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Cheat sheetsLimits and derivatives
Connect an expression to what happens near an input, then connect a derivative to a rate of change. Explain the quantity and its units before calculating.
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Explore limits, derivatives and their contextual applications, including graph analysis, optimization, signed accumulation, area and volume through complete explanations, labeled graphs, worked examples and original practice. Units 1–6 and Unit 8 are available; Unit 7 remains an outline.
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Your AP Calculus AB
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Choose a unit, expand an official topic, and open a focused lesson. Units 1–6 and Unit 8 are available as review editions; Unit 7 remains a curriculum outline.
8 units142 focused lessonsLearn · Explore · Practice · Review
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01 Limits and Continuity 24 lessons · Review edition
Connect average change, limits, continuity, asymptotes and the Intermediate Value Theorem through labeled graphs, tables, algebra and explanations. 48 original questions, 72 recall cards and 24 written challenges. Optional rotatable secant graph; complete 2D alternatives. Independent teacher review and student testing remain pending.
1.1 Introducing Calculus: Can Change Occur at an Instant?
1.2 Defining Limits and Using Limit Notation
1.3 Estimating Limit Values from Graphs
1.4 Estimating Limit Values from Tables
1.5 Determining Limits Using Algebraic Properties of Limits
1.6 Determining Limits Using Algebraic Manipulation
1.7 Selecting Procedures for Determining Limits
1.8 Determining Limits Using the Squeeze Theorem
1.9 Connecting Multiple Representations of Limits
1.10 Exploring Types of Discontinuities
1.11 Defining Continuity at a Point
1.12 Confirming Continuity over an Interval
1.13 Removing Discontinuities
1.14 Connecting Infinite Limits and Vertical Asymptotes
1.15 Connecting Limits at Infinity and Horizontal Asymptotes
1.16 Working with the Intermediate Value Theorem (IVT)
02 Differentiation: Definition and Fundamental Properties 21 lessons · Review edition
Build derivatives from limits, connect slopes to derivative graphs, test differentiability and apply fundamental rules. 42 explained original questions, 63 recall cards and 21 written challenges. Optional linked 3D graph planes with complete 2D alternatives. Independent teacher review and student testing remain pending.
2.1 Defining Average and Instantaneous Rates of Change at a Point
2.2 Defining the Derivative of a Function and Using Derivative Notation
2.3 Estimating Derivatives of a Function at a Point
2.4 Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist
2.5 Applying the Power Rule
2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple
2.7 Derivatives of cos x, sin x, eˣ, and ln x
2.8 The Product Rule
2.9 The Quotient Rule
2.10 Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions
03 Differentiation: Composite, Implicit, and Inverse Functions 18 lessons · Review edition
Connect nested rates, differentiate implicit relations and inverses, choose derivative procedures and compute higher derivatives. 36 explained original questions, 54 recall cards and 18 written challenges. Optional 3D inverse-graph folding with complete 2D alternatives. Independent teacher review and student testing remain pending.
3.1 The Chain Rule
3.2 Implicit Differentiation
3.3 Differentiating Inverse Functions
3.4 Differentiating Inverse Trigonometric Functions
3.5 Selecting Procedures for Calculating Derivatives
3.6 Calculating Higher-Order Derivatives
04 Contextual Applications of Differentiation 18 lessons · Review edition
Interpret rates in context, connect motion quantities, solve related rates, estimate with tangent lines and apply L’Hôpital’s rule with its conditions. 36 explained original questions, 54 recall cards and 18 written challenges. Optional 3D conical-tank exploration with complete 2D alternatives. Independent teacher review and student testing remain pending.
4.1 Interpreting the Meaning of the Derivative in Context
4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration
4.3 Rates of Change in Applied Contexts Other Than Motion
4.4 Introduction to Related Rates
4.5 Solving Related Rates Problems
4.6 Approximating Values of a Function Using Local Linearity and Linearization
4.7 Using L’Hospital’s Rule for Determining Limits of Indeterminate Forms
05 Analytical Applications of Differentiation 20 lessons · Review edition
Justify function behavior with theorems, signs and graphs; compare extrema; solve optimization problems; analyze implicit curves. 40 explained original questions, 60 recall cards and 20 written challenges. Optional 3D box-folding exploration with complete 2D alternatives. Independent teacher review and student testing remain pending.
