Precalculus

Course Info

Table of Contents

Chapter 1 – FUNCTIONS AND THEIR GRAPHS

  • 1.1  Lines in the Plane
  • 1.2  Functions
  • 1.3  Graphs of Functions
  • 1.4  Shifting, Reflecting, and Stretching Graphs
  • 1.5  Combinations of Functions
  • 1.6  Inverse Functions
  • 1.7  Linear Models and Scatter Plots

Chapter 2 – POLYNOMIAL AND RATIONAL FUNCTIONS

  • 2.1  Quadratic Functions
  • 2.2  Polynomial Functions of Higher Degree
  • 2.3  Real Zeros of Polynomial Functions
  • 2.4  Complex Numbers
  • 2.5  The Fundamental Theorem of Algebra
  • 2.6  Rational Functions and Asymptotes
  • 2.7  Graphs of Rational Functions
  • 2.8  Quadratic Models

Chapter 3 – EXPONENTIAL AND LOGARITHMIC FUNCTIONS

  • 3.1  Exponential Functions and Their Graphs
  • 3.2  Logarithmic Functions and Their Graphs
  • 3.3  Properties of Logarithms
  • 3.4  Solving Exponential and Logarithmic Equations
  • 3.5  Exponential and Logarithmic Models
  • 3.6  Nonlinear Models

Chapter 4 – TRIGONOMETRIC FUNCTIONS

  • 4.1  Radian and Degree Measure
  • 4.2  Trigonometric Functions: The Unit Circle
  • 4.3  Right Triangle Trigonometry
  • 4.4  Trigonometric Functions of Any Angle
  • 4.5  Graphs of Sine and Cosine Functions
  • 4.6  Graphs of Other Trigonometric Functions
  • 4.7  Inverse Trigonometric Functions
  • 4.8  Applications and Models

Chapter 5 – ANALYTIC TRIGONOMETRY

  • 5.1  Using Fundamental Identities
  • 5.2  Verifying Trigonometric Identities
  • 5.3  Solving Trigonometric Equations
  • 5.4  Sum and Difference Formulas
  • 5.5  Multiple-Angle and Product-to-Sum Formulas

 

 

Chapter 6 – ADDITIONAL TOPICS IN TRIGONOMETRY

  • 6.1  Law of Sines
  • 6.2  Law of Cosines
  • 6.3  Vectors in the Plane
  • 6.4  Vectors and Dot Products
  • 6.5  Trigonometric Form of a Complex Number

Chapter 7 – LINEAR SYSTEMS AND MATRICES

  • 7.1  Solving Systems of Equations
  • 7.2  Systems of Linear Equations in Two Variables
  • 7.3  Multivariable Linear Systems
  • 7.4  Matrices and Systems of Equations
  • 7.5  Operations with Matrices
  • 7.6  The Inverse of a Square Matrix
  • 7.7  The Determinant of a Square Matrix
  • 7.8  Applications of Matrices and Determinants

Chapter 8 – SEQUENCES, SERIES, AND PROBABILITY

  • 8.1  Sequences and Series
  • 8.2  Arithmetic Sequences and Partial Sums
  • 8.3  Geometric Sequences and Series
  • 8.4  Mathematical Induction
  • 8.5  The Binomial Theorem
  • 8.6  Counting Principles
  • 8.7  Probability

Chapter 9 – TOPICS IN ANALYTIC GEOMETRY

  • 9.1  Circles and Parabolas
  • 9.2  Ellipses
  • 9.3  Hyperbolas
  • 9.4  Rotation and Systems of Quadratic Equations
  • 9.5  Parametric Equations
  • 9.6  Polar Coordinates
  • 9.7  Graphs of Polar Equations
  • 9.8  Polar Equations of Conics

Chapter 10 – ANALYTIC GEOMETRY IN THREE DIMENSIONS

  • 10.1  The Three-Dimensional Coordinate System
  • 10.2  Vectors in Space
  • 10.3  The Cross Product of Two Vectors
  • 10.4  Lines and Planes in Space

Chapter 11 – LIMITS AND AN INTRODUCTION TO CALCULUS

  • 11.1  Introduction to Limits
  • 11.2  Techniques for Evaluating Limits
  • 11.3  The Tangent Line Problem
  • 11.4  Limits at Infinity and Limits of Sequences
  • 11.5  The Area Problem

 

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