Topics From Analytical Geometry

10.0 An Introdcution to Analytical Geometry (on the Web)

10.1 The Circle and the Ellipse

10.2 The Hyperbola

10.3 Non-Linear Systems of Equations and Inequalities

10.4 Foci and the Analytic Ellipse and Hyperbola

10.5 The Analytic Parabola

10.6 Polar Coordinates, Equations and Graphs

10.7 More on the Conic Sections: Rotation of Axes and Polar Form

10.8 Parametric Equations of Graphs

Chapter 11: Additional Topics In Algebra

11.1 Sequences and Series

11.2 Arithmetic Sequences

11.3 Geometric Sequences

11.4 Mathematical Induction

11.5 Fundamentals of Quick-Counting

11.6 Counting Techniques: Permutations and Combinations

11.7 Introduction to Probability

11.8 The Binomial Theorem and Binomial Probabilities

11.9 Conditional Probability and Expected Value

11.10 Probability and the Normal Curve - Applications for Today
Chapter R: Review of Basic Concepts and Skills

R.1 The Language, Notation and Numbers of Mathematics

R.2 Algebraic Expressions and the Properties of Real Numbers

R.3 Exponents, Polynomials and Operations on Polynomials

R.4 Factoring Polynomials

R.5 Rational Expressions

R.6 Radicals and Rational Exponents

R.7 Geometry Review with Unit Conversions

R.8 Expressions, Tables and Graphing Calculators