AP Calculus Cheatsheets

AP Calculus, unit by unit

What each unit's one-page cheatsheet covers. Open a unit to read the start of its sheet.

1. AP Calculus AB · Unit 1: Limits and Continuity

   Limits: Definition & Notation · When Limits Do Not Exist · Estimating Limits: Graphs & Tables · Limit Laws & Algebraic Manipulation · Squeeze Theorem · Continuity at a Point · Types of Discontinuities · Piecewise Continuity & Removing Discontinuities · Infinite Limits & Asymptotes · Intermediate Value Theorem (IVT)

2. AP Calculus AB · Unit 2: Differentiation: Definition and Fundamental Properties

   Average vs. Instantaneous Rate of Change · Trigonometric Derivatives · Product Rule · Derivative Notation & Tangent Lines · Derivatives of Exponential & Logarithmic Functions · Quotient Rule · Estimating Derivatives · Differentiability & Continuity · Power Rule & Basic Derivative Rules

3. AP Calculus AB · Unit 3: Differentiation: Composite, Implicit, and Inverse Functions

   The Chain Rule: Core Formula & Setup · Chain Rule in Context: Rates & Relationships · Notation & Communication · Implicit Differentiation Process · Inverse Function Derivatives · Inverse Trigonometric Derivatives · Selecting the Right Procedure · Higher-Order Derivatives · Common Pitfalls & Verification

4. AP Calculus AB · Unit 4: Contextual Applications of Differentiation

   Derivative as Rate of Change · Rectilinear Motion: Position, Velocity, Acceleration · Linearization and Local Approximation · Rates of Change Beyond Motion · Identifying the Right Tool · Problem-Solving Decision Tree · Related Rates: Setup and Execution · L'Hospital's Rule for Indeterminate Forms · Units and Interpretation Checklist

5. AP Calculus AB · Unit 5: Analytical Applications of Differentiation

   Mean Value Theorem (MVT) · Implicit Differentiation & Implicit Relations · Graphing & Interpretation Checklist · Critical Points & Extrema · First Derivative Test · Optimization: Setup & Strategy · Increasing/Decreasing & Concavity · Second Derivative Test · Connecting f, f', and f''

6. AP Calculus AB · Unit 6: Integration and Accumulation of Change

   Accumulation + Net Change · Riemann Sums → Definite Integral · Table + Graph Setup Checks · Accumulation Functions + FTC Part 1 · Integral Properties · Read g(x) = ∫axf(t)dt from f · Variable-Limit Derivative Checklist · FTC Part 2: Evaluate · Antiderivatives + Techniques · Technique + FRQ Checklist · Common Antiderivative Errors

7. AP Calculus AB · Unit 7: Differential Equations

   Modeling & Verifying Solutions · Slope Fields · Separation of Variables · Particular Solutions & Initial Conditions · Exponential Growth & Decay · Problem-Solving Checklist

8. AP Calculus AB · Unit 8: Applications of Integration

   Average Value of a Function · Cross-Section Volumes · Disc Method (Axis of Revolution) · Position, Velocity, Acceleration · Area Between Curves (y-axis) · Problem-Solving Checklist · Accumulation & Net Change · Area Between Curves (x-axis) · Washer Method (Axis of Revolution)

9. AP Calculus BC · Unit 1: Limits and Continuity

   Limits: Definition & Notation · Squeeze Theorem & Key Trig Limits · Continuity on Intervals & Function Classes · One-Sided Limits & When They Fail · Estimating Limits: Graphs & Tables · Types of Discontinuities · Limit Theorems & Algebraic Techniques · Continuity at a Point · Infinite Limits, Asymptotes & IVT

10. AP Calculus BC · Unit 2: Differentiation: Definition and Fundamental Properties

    Average vs. Instantaneous Rate of Change · Differentiability & Continuity · Product Rule · Derivative Notation & Meaning · Trigonometric & Exponential Derivatives · Quotient Rule · Estimating Derivatives · Power Rule & Basic Rules · Choosing the Right Rule

11. AP Calculus BC · Unit 3: Differentiation: Composite, Implicit, and Inverse Functions

    The Chain Rule: Core Concept & Leibniz Notation · Implicit Differentiation Strategy · Inverse Function Derivatives · Inverse Trigonometric Derivatives · Selecting the Right Procedure · Higher-Order Derivatives · Chain Rule in Context: Rates & Relationships · Common Pitfalls & Verification · Unit 3 Summary: What to Master

12. AP Calculus BC · Unit 4: Contextual Applications of Differentiation

    Derivative as Rate of Change · Rectilinear Motion: Position, Velocity, Acceleration · Related Rates: Setup & Execution · Rates of Change Beyond Motion · Linearization & Local Linearity · L'Hospital's Rule · Identifying & Applying Rules · Extracting & Interpreting Information · Verification & Justification

13. AP Calculus BC · Unit 5: Analytical Applications of Differentiation

    Mean Value Theorem (MVT) · Extreme Value Theorem & Critical Points · Increasing/Decreasing & First Derivative Test · Second Derivative Test & Concavity · Absolute Extrema & Optimization · Connecting f, f', and f'' · Implicit Differentiation & Implicit Relations · Common Mistakes & Verification

14. AP Calculus BC · Unit 7: Differential Equations

    Modeling & Verifying Solutions · Slope Fields & Euler's Method · Separation of Variables · Particular Solutions & Initial Conditions · Exponential Growth & Decay · Logistic Growth Model · Solving Strategy · Interpretation & Context · Verification Checklist

15. AP Calculus BC · Unit 8: Applications of Integration

    Average Value of a Function · Accumulation & Net Change · Washer Method (Solids of Revolution with Holes) · Position, Velocity, Acceleration (Rectilinear Motion) · Volumes: Cross Sections (Squares, Rectangles, Triangles, Semicircles) · Disc Method (Solids of Revolution) · Area Between Curves (x or y as variable) · Arc Length (BC Only) · Problem-Solving Decision Tree

16. AP Calculus BC · Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions (BC only)

    Parametric Derivatives: dy/dx and d²y/dx² · Vector-Valued Functions: Derivatives & Integrals · Problem-Solving Checklist · Arc Length for Parametric Curves · Polar Area: Single Curve · Polar Area: Two Curves · Motion: Velocity, Speed, Acceleration, Displacement · Polar Coordinates: Setup & Derivatives · Notation & Language

17. AP Calculus BC · Unit 10: Infinite Sequences and Series (BC only)

    Convergence & Partial Sums · Integral & p-Series Tests · Comparison Tests · Alternating Series & Ratio Test · Power Series & Radius of Convergence · Constructing Power Series · Absolute vs. Conditional Convergence · Error Bounds for Approximations · Taylor & Maclaurin Series