The AP (Advanced Placement) Calculus AB Course and Exam Description, or CED, is the CollegeBoard document that tells teachers exactly what shows up on the May exam. It breaks the course into eight units, weights each unit on the multiple-choice section, and lists four mathematical practices (implementing mathematical processes, connecting representations, justification, and communication and notation) that thread through every FRQ rubric.
This guide is the working summary: every unit, its exam weight, what it tests, and what students most commonly under-prepare for. If you'd rather practice the underlying content, Cognito's AP Calc AB past papers walk through every recent released paper by year.
How the CED is structured
The eight units run in a natural order: limits, derivatives, applications of derivatives, integrals, differential equations, applications of integrals. Each unit maps to one or more of the three big ideas the CED calls out (change, limits, analysis of functions). The mathematical practices show up directly in FRQ rubrics: 'implementing mathematical processes' means computational correctness, 'connecting representations' means moving between graphs, tables and formulas, 'justification' means supporting a conclusion with a theorem or the sign of a derivative, and 'communication and notation' means writing it down in correct mathematical form.
The eight units and their exam weights
| Unit | Topic | Exam weight (MCQ) |
|---|---|---|
| 1 | Limits and continuity | 10–12% |
| 2 | Differentiation: definition and fundamental properties | