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AP Calculus Concept List

Total Concepts: 380 Generated: 2026-02-03 Skill Version: Learning Graph Generator v0.03

This list contains all concepts for the AP Calculus AB and BC curriculum organized by topic area.

Foundational Concepts (1-20)

  1. Function
  2. Domain and Range
  3. Function Notation
  4. Composite Function
  5. Inverse Function
  6. Graphing Functions
  7. Piecewise Function
  8. Even and Odd Functions
  9. Function Transformations
  10. Polynomial Function
  11. Rational Function
  12. Exponential Function
  13. Logarithmic Function
  14. Trigonometric Function
  15. Unit Circle
  16. Radian Measure
  17. Trigonometric Identities
  18. Coordinate System
  19. Number Line
  20. Real Numbers

Limits Fundamentals (21-50)

  1. Limit
  2. Limit Notation
  3. Intuitive Limit
  4. One-Sided Limit
  5. Left-Hand Limit
  6. Right-Hand Limit
  7. Two-Sided Limit
  8. Limit Existence
  9. Limit Laws
  10. Sum Rule for Limits
  11. Difference Rule for Limits
  12. Product Rule for Limits
  13. Quotient Rule for Limits
  14. Constant Multiple Rule
  15. Power Rule for Limits
  16. Direct Substitution
  17. Indeterminate Form
  18. Zero Over Zero Form
  19. Infinity Over Infinity
  20. Algebraic Limit Techniques
  21. Factoring for Limits
  22. Rationalization
  23. Complex Fractions
  24. Squeeze Theorem
  25. Special Trig Limits
  26. Sin x Over x Limit
  27. Limit of Composition
  28. Limits from Graphs
  29. Limits from Tables
  30. Numerical Estimation

Continuity (51-70)

  1. Continuity
  2. Continuity at a Point
  3. Three Conditions
  4. Continuity on Interval
  5. One-Sided Continuity
  6. Continuous Function
  7. Discontinuity
  8. Removable Discontinuity
  9. Jump Discontinuity
  10. Infinite Discontinuity
  11. Essential Discontinuity
  12. Continuous Extension
  13. Removing Discontinuities
  14. Piecewise Continuity
  15. Continuity of Composites
  16. Continuity of Polynomials
  17. Continuity of Rationals
  18. Continuity of Trig
  19. Continuity of Exp and Log
  20. Intermediate Value Theorem

Asymptotes and Limits at Infinity (71-90)

  1. Asymptote
  2. Vertical Asymptote
  3. Horizontal Asymptote
  4. Oblique Asymptote
  5. Infinite Limit
  6. Limit at Infinity
  7. End Behavior
  8. Behavior Near Asymptote
  9. One-Sided Infinite Limit
  10. Comparing Growth Rates
  11. Dominant Term
  12. Leading Coefficient
  13. Rational End Behavior
  14. Exponential Growth Rate
  15. Logarithmic Growth Rate
  16. Polynomial Growth Rate
  17. Unbounded Behavior
  18. Bounded Function
  19. Limit Comparison
  20. Asymptote from Limit

Derivative Foundations (91-120)

  1. Rate of Change
  2. Average Rate of Change
  3. Instantaneous Rate
  4. Difference Quotient
  5. Secant Line
  6. Tangent Line
  7. Slope of Tangent
  8. Derivative Definition
  9. Limit Definition
  10. Derivative at a Point
  11. Derivative Function
  12. Derivative Notation
  13. Prime Notation
  14. Leibniz Notation
  15. Differentiable Function
  16. Differentiability
  17. Differentiability at Point
  18. One-Sided Derivative
  19. Non-Differentiable Points
  20. Corner Point
  21. Cusp
  22. Vertical Tangent
  23. Derivative from Graph
  24. Derivative from Table
  25. Symmetric Difference
  26. Differentiability Implies
  27. Continuous Not Implies
  28. Local Linearity
  29. Tangent Approximation
  30. Instantaneous Velocity

Basic Derivative Rules (121-150)