5.1 Using the Mean Value Theorem
5.2 Extreme Value Theorem, Global Versus Local Extrema, and Critical Points
5.3 Determining Intervals on Which a Function Is Increasing or Decreasing
5.4 Using the First Derivative Test to Determine Relative (Local) Extrema
5.5 Using the Candidates Test to Determine Absolute (Global) Extrema
5.6 Determining Concavity of Functions over Their Domains
5.7 Using the Second Derivative Test to Determine Extrema
5.8 Sketching Graphs of Functions and Their Derivatives
5.9 Connecting a Function, Its First Derivative, and Its Second Derivative
5.10 Introduction to Optimization Problems
5.11 Solving Optimization Problems
5.12 Exploring Behaviors of Implicit Relations
06 Integration and Accumulation of Change 21 lessons · Review edition
Connect rates to signed accumulation, approximate with Riemann sums, apply the Fundamental Theorem and select AB integration methods. 42 explained original questions, 63 recall cards and 21 written challenges. Optional 3D tank exploration with complete 2D alternatives. Official topics 6.11–6.13 are BC-only and intentionally omitted. Independent teacher review and student testing remain pending.
6.1 Exploring Accumulations of Change
6.2 Approximating Areas with Riemann Sums
6.3 Riemann Sums, Summation Notation, and Definite Integral Notation
6.4 The Fundamental Theorem of Calculus and Accumulation Functions
6.5 Interpreting the Behavior of Accumulation Functions Involving Area
6.6 Applying Properties of Definite Integrals
6.7 The Fundamental Theorem of Calculus and Definite Integrals
6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation
6.9 Integrating Using Substitution
6.10 Integrating Functions Using Long Division and Completing the Square
6.14 Selecting Techniques for Antidifferentiation
7 Differential EquationsCurriculum outline · Lessons not yet published
Use the official framework and topic specifications to see the detailed requirements for this area. Refresh Kid self-study lessons are not yet published here.
08 Applications of Integration 20 lessons · Review edition
Connect integrals to average values, motion, stored amounts, areas and volumes. 40 explained original questions, 60 recall cards and 20 written challenges. Inspect square, rectangular, triangular and semicircular sections, disks and washers in optional 3D with complete 2D alternatives. AB topics 8.1–8.12; BC-only arc length is excluded. Independent teacher review and student testing remain pending.
8.1 Finding the Average Value of a Function on an Interval
8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals
8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts
8.4 Finding the Area Between Curves Expressed as Functions of x
8.5 Finding the Area Between Curves Expressed as Functions of y
8.6 Finding the Area Between Curves That Intersect at More Than Two Points
8.7 Volumes with Cross Sections: Squares and Rectangles
8.8 Volumes with Cross Sections: Triangles and Semicircles
8.9 Volume with Disc Method: Revolving Around the x- or y-Axis
8.10 Volume with Disc Method: Revolving Around Other Axes
8.11 Volume with Washer Method: Revolving Around the x- or y-Axis
8.12 Volume with Washer Method: Revolving Around Other Axes
Curriculum sources & scope · AP Calculus AB
College Board
Shared AB/BC CED plus Fall 2026 corrections; eight AB units.
Complete official content is in the CED unit guides, including topic IDs, learning objectives, essential knowledge and course skills. The outline on this page is navigation only.
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Integrals and applications
Name what is accumulating and over which interval. Check the sign and units so a calculation answers the question that was asked.
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Yes. The 142 available review-edition lessons are free to access. Units 1–6 and 8 have lessons; Unit 7 remains an outline. Independent teacher review and student usability testing remain pending. Tutoring is optional.
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01 Limits and continuity
02 Differentiation and applications
03 Integration and accumulation
04 Differential equations and applications of integration
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