AP Calculus AB ยท all 8 units

Free AP Calculus AB lessons, worked step by step

Start with the 8 free topics, taken from all 8 units of the course and with no account needed: read the idea, follow the worked examples, then practise. Every practice question brings new numbers each time, so you learn the method, not the answer.

Start the first free lesson See AP Calculus AB Prep

Limits and Continuity

10 topics, 1 free

  1. Introducing Calculus; Defining Limits and Limit Notation Free
  2. Estimating Limits from Graphs and Tables AP Calculus AB Prep
  3. Limits by Algebraic Properties and Algebraic Manipulation AP Calculus AB Prep
  4. Choosing the Method; the Squeeze Theorem AP Calculus AB Prep
  5. Connecting Representations of Limits AP Calculus AB Prep
  6. Types of Discontinuity; Continuity at a Point AP Calculus AB Prep
  7. Continuity over an Interval; Removing Discontinuities AP Calculus AB Prep
  8. Infinite Limits and Vertical Asymptotes AP Calculus AB Prep
  9. Limits at Infinity and Horizontal Asymptotes AP Calculus AB Prep
  10. The Intermediate Value Theorem AP Calculus AB Prep

Differentiation: Definition and Fundamental Properties

8 topics, 1 free

  1. Average and Instantaneous Rates of Change AP Calculus AB Prep
  2. The Derivative and Derivative Notation Free
  3. Estimating Derivatives at a Point AP Calculus AB Prep
  4. Differentiability and Continuity AP Calculus AB Prep
  5. The Power Rule; Constant, Sum, Difference and Constant Multiple Rules AP Calculus AB Prep
  6. Derivatives of cos x, sin x, e^x and ln x AP Calculus AB Prep
  7. The Product Rule and the Quotient Rule AP Calculus AB Prep
  8. Derivatives of tan, cot, sec and csc AP Calculus AB Prep

Differentiation: Composite, Implicit and Inverse Functions

5 topics, 1 free

  1. The Chain Rule Free
  2. Implicit Differentiation AP Calculus AB Prep
  3. Differentiating Inverse Functions AP Calculus AB Prep
  4. Differentiating Inverse Trigonometric Functions AP Calculus AB Prep
  5. Choosing the Rule; Higher-Order Derivatives AP Calculus AB Prep

Contextual Applications of Differentiation

6 topics, 1 free

  1. The Meaning of the Derivative in Context AP Calculus AB Prep
  2. Straight-Line Motion: Position, Velocity, Acceleration AP Calculus AB Prep
  3. Rates of Change in Contexts Other Than Motion AP Calculus AB Prep
  4. Related Rates Free
  5. Local Linearity and Linearization AP Calculus AB Prep
  6. L'Hospital's Rule AP Calculus AB Prep

Analytical Applications of Differentiation

10 topics, 1 free

  1. The Mean Value Theorem AP Calculus AB Prep
  2. The Extreme Value Theorem; Global and Local Extrema; Critical Points AP Calculus AB Prep
  3. Intervals of Increase and Decrease AP Calculus AB Prep
  4. The First Derivative Test AP Calculus AB Prep
  5. The Candidates Test for Absolute Extrema Free
  6. Concavity AP Calculus AB Prep
  7. The Second Derivative Test AP Calculus AB Prep
  8. Graphs of a Function and Its First and Second Derivatives AP Calculus AB Prep
  9. Optimization AP Calculus AB Prep
  10. Behaviour of Implicit Relations AP Calculus AB Prep

Integration and Accumulation of Change

11 topics, 1 free

  1. Accumulation of Change AP Calculus AB Prep
  2. Approximating Areas with Riemann Sums AP Calculus AB Prep
  3. Riemann Sums, Summation Notation and the Definite Integral AP Calculus AB Prep
  4. The Fundamental Theorem and Accumulation Functions Free
  5. Behaviour of Accumulation Functions AP Calculus AB Prep
  6. Properties of Definite Integrals AP Calculus AB Prep
  7. The Fundamental Theorem and Definite Integrals AP Calculus AB Prep
  8. Antiderivatives and Indefinite Integrals: Basic Rules AP Calculus AB Prep
  9. Integration by Substitution AP Calculus AB Prep
  10. Long Division and Completing the Square AP Calculus AB Prep
  11. Choosing the Technique AP Calculus AB Prep

Differential Equations

4 topics, 1 free

  1. Modeling with Differential Equations; Verifying Solutions AP Calculus AB Prep
  2. Slope Fields: Sketching and Reasoning Free
  3. Separation of Variables: General and Particular Solutions AP Calculus AB Prep
  4. Exponential Models AP Calculus AB Prep

Applications of Integration

9 topics, 1 free

  1. Average Value of a Function AP Calculus AB Prep
  2. Position, Velocity and Acceleration with Integrals AP Calculus AB Prep
  3. Accumulation in Applied Contexts AP Calculus AB Prep
  4. Area Between Curves (Functions of x and of y) Free
  5. Area Between Curves Meeting More Than Twice AP Calculus AB Prep
  6. Cross Sections: Squares and Rectangles AP Calculus AB Prep
  7. Cross Sections: Triangles and Semicircles AP Calculus AB Prep
  8. Volumes by Discs AP Calculus AB Prep
  9. Volumes by Washers AP Calculus AB Prep