PreCalculus

About this Project

Project and contact information.

New Preface

Old Preface

Introduction to Functions

Functions and their Representations

Exercises for Functions and their Representations

Constant and Linear Functions

Linear Functions

Linear Regression

The Average Rate of Change of a Function

Exercises for Constant and Linear Functions

Absolute Value Functions

Exercises for Absolute Value Functions

Quadratic Functions

Exercises for Quadratic Functions

Polynomial Functions

Graphs of Polynomial Functions

Exercises for Graphs of Polynomials

The Remainder and Factor Theorems

Exercises for Polydivision

Real Zeros of Polynomials

Exercises for Real Zeros

Complex Zeros and the Fundamental Theorem of Algebra

Exercises for Complex Zeros

Rational Functions

Introduction to Rational Functions

Exercises for Intro Rational

Rational Graphs

Exercises for Rational Graphs

Rational Inequalities

Exercises for Rational Inequalities

Root, Radical and Power Functions

Root and Radical Functions

Exercises for Root Radical Functions

Power Functions

Exercises for Power Functions

Equations and Inequalities involving Power Functions

Exercises for Power (In)Equalities

Further Topics on Functions

Graphs of Functions

Exercises for Graphs of Functions

Function Arithmetic

Exercises for Function Arithmetic

Function Composition

Exercises for Function Composition

Transformations of Graphs

Exercises for Transformations

Relations and Implicit Functions

Exercises for Relations

Inverse Functions

Exercises for Inverse Functions

The Algebra of Difference Quotients

Exercises for The Algebra of Difference Quotients

First Steps into Calculus

A (more) Formal Introduction to Limits

Exercises for Intro Limits

Introduction to Derivatives

Exercises for Introduction to Derivatives

The Shape of Graphs

Exercises for The Shape of Graphs

Exponential and Logarithmic Functions

Exponential Functions

Exercises for Exponential Functions

Logarithmic Functions

Exercises for Logarithmic Functions

Properties of Logarithms

Exercises for Properties of Logarithms

Equations and Inequalities involving Exponential Functions

Exercises for Exponential Equations and Inequalities

Equations and Inequalities involving Logarithmic Functions

Exercises for Logarithmic Equations and Inequalities

Applications of Exponential and Logarithmic Functions

Exercises for Applications of Exponential and Logarithmic Functions

The Conic Sections

Introduction to Conics

Parabolas

Exercises for Parabolas

Circles

Exercises for Circles

Ellipses

Exercises for Ellipses

Hyperbolas

Exercises for Hyperbolas

Systems of Equations and Matrices

Systems of Linear Equations: Gaussian Elimination

Exercises for Lin Systems

Systems of Linear Equations: Augmented Matrices

Exercises for Aug Matrices

Matrix Arithmetic

Exercises for Mat Arithmetic

Systems of Linear Equations: Matrix Inverses

Exercises for Mat Methods

Determinants and Cramer’s Rule

Exercises for Determinants

Partial Fraction Decomposition

Exercises for Par Frac

Systems of Non-Linear Equations

Exercises for Non Linear Equations

Inequalities and Regions in the Plane

Exercises for Non Linear Inequalities

Sequences and the Binomial Theorem

Sequences

Exercises for Sequences

Summation Notation

Exercises for Summation

Mathematical Induction

Exercises for Induction

The Binomial Theorem

Exercises for Binomial

Foundations of Trigonometry

The Radian Measure of Angles

Exercises for Radian Measure

The Circular Functions: Sine and Cosine

Exercises for The Circular Functions Sine and Cosine

Graphs of Sine and Cosine

Exercises for Graphs of Sine and Cosine

The Circular Functions: Tangent, Secant, Cosecant, and Cotangent

Exercises for The Other Circular Functions

Graphs of Secant, Cosecant, Tangent, and Cotangent Functions

Exercises for Graphs of Other Circular Functions

Analytical Trigonometry

The Pythagorean Identities

Exercises for Fundamental Trigonometric Identities

More Identities

Exercises for More Trigonometric Identities

The Inverse Circular Functions

Exercises for the Inverse Trigonometric Functions

Equations and Inequalities Involving the Circular Functions

Exercises for Trigonometric Equations and Inequalities

Geometric Applications of Trigonometry

The Law of Sines

Exercises for The Law of Sines

The Law of Cosines

Exercises for The Law of Cosines

Vectors

Exercises for Vectors

The Dot Product

Exercises for The Dot Product

Polar Coordinates and Parametric Equations

Polar Coordinates

Exercises for Polar Coordinates

The Graphs of Polar Equations

Exercises for Polar Graphs

The Polar Form of Complex Numbers

Exercises for Polar Complex

The Polar Form of the Conic Sections

Exercises for Polar Conics

Parametric Equations

Exercises for Parametric Equations

Appendix

Basic Set Theory and Interval Notation

Exercises for Set Theory

Real Number Arithmetic

Exercises for Real Number Arithmetic

The Cartesian Coordinate Plane

Exercises for Cartesian Plane

Linear Equations and Inequalities

Exercises for Appendix: Linear Equations and Inequalities

Graphing Lines

Exercises for Lines

Systems of Two Linear Equations in Two Unknowns

Exercises for Appendix: Linear Systems

Absolute Value Equations and Inequalities

Exercises for Abs Val Eq Ineq

Polynomial Arithmetic

Exercises for Poly Arith

Basic Factoring Techniques

Exercises for Appendix: Basic Factoring Techniques

Quadratic Equations

Exercises for Appendix: Quadratic Equations

Complex Numbers

Exercises forAppendix: Complex Numbers

Rational Expressions and Equations

Exercises for Appendix: Rational Expressions and Equations

Radical Equations

Exercises for Appendix: Exercises for Radical Expressions and Equations

Variation

Exercises for Appendix: Variation

Angles in Degrees

Exercises for Appendix: Angles in Degrees

Right Triangle Trigonometry

Exercises for Appendix: Right Triangle Trigonometry

Downloads
with-answers