Pre-Calculus

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Chapter 1 – Functions

  • Introduction to Functions
  • 1.1 Functions and Function Notation
  • 1.2 Domain and Range
  • 1.3 Rates of Change and Behavior of Graphs
  • 1.4 Composition of Functions
  • 1.5 Transformation of Functions
  • 1.6 Absolute Value Functions
  • 1.7 Inverse Functions

Chapter 2 – Linear Functions

  • Introduction to Linear Functions
  • 2.1 Linear Functions
  • 2.2 Graphs of Linear Functions
  • 2.3 Modeling with Linear Functions
  • 2.4 Fitting Linear Models to Data

Chapter 3 – Polynomial and Rational Functions

  • Introduction to Polynomial and Rational Functions
  • 3.1 Complex Numbers
  • 3.2 Quadratic Functions
  • 3.3 Power Functions and Polynomial Functions
  • 3.4 Graphs of Polynomial Functions
  • 3.5 Dividing Polynomials
  • 3.6 Zeros of Polynomial Functions
  • 3.7 Rational Functions
  • 3.8 Inverses and Radical Functions
  • 3.9 Modeling Using Variation

Chapter 4 – Exponential and Logarithmic Functions

  • Introduction to Exponential and Logarithmic Functions
  • 4.1 Exponential Functions
  • 4.2 Graphs of Exponential Functions
  • 4.3 Logarithmic Functions
  • 4.4 Graphs of Logarithmic Functions
  • 4.5 Logarithmic Properties
  • 4.6 Exponential and Logarithmic Equations
  • 4.7 Exponential and Logarithmic Models
  • 4.8 Fitting Exponential Models to Data

Chapter 5 – Trigonometric Functions

  • Introduction to Trigonometric Functions
  • 5.1 Angles
  • 5.2 Unit Circle: Sine and Cosine Functions
  • 5.3 The Other Trigonometric Functions
  • 5.4 Right Triangle Trigonometry

Chapter 6 – Periodic Functions

  • Introduction to Periodic Functions
  • 6.1 Graphs of the Sine and Cosine Functions
  • 6.2 Graphs of the Other Trigonometric Functions
  • 6.3 Inverse Trigonometric Functions

Chapter 7 – Trigonometric Identities and Equations

  • Introduction to Trigonometric Identities and Equations
  • 7.1 Solving Trigonometric Equations with Identities
  • 7.2 Sum and Difference Identities
  • 7.3 Double-Angle, Half-Angle, and Reduction Formulas
  • 7.4 Sum-to-Product and Product-to-Sum Formulas
  • 7.5 Solving Trigonometric Equations
  • 7.6 Modeling with Trigonometric Equations

Chapter 8 – Further Applications of Trigonometry

  • Introduction to Further Applications of Trigonometry
  • 8.1 Non-right Triangles: Law of Sines
  • 8.2 Non-right Triangles: Law of Cosines
  • 8.3 Polar Coordinates
  • 8.4 Polar Coordinates: Graphs
  • 8.5 Polar Form of Complex Numbers
  • 8.6 Parametric Equations
  • 8.7 Parametric Equations: Graphs
  • 8.8 Vectors

Chapter 9 – Systems of Equations and Inequalities

  • Introduction to Systems of Equations and Inequalities
  • 9.1 Systems of Linear Equations: Two Variables
  • 9.2 Systems of Linear Equations: Three Variables
  • 9.3 Systems of Nonlinear Equations and Inequalities: Two Variables
  • 9.4 Partial Fractions
  • 9.5 Matrices and Matrix Operations
  • 9.6 Solving Systems with Gaussian Elimination
  • 9.7 Solving Systems with Inverses
  • 9.8 Solving Systems with Cramer’s Rule

Chapter 10 – Analytic Geometry

  • Introduction to Analytic Geometry
  • 10.1 The Ellipse
  • 10.2 The Hyperbola
  • 10.3 The Parabola
  • 10.4 Rotation of Axes
  • 10.5 Conic Sections in Polar Coordinates

Chapter 11 – Sequences, Probability and Counting Theory

  • Introduction to Sequences, Probability and Counting Theory
  • 11.1 Sequences and Their Notations
  • 11.2 Arithmetic Sequences
  • 11.3 Geometric Sequences
  • 11.4 Series and Their Notations
  • 11.5 Counting Principles
  • 11.6 Binomial Theorem
  • 11.7 Probability

Chapter 12 – Introduction to Calculus

  • Introduction to Calculus
  • 12.1 Finding Limits: Numerical and Graphical Approaches
  • 12.2 Finding Limits: Properties of Limits
  • 12.3 Continuity
  • 12.4 Derivatives
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