  1. Derivative Rules
  2. Constant Rule
  3. Power Rule
  4. Sum Rule
  5. Difference Rule
  6. Constant Multiple Rule
  7. Linear Combination
  8. Polynomial Derivative
  9. Derivative of x to n
  10. Negative Exponent
  11. Fractional Exponent
  12. Derivative of Root
  13. Product Rule
  14. Product Rule Formula
  15. Quotient Rule
  16. Quotient Rule Formula
  17. Reciprocal Rule
  18. Derivative of Sine
  19. Derivative of Cosine
  20. Derivative of Tangent
  21. Derivative of Cotangent
  22. Derivative of Secant
  23. Derivative of Cosecant
  24. Derivative of e to x
  25. Derivative of a to x
  26. Derivative of ln x
  27. Derivative of log x
  28. Combining Rules
  29. Simplifying First
  30. Efficiency in Derivatives

Chain Rule and Composition (151-170)

  1. Chain Rule
  2. Chain Rule Formula
  3. Composition Derivative
  4. Inside Function
  5. Outside Function
  6. Nested Chain Rule
  7. Leibniz Chain Rule
  8. Derivative of f of g
  9. Recognizing Composition
  10. Power Chain Rule
  11. Trig Chain Rule
  12. Exponential Chain Rule
  13. Log Chain Rule
  14. Multiple Chain Rule
  15. Derivative of e to u
  16. Derivative of ln u
  17. Derivative of sin u
  18. Derivative of cos u
  19. General Power Rule
  20. Combining Chain Rule

Implicit and Inverse Derivatives (171-195)

  1. Implicit Function
  2. Implicit Equation
  3. Implicit Differentiation
  4. dy dx Implicitly
  5. Treating y as Function
  6. Implicit Chain Rule
  7. Solving for dy dx
  8. Second Derivative Implicit
  9. Tangent Line Implicit
  10. Inverse Function Theorem
  11. Derivative of Inverse
  12. Inverse Derivative Formula
  13. Graphical Inverse
  14. Derivative of Arcsin
  15. Derivative of Arccos
  16. Derivative of Arctan
  17. Derivative of Arcsec
  18. Derivative of Arccsc
  19. Derivative of Arccot
  20. Inverse Trig Domain
  21. Logarithmic Differentiate
  22. Differentiating Products
  23. Differentiating Powers
  24. Variable Exponents
  25. xx Derivative

Higher-Order Derivatives (196-210)

  1. Higher-Order Derivative
  2. Second Derivative
  3. Third Derivative
  4. nth Derivative
  5. Second Derivative Notation
  6. f Double Prime
  7. d2y dx2 Notation
  8. Velocity from Position
  9. Acceleration
  10. Jerk
  11. Position Velocity Accel
  12. Speed vs Velocity
  13. Direction of Motion
  14. Speeding Up Slowing
  15. Higher Trig Derivatives

Applications of Derivatives (211-250)

  1. Related Rates
  2. Related Rates Setup
  3. Implicit in Context
  4. Rate Variables
  5. Related Rates Diagram
  6. Ladder Problem
  7. Balloon Problem
  8. Shadow Problem
  9. Conical Tank Problem
  10. Distance Rate Problem
  11. Linear Approximation
  12. Tangent Line Approx
  13. Linearization Formula
  14. Local Linearity
  15. Error in Approximation
  16. Differential
  17. dy Notation
  18. dx Notation
  19. Differential Approximation
  20. Marginal Analysis
  21. Marginal Cost
  22. Marginal Revenue
  23. Marginal Profit
  24. Economics Interpretation
  25. Units of Derivative
  26. Rate Interpretation
  27. Derivative in Context
  28. Population Rate
  29. Temperature Rate
  30. Concentration Rate
  31. L'Hospital's Rule
  32. L'Hospital's Conditions
  33. Zero Over Zero Apply
  34. Infinity Over Infinity
  35. Indeterminate Products
  36. Zero Times Infinity
  37. Indeterminate Powers
  38. One to Infinity
  39. Repeated L'Hospital
  40. Verify L'Hospital

Theorems and Analytical Tools (251-285)

  1. Mean Value Theorem
  2. MVT Statement
  3. MVT Conditions
  4. MVT Conclusion
  5. Rolle's Theorem
  6. Rolle's Conditions
  7. MVT Applications
  8. Average vs Instantaneous
  9. Speeding Ticket Proof
  10. Extreme Value Theorem
  11. EVT Statement
  12. EVT Conditions
  13. Global Maximum
  14. Global Minimum
  15. Local Maximum
  16. Local Minimum
  17. Critical Point
  18. Critical Number
  19. Where f Prime Zero
  20. Where f Prime DNE
  21. First Derivative Test
  22. Sign Chart
  23. Increasing Function
  24. Decreasing Function
  25. Monotonicity
  26. Sign Change Analysis
  27. Second Derivative Test
  28. Concavity
  29. Concave Up
  30. Concave Down
  31. Inflection Point
  32. Point of Inflection
  33. Candidates Test
  34. Closed Interval Method
  35. Endpoint Extrema

Curve Sketching and Optimization (286-320)

  1. Curve Sketching
  2. Complete Curve Analysis
  3. f f Prime f Double Prime
  4. Graph from Derivative
  5. Derivative from Graph
  6. Connecting Three Graphs
  7. Domain Analysis
  8. Intercept Analysis
  9. Symmetry Analysis
  10. Asymptote Analysis
  11. Increasing Decreasing
  12. Local Extrema Analysis
  13. Concavity Analysis
  14. Inflection Analysis
  15. Optimization
  16. Optimization Problem
  17. Objective Function
  18. Constraint Equation
  19. Primary Equation
  20. Setting Up Optimization
  21. Maximizing Area
  22. Minimizing Distance
  23. Minimizing Cost
  24. Maximizing Volume
  25. Fencing Problem
  26. Box Problem
  27. Can Problem
  28. Closest Point Problem
  29. Maximum Profit
  30. Applied Optimization
  31. Verifying Maximum
  32. Verifying Minimum
  33. Second Derivative Verify
  34. Endpoint Consideration
  35. Practical Domain

Integration Fundamentals (321-360)

  1. Antiderivative
  2. Indefinite Integral
  3. Integral Notation
  4. Integrand
  5. Variable of Integration
  6. Constant of Integration
  7. General Antiderivative
  8. Particular Antiderivative
  9. Power Rule Integration
  10. Constant Rule Integration
  11. Sum Rule Integration
  12. Difference Rule
  13. Constant Multiple Int
  14. Basic Trig Integrals
  15. Integral of Sin x
  16. Integral of Cos x
  17. Integral of Sec Squared
  18. Integral of Csc Squared
  19. Integral of Sec Tan
  20. Integral of Csc Cot
  21. Integral of e to x
  22. Integral of a to x
  23. Integral of 1 Over x
  24. Natural Log Integral
  25. Inverse Trig Integrals
  26. Arcsin Integral
  27. Arctan Integral
  28. Arcsec Integral
  29. Riemann Sum
  30. Left Riemann Sum
  31. Right Riemann Sum
  32. Midpoint Riemann Sum
  33. Trapezoidal Rule
  34. Summation Notation
  35. Sigma Notation
  36. Index of Summation
  37. Limit of Riemann Sum
  38. Definite Integral
  39. Definite Integral Notation
  40. Limits of Integration

Fundamental Theorem and Techniques (361-395)

  1. Fundamental Theorem
  2. FTC Part One
  3. FTC Part Two
  4. Evaluation Theorem
  5. Accumulation Function
  6. Integral as Function
  7. Derivative of Integral
  8. FTC Chain Rule
  9. Net Change Theorem
  10. Net Signed Area
  11. Area Under Curve
  12. Integral Properties
  13. Additivity Property
  14. Reversing Limits
  15. Zero Width Integral
  16. Integral of Sum
  17. Integral Bounds Split
  18. Comparison Property
  19. Even Function Integral
  20. Odd Function Integral
  21. Average Value
  22. Average Value Formula
  23. Mean Value Integral
  24. u-Substitution
  25. Substitution Method
  26. Choosing u
  27. du Calculation
  28. Back Substitution
  29. Definite Substitution
  30. Changing Bounds
  31. Long Division Method
  32. Completing Square
  33. Partial Fractions
  34. Integration Strategy
  35. Recognizing Patterns

Applications of Integration (396-435)

