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APIntermediate
AP Calculus AB
Learn core differentiation and integration with a strong foundation before advancing into BC.
📚 8 units🤖 AI-guided support✅ Practice questions included
Course Units
2025–26 College Board CED1
Limits and Continuity10–12% of exam
1.1
What a Limit Actually Means
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1.2
Algebraic Limit Evaluation Techniques
Coming Soon
1.3
Limits at Infinity and Asymptotic Behavior
Coming Soon
1.4
Squeeze Theorem and Special Trig Limits
Coming Soon
1.5
Continuity — Three Conditions
Coming Soon
1.6
The Epsilon-Delta Definition of Limit
Coming Soon
1.7
Limits Involving Piecewise Functions
Coming Soon
1.8
Intermediate Value Theorem and Extreme Value Theorem
Coming Soon
2
Differentiation: Definition and Fundamental Properties10–12% of exam
2.1
Derivative as a Limit — The Formal Definition
Coming Soon
2.2
Power Rule, Constant Multiple, Sum/Difference Rules
Coming Soon
2.3
Derivatives of Trigonometric Functions
Coming Soon
2.4
Product and Quotient Rules
Coming Soon
2.5
Derivatives of Exponential and Logarithmic Functions
Coming Soon
2.6
Rates of Change and the Derivative's Meaning
Coming Soon
2.7
Differentiability at a Point — When Derivatives Fail
Coming Soon
2.8
Linear Approximation and Differentials
Coming Soon
3
Differentiation: Composite, Implicit, and Inverse Functions9–13% of exam
3.1
Chain Rule — The Most Used Rule
Coming Soon
3.2
Implicit Differentiation
Coming Soon
3.3
Derivatives of Inverse Functions
Coming Soon
3.4
Related Rates — Connecting Changing Quantities
Coming Soon
3.5
Logarithmic Differentiation
Coming Soon
3.6
Higher-Order Derivatives and Their Meaning
Coming Soon
3.7
Parametric Differentiation — dy/dx from x(t) and y(t)
Coming Soon
3.8
Implicit Curves — Tangent Lines and Second Derivatives
Coming Soon
4
Contextual Applications of Differentiation10–15% of exam
4.1
Straight-Line Motion — Position, Velocity, Acceleration
Coming Soon
4.2
Rates of Change in Applied Contexts
Coming Soon
4.3
Related Rates — Volume, Area, Distance
Coming Soon
4.4
L'Hôpital's Rule — When and How to Use It
Coming Soon
4.5
Linear Approximation in Applied Problems
Coming Soon
4.6
Tangent Lines and Normal Lines to Curves
Coming Soon
4.7
Population and Accumulation Models
Coming Soon
4.8
Implicit and Related Rate Problems — Advanced Setups
Coming Soon
5
Analytical Applications of Differentiation15–18% of exam
5.1
Mean Value Theorem — The Central Theorem
Coming Soon
5.2
Extreme Values — Finding Absolute Max and Min
Coming Soon
5.3
First Derivative Test for Local Extrema
Coming Soon
5.4
Second Derivative Test and Concavity
Coming Soon
5.5
Graph Sketching From Derivative Information
Coming Soon
5.6
Optimization — Setting Up and Solving
Coming Soon
5.7
Rolle's Theorem and Mean Value Theorem Applications
Coming Soon
5.8
Particle Motion — Using Derivatives to Analyze
Coming Soon
6
Integration and Accumulation of Change17–20% of exam
6.1
Antiderivatives and Indefinite Integrals
Coming Soon
6.2
Definite Integrals as Area and Accumulation
Coming Soon
6.3
Fundamental Theorem of Calculus — Both Parts
Coming Soon
6.4
u-Substitution for Integration
Coming Soon
6.5
Interpreting the Integral in Context
Coming Soon
6.6
Integration of Transcendental Functions
Coming Soon
6.7
Numerical Integration — Riemann Sums and Trapezoidal Rule
Coming Soon
6.8
Properties of Definite Integrals
Coming Soon
7
Differential Equations6–12% of exam
7.1
Slope Fields — Visualizing Differential Equations
Coming Soon
7.2
Euler's Method — Numerical Approximation
Coming Soon
7.3
Separable Differential Equations
Coming Soon
7.4
Exponential Growth and Decay Models
Coming Soon
7.5
Logistic Growth and Carrying Capacity
Coming Soon
7.6
Verifying Solutions to Differential Equations
Coming Soon
7.7
Accumulation and Net Change from Rate Functions
Coming Soon
7.8
Systems of Differential Equations — Introduction
Coming Soon
8
Applications of Integration10–15% of exam
8.1
Area Between Curves
Coming Soon
8.2
Volumes by Disk and Washer Methods
Coming Soon
8.3
Volumes by Shell Method
Coming Soon
8.4
Volumes of Solids with Known Cross Sections
Coming Soon
8.5
Arc Length and Surface Area
Coming Soon
8.6
Average Value of a Function
Coming Soon
8.7
Integration in Motion Problems — Total Distance
Coming Soon
8.8
Accumulation Problems — Complex Scenarios
Coming Soon