Calculus I and II

AP Calculus

Pre- Calculus

  • Algebra
    • Interpretation of Expressions, Operations and Identities
  • Order Matters!
    • Notation for Grouping
    • Parentheses For the Quadratic Formula
    • Guide to Pronunciation
  • Functions and Notation
    • functional “f(x)” notation
    • placeholders (dummy variables)
  • Reading and Writing Mathematics
    • Placeholders (dummy variables) and unknowns
    • How to write Methods
    • Methods as Formulas
    • Methods as Identities
    • Methods as Relations between Equations
  • Graphs
    • Terminology of Graphs
    • Expressions and Graphs
    • Graphing with Calculators,
    • Selecting a Window
    • Limitations of Calculator Graphs
    • Graphing Expressions to Solve Equations,
    • Maximizing or Minimizing an Expression
    • Graphs Without Expressions
  • Four Ways to Solve Equations
    • The “Inverse-Reverse” Method
    • The Zero Product Rule Method
    • The Quadratic Formula
    • Guess-and-Check (“trial and error”)


  • Functions and Graphs
    • Finding Windows
  • Composition and Decomposition
    • Composition and Inverses
    • Composition and Graphs
  • Relations and Inverses


  • Lines
    • Slope
    • Proportional
    • Parameters
    • Solving Linear Equations
    • Applications
    • Parallel and Perpendicular Lines
  • Quadratics
    • Symmetry
    • Location Changes, completing the square
    • The Quadratic Formula
    • Scale Changes
  • Distance, Circles, and Ellipses
    • Distance in the Plane
    • Circles
  • Graphical Factoring
    • The Factor Theorem
  • Word Problems
    • Build Your Own Formula
    • Evaluation and Solving
  • More on Word Problems


  • Powers and Polynomials
    • Polynomials
    • Graphs of Polynomials
    • End Behavior
    • The Use of Polynomials, Approximation
  • Polynomial Equations
    • Solving Monomial Equations
    • Solving Polynomial Equations
    • Calculator-Aided Factoring Techniques
  • Fractional Powers
    • Fractional Powers
    • Square Root
  • Percents, Money, and Compounding
    • Composition of Functions
    • Money, Compound Interest
    • Average Rate of Change
  • Rational Functions
    • Solving Rational Equations
    • Graphs
    • Asymptotes
    • End-Behavior
    • Uses of Rational Functions
  • Inequalities
    • Interval Notation
    • Graphical Solutions
    • Absolute Values
    • Inequalities for Calculus
    • Solving Linear Inequalities
    • Zeros and Inequalities


  • Exponents and Logarithms
    • Scientific Notation
    • Exponents and Logarithms
    • Properties of Exponential Functions
    • Properties of Logarithms
  • Base 2 and BaseĀ e
    • Base 2 (doubling time models)
    • Exponential Growth
    • Base 1/2 (half-life models)
    • Compound Interest
    • BaseĀ e
    • Polynomial Approximations
    • Change-of-Base
  • Applications
    • Richter Scale
    • Decibels
    • Exponential Models
    • Growth of Money
  • More Applications
    • Power Models, Kepler’s Laws


  • Geometry for Trigonometry
    • Solving a Triangle
    • Pythagorean Theorem
    • Ambiguous Cases, Recognizing the Cases
  • Trigonometric Functions
    • Sine, Inverse Sine
    • Solving Right Triangles
    • Cosine, Inverse Cosine
    • Tangent, Inverse Tangent
    • Reference Angles, Basic Facts
  • Solving Triangles
    • Area
    • The Law of Sines
    • The Law of Cosines
  • Solving Figures
    • Solving Triangles
    • More Complex Figures
    • Navigation


  • Arc Length and Radians
    • Arc Length
    • Area of a Sector
  • Trigonometric Identities
    • From Unit-Circle Pictures
    • Reference Angles
    • Solving Trigonometric Equations
    • Other Trigonometric Functions
    • Identities from Right-Triangle Pictures
    • Trigonometric Substitution
  • More Identities
    • The Sum and Difference Identities
    • Double- and Half-Angle Identities, Squared Identities
  • Waves
    • Describing Sine Waves
    • Adding Sine Waves
    • Applications

Math Lesson

A REVIEW OF BASIC ALGEBRA. Sets of Real Numbers. Integer Exponents and Scientific Notation. Rational Exponents and Radicals. Polynomials. Factoring Polynomials. Algebraic Fractions.

1. EQUATIONS AND INEQUALITIES. Equations. Applications of Linear Equations. Quadratic Equations. Applications of Quadratic Equations. Complex Numbers. Polynomial and Radical Equations. Inequalities. Absolute Value.

2. THE RECTANGULAR COORDINATE SYSTEM AND GRAPHS OF EQUATIONS. The Rectangular Coordinate System. The Slope of a Nonvertical Line. Writing Equations of Lines. Graphs of Equations. Proportion and Variation.

3. FUNCTIONS. Functions and Function Notation. Quadratic Functions. Polynomial and Other Functions. Translating and Stretching Graphs. Rational Functions. Operations on Functions. Inverse Functions.

4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions and Their Graphs. Applications of Exponential Functions. Logarithmic Functions and Their Graphs. Applications of Logarithmic Functions. Properties of Logarithms. Exponential and Logarithmic Equations.

5. SOLVING POLYNOMIAL EQUATIONS. The Remainder and Factor Theorems; Synthetic Division. Descartes’ Rule of Signs and Bounds on Roots. Rational Roots of Polynomial Equations. Irrational Roots of Polynomial Equations.

6. LINEAR SYSTEMS. Systems of Linear Equations. Gaussian Eliminations and Matrix Methods. Matrix Algebra. Matrix Inversion. Determinants. Partial Fractions. Graphs of Linear Inequalities. Linear Programming.

7. CONIC SECTIONS AND QUADRATIC SYSTEMS. The Circle and the Parabola. The Ellipse. The Hyperbola. Solving Simultaneous Second-Degree Equations.

8. NATURAL NUMBER FUNCTIONS AND PROBABILITY. The Binomial Theorem. Sequences, Series, and Summation Notation. Arithmetic Sequences. Geometric Sequences. Mathematical Induction. Permutations and Combinations. Probability. Computation of Compound Probabilities. Odds and Mathematical Expectation.

9. THE MATHEMATICS OF FINANCE. Interest. Annuities and Future Value. Present Value of an Annuit