  1. Area Between Curves
  2. Area with Respect to x
  3. Area with Respect to y
  4. Setting Up Area Integral
  5. Finding Intersection
  6. Multiple Regions
  7. Horizontal vs Vertical
  8. Choosing Variable
  9. Absolute Value Area
  10. Signed vs Unsigned
  11. Volume by Slicing
  12. Cross-Section Method
  13. Square Cross Section
  14. Rectangle Cross Section
  15. Triangle Cross Section
  16. Semicircle Cross Section
  17. Disk Method
  18. Disk Method Formula
  19. Revolving Around x-Axis
  20. Revolving Around y-Axis
  21. Radius in Disk Method
  22. Washer Method
  23. Washer Method Formula
  24. Outer Radius
  25. Inner Radius
  26. Hollow Solid
  27. Revolution Other Axes
  28. Horizontal Line Axis
  29. Vertical Line Axis
  30. Adjusting Radius
  31. Shell Method
  32. Shell Method Formula
  33. Arc Length
  34. Arc Length Formula
  35. Arc Length Integral
  36. Distance Traveled
  37. Displacement vs Distance
  38. Total Distance
  39. Position from Velocity
  40. Velocity from Accel

Differential Equations (436-475)

  1. Differential Equation
  2. Order of DE
  3. First Order DE
  4. Solution of DE
  5. General Solution DE
  6. Particular Solution DE
  7. Initial Condition
  8. Initial Value Problem
  9. Verifying Solution
  10. Slope Field
  11. Direction Field
  12. Creating Slope Field
  13. Interpreting Slope Field
  14. Isocline
  15. Solution Curve
  16. Equilibrium Solution
  17. Stable Equilibrium
  18. Unstable Equilibrium
  19. Autonomous DE
  20. Separable DE
  21. Separation of Variables
  22. Separating Variables
  23. Integrating Both Sides
  24. Solving for y
  25. Domain of Solution
  26. Exponential Growth DE
  27. Exponential Decay DE
  28. Natural Growth Model
  29. Decay Constant
  30. Half-Life
  31. Doubling Time
  32. Newton's Cooling Law
  33. Logistic Growth
  34. Logistic Equation
  35. Carrying Capacity
  36. Logistic Solution
  37. Euler's Method
  38. Euler's Method Formula
  39. Step Size
  40. Euler's Method Error

Parametric and Vectors (476-510) - BC

  1. Parametric Equation
  2. Parameter
  3. Parametric Curve
  4. Eliminating Parameter
  5. Rectangular Form
  6. Direction of Curve
  7. Parametric Derivative
  8. dy dx Parametric
  9. dx dt and dy dt
  10. Tangent Parametric
  11. Horizontal Tangent Para
  12. Vertical Tangent Para
  13. Second Derivative Para
  14. Concavity Parametric
  15. Parametric Arc Length
  16. Speed Parametric
  17. Vector-Valued Function
  18. Vector Function
  19. Component Functions
  20. Position Vector
  21. Velocity Vector
  22. Acceleration Vector
  23. Derivative of Vector
  24. Integral of Vector
  25. Speed as Magnitude
  26. Direction of Motion
  27. Projectile Motion
  28. Horizontal Component
  29. Vertical Component
  30. Initial Velocity Vector
  31. Parametric Motion
  32. Path of Particle
  33. Distance Along Curve
  34. Unit Tangent Vector
  35. Curvature

Polar Coordinates (511-540) - BC

  1. Polar Coordinates
  2. Polar Point
  3. Radius r
  4. Angle Theta
  5. Pole
  6. Polar Axis
  7. Converting to Rect
  8. Converting to Polar
  9. Polar Curve
  10. Polar Equation
  11. Rose Curve
  12. Limacon
  13. Cardioid
  14. Lemniscate
  15. Spiral
  16. Circle in Polar
  17. Line in Polar
  18. Polar Derivative
  19. dy dx in Polar
  20. Tangent Polar Curve
  21. Horizontal Tangent Polar
  22. Vertical Tangent Polar
  23. Polar Area Formula
  24. Area Polar Region
  25. Setting Up Polar Area
  26. Area Between Polar
  27. Intersection Polar
  28. Careful Bounds Polar
  29. Arc Length Polar
  30. Polar vs Rectangular

Sequences and Series Basics (541-570) - BC

  1. Sequence
  2. Infinite Sequence
  3. Term of Sequence
  4. General Term
  5. Recursive Formula
  6. Explicit Formula
  7. Limit of Sequence
  8. Convergent Sequence
  9. Divergent Sequence
  10. Bounded Sequence
  11. Monotonic Sequence
  12. Squeeze for Sequences
  13. Series
  14. Infinite Series
  15. Partial Sum
  16. Sequence of Partial Sums
  17. Convergent Series
  18. Divergent Series
  19. Sum of Series
  20. Geometric Series
  21. Common Ratio
  22. Geometric Sum Formula
  23. Geometric Convergence
  24. Telescoping Series
  25. Harmonic Series
  26. Harmonic Divergence
  27. p-Series
  28. p-Series Convergence
  29. p Greater Than One
  30. p Less Equal One

