Math Made Easy’s AP Calculus AB lessons cover all 8 chapters, from limits and continuity to areas, volumes and accumulated change. Every AP Calculus AB lesson is free and aligned to the College Board AP Calculus AB framework. Mathbot, our blue robot coach, guides seniors preparing for the AP exam through worked examples first.
What the AP Calculus AB lessons teach
- Limits and Continuity
- Definition of the Derivative and Basic Rules
- Derivatives in Context: Motion and Related Rates
- Analyzing Functions with Derivatives
- Differential Equations
Work in order: read a lesson such as Limits and Continuity, solve the matching worksheet, check it against the answer key, take the chapter test, and finish with the 10-question quiz. The related rates and motion lessons turn word problems into one repeatable setup: draw, name variables, differentiate, substitute.
Write notation and units in every contextual problem, because AP scorers look for an interpretation sentence. Domains covered by the AP Calculus AB lessons: limits, derivatives, integrals and differential equations.
Chapter 1 · AP Calculus AB · AP Calculus AB Unit 1
Limits and Continuity: Approaching a Value
Find limits from graphs, tables, and algebra, including one-sided limits and limits at infinity, and use the squeeze theorem, continuity, and the Intermediate Value Theorem. You will classify jump, removable, and infinite discontinuities and read asymptotes. Do the lesson, then the worksheet and answer key, then the scored test on limits; the short quiz gives a fast check on the way.
- One-sided limits
- Continuity
- Discontinuities
Chapter 2 · AP Calculus AB · AP Calculus AB Unit 2
Derivative Definition and Differentiation Rules
Move from average to instantaneous rate of change, write the limit definition of the derivative, and test differentiability. Then apply the power, product, and quotient rules and the derivatives of sin x, cos x, e^x, and ln x. Lesson first, worksheet next: the answer key confirms each derivatives result, and the quiz and test with scoring guide close the chapter.
- Limit definition
- Power rule
- Product and quotient rules
Chapter 3 · AP Calculus AB · AP Calculus AB Unit 3
Chain Rule and Implicit Differentiation
Differentiate composite functions with the chain rule, use implicit differentiation, and find derivatives of inverse and inverse trigonometric functions and higher-order derivatives. For x^2 + y^2 = 25, you will show dy/dx = -x/y. Read the lesson on advanced differentiation, solve the worksheet and check it with the answer key, then take the quiz and the test.
- Chain rule
- Implicit differentiation
- Inverse derivatives
Chapter 4 · AP Calculus AB · AP Calculus AB Unit 4
Motion, Related Rates and Linearization
Interpret a derivative with units, connect position, velocity, and acceleration, and solve related rates and linearization problems, plus L'Hopital's rule. A ladder sliding down a wall at 2 feet per second is a classic related-rates setup. Work through the derivative applications lesson, test yourself on the worksheet with its answer key, and finish with the quiz and the scored test.
- Motion
- Related rates
- Linearization
Chapter 5 · AP Calculus AB · AP Calculus AB Unit 5
Using Derivatives to Analyze Graphs and Optimize
Apply the Mean Value and Extreme Value Theorems, use first and second derivative tests, read increasing, decreasing, and concavity, sketch curves, and optimize. Maximizing the area of a rectangle with 100 feet of fence gives a 25 by 25 square. Mathbot suggests the lesson first, then the worksheet with answer key, and finally the quiz and test to prove your function analysis skills.
- Mean Value Theorem
- Derivative tests
- Optimization
Chapter 6 · AP Calculus AB · AP Calculus AB Unit 6
Integrals, Riemann Sums and Accumulation
Build Riemann sums with left, right, midpoint, and trapezoidal rules, define the definite integral, and use the Fundamental Theorem of Calculus with antiderivatives and u-substitution. You will interpret an integral of a rate as accumulated change. Every page pairs a lesson with a worksheet and answer key, plus a quiz and a test whose scoring guide shows where integration points were earned.
- Riemann sums
- Fundamental Theorem
- u-substitution
Chapter 7 · AP Calculus AB · AP Calculus AB Unit 7
Modeling Change with Separable Equations
Model situations with differential equations, sketch and read slope fields, verify solutions, and solve by separation of variables, including exponential growth and decay. From dy/dx = 0.2y with y(0) = 50 you will build y = 50e^(0.2x). Read, solve the worksheet, grade it with the answer key; the quiz is a quick check on differential equations, and the test comes with a scoring guide.
- Slope fields
- Separation of variables
- Growth and decay
Chapter 8 · AP Calculus AB · AP Calculus AB Unit 8
Applications of Integration: Area and Volume
Use integrals for average value, motion, net change, and area between curves, then find volumes by cross sections and by the disc and washer methods. Rotating y = x from 0 to 2 about the x-axis gives a cone-shaped volume of 8 pi/3. Learn integral applications in the lesson, build speed on the worksheet, correct mistakes with the answer key, and confirm mastery with the quiz and test.
- Area between curves
- Disc and washer
- Average value
Grade 12 AP Calculus AB Lessons: frequently asked questions
Are the lessons free?
Yes. All 8 lessons are free to read, with no account needed. Each AP Calculus AB lesson points ahead to its worksheet, test and quiz.
Which standards do the lessons follow?
They follow the College Board AP Calculus AB course framework, which sets out the course units on limits, derivatives, integrals and differential equations. The eight chapters line up with those units in order, so each AP Calculus AB lesson maps to one unit.
What should I know before starting AP Calculus AB?
Students should have finished Precalculus, with strong command of functions, trigonometry, exponentials and logarithms. If a gap shows up, begin with the lesson on limits and continuity.
How are the lessons organized?
Eight units run from limits through derivatives and integrals to differential equations, in the same order as the course framework. The AP Calculus AB chapters can be read in order or picked by topic.
What comes after AP Calculus AB?
After AB, students can move on to AP Calculus BC topics or take college calculus and statistics. Finishing the 8 chapters on limits and continuity through areas, volumes and accumulated change leaves students ready for that step.