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