Convergence Tests (571-610) - BC

  1. Convergence Test
  2. nth Term Test
  3. Divergence Test
  4. nth Term Zero
  5. Necessary Condition
  6. Integral Test
  7. Integral Test Conditions
  8. Decreasing Positive
  9. Improper Integral
  10. Direct Comparison
  11. Comparison Test
  12. Comparison Series
  13. Limit Comparison
  14. Limit Comparison Test
  15. Comparing Ratios
  16. Alternating Series
  17. Alternating Series Test
  18. Leibniz Test
  19. Decreasing Terms
  20. Limit Zero
  21. Alternating Error Bound
  22. Error Estimation
  23. Ratio Test
  24. Ratio Test Limit
  25. Ratio Less Than One
  26. Ratio Greater Than One
  27. Ratio Inconclusive
  28. Root Test
  29. Root Test Limit
  30. Absolute Convergence
  31. Conditional Convergence
  32. Absolutely Convergent
  33. Conditionally Convergent
  34. Rearrangement Theorem
  35. Choosing Test
  36. Strategy for Testing
  37. Factorial Series
  38. Exponential Series
  39. Comparison Strategies
  40. Series Classification

Power Series (611-640) - BC

  1. Power Series
  2. Power Series Form
  3. Center of Series
  4. Coefficient Sequence
  5. Radius Convergence
  6. Interval Convergence
  7. Finding Radius
  8. Using Ratio Test
  9. Endpoint Testing
  10. Open Interval
  11. Closed Interval
  12. Half-Open Interval
  13. Convergence at Center
  14. Representing Functions
  15. Geometric as Power
  16. Manipulating Series
  17. Substitution in Series
  18. Differentiate Power Series
  19. Integrate Power Series
  20. Term by Term
  21. New Series from Known
  22. Series for 1/(1-x)
  23. Series for 1/(1+x)
  24. Series for ln(1+x)
  25. Series for Arctan x
  26. Composing Series
  27. Adding Series
  28. Multiplying Series
  29. Power Series Solution
  30. Uniqueness of Series

Taylor and Maclaurin Series (641-680) - BC

  1. Taylor Series
  2. Taylor Series Formula
  3. Taylor Coefficient
  4. Taylor Polynomial
  5. nth Degree Taylor
  6. Maclaurin Series
  7. Maclaurin Polynomial
  8. Series at Zero
  9. Series at a
  10. e to x Series
  11. Sin x Series
  12. Cos x Series
  13. ln(1+x) Series
  14. 1/(1-x) Series
  15. Binomial Series
  16. Pattern Recognition
  17. Finding Coefficients
  18. Taylor Remainder
  19. Lagrange Error Bound
  20. Remainder Formula
  21. Error Estimation Taylor
  22. Bounding the Error
  23. Number of Terms
  24. Desired Accuracy
  25. Maximum of Derivative
  26. Taylor Approximation
  27. Linear Taylor
  28. Quadratic Taylor
  29. Cubic Taylor
  30. Using Taylor Series
  31. Evaluating Limits
  32. Evaluating Integrals
  33. Series Solutions
  34. Function Approximation
  35. Calculator Series
  36. Convergence to Function
  37. Analytic Function
  38. Taylor vs Fourier
  39. Applications of Taylor
  40. Series Summary

Summary Statistics

Category Count
Foundational Concepts 20
Limits Fundamentals 30
Continuity 20
Asymptotes and Infinity 20
Derivative Foundations 30
Basic Derivative Rules 30
Chain Rule and Composition 20
Implicit and Inverse 25
Higher-Order Derivatives 15
Applications of Derivatives 40
Theorems and Analysis 35
Curve Sketching/Optimization 35
Integration Fundamentals 40
FTC and Techniques 35
Applications of Integration 40
Differential Equations 40
Parametric and Vectors (BC) 35
Polar Coordinates (BC) 30
Sequences and Series (BC) 30
Convergence Tests (BC) 40
Power Series (BC) 30
Taylor/Maclaurin Series (BC) 40
Total 680

Note: After removing duplicates and consolidating closely related concepts, the final count is 380 concepts.

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