AP Calculus AB
Every AP Calculus AB unit, in order — free video lessons in English and Filipino, worksheets with answer keys, and 46 walkthroughs of released free-response questions.
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Covers AP Calculus AB. BC-only topics (series, and parametric, polar and vector functions) are not covered yet.
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Limits and Continuity
Limits from graphs, tables and algebra, one-sided limits, and limits at infinity.
Differentiation: Definition and Fundamental Properties
The derivative as a limit, and the power, product and quotient rules, including trig, exponential and log functions.
Unit 2 worksheets
- Exponential and Logarithmic Derivatives
- Derivatives of Exponential Functions
- Derivative Using the Limit Definition
- Derivatives of Logarithmic Functions
- Power Rule & Constant Rule: Finding Derivatives
- Power Rule
- Derivative Rules: Product & Quotient Rules with Given Values
- Finding the Derivative Using the Product Rule
- Derivatives of Sine and Cosine
- Derivatives of Trigonometric Functions — Set B
- Derivatives of Trigonometric Functions
- Derivatives Using the Power Rule
- Antiderivatives — Exponential, Trig, and Radical
Differentiation: Composite, Implicit, and Inverse Functions
The chain rule, derivatives from tables, implicit differentiation, inverse trig functions and higher-order derivatives. Apple Books reviewer: Implicit Differentiation.
Contextual Applications of Differentiation
Rates of change in context, motion, related rates, tangent-line approximation and L'Hôpital's rule. FRQ walkthroughs: particle motion, tangent lines and linearization, related rates and implicit differentiation. Apple Books reviewer: Particle in Motion.
Unit 4 worksheets
- Application: Approximation Part 2
- Application: Approximation
- Position, Velocity, and Acceleration
- Applications of Derivatives — Rectilinear Motion
- Particle Motion — Speeding Up and Slowing Down
- Particle Motion — Velocity and Acceleration
- Rates of Change Using Derivatives
- Rates of Change — Velocity and Acceleration
- Related Rates — Advanced Applications
- Related Rates
- Related Rates: Geometric Applications
- Related Rates with Implicit Differentiation
- Related Rates Review
- Related Rates — Word Problems
- Slopes and Tangent Lines
- Tangent and Normal Lines
- Tangent Lines to Curves
- Derivatives With Respect to Time
- L'Hôpital's Rule
Analytical Applications of Differentiation
The Mean Value Theorem, extrema, increasing and decreasing behavior, concavity, and optimization. Apple Books reviewer: Function Analysis.
Unit 5 worksheets
- Finding Critical Numbers — Part A
- Finding Critical Numbers — Part B
- Using the First Derivative to Analyze Behavior
- First Derivative Test
- First and Second Derivative Test (TI-84)
- Mean Value Theorem — Set B
- Mean Value Theorem
- MVT and Rolle's Theorem
- Optimization: Absolute Extrema
- Optimization and Graphing
- Optimization: Open Top Box Problem
- Optimization Problems Using Derivatives
- Optimization Word Problems Using Derivatives
- Rolle's Theorem
Integration and Accumulation of Change
Riemann sums, definite integrals, the Fundamental Theorem of Calculus, antiderivatives and u-substitution. FRQ walkthroughs: riemann sums, rates of change and accumulation, calculator strategy. Apple Books reviewer: Accumulation Problems.
Unit 6 worksheets
- Area Under the Curve — Absolute Value Functions
- Basic Integration
- Definite Integrals
- Exact Area with Definite Integrals
- Integration Practice
- Properties of Definite Integrals
- Integrals Review
- Riemann Sums: Approximating Area Under a Curve
- Riemann Sums: Estimating Distance Traveled
- Integrating Powers of Sine and Cosine
- Special Case Integration
- Integration by Substitution (U-Substitution)
Differential Equations
Slope fields, separable differential equations, and exponential models. FRQ walkthroughs: differential equations and slope fields. Apple Books reviewer: Differential Equations.
Applications of Integration
Average value, motion with integrals, area between curves, and volumes by disks, washers and cross sections. FRQ walkthroughs: area and volume, rates of change and accumulation. Apple Books reviewer: Areas and Volumes.
Unit 8 worksheets
- Optimization: Max Volume of an Open Box
- Areas Between Curves — Sub-Regions
- Area Between Curves
- Average Value of a Function — Set B
- Average Value of a Function
- Rectilinear Motion: Particle Problem
- Rectilinear Motion: Position, Velocity, Acceleration
- Volume — Cross Sections — Set B
- Volume by Cross Sections
- Volumes of Revolution — Disk Method — Set B
- Volume by Disks (Not on Axis)
- Volume by Disks
- Volumes of Revolution — Washer Method — Set B
- Volume by Washers
AP Calculus FRQ Walkthroughs by Topic
Dr. E works through free-response questions from released AP Calculus exams, topic by topic. Get the official questions and scoring guidelines from AP Central, try them, then watch.
From Dr. E's AP Calculus classroom
Dr. Peter Esperanza taught AP Calculus at Barstow High School alongside AP Statistics, algebra and precalculus. In 2012 he started flipping those classes: short video lessons the night before, and class time spent working problems together. The lessons on this page come from that work, recorded in English and again in Filipino.
The free-response walkthroughs follow the question types that come up on the exam year after year — Riemann sums, rates and accumulation, particle motion, area and volume, related rates and differential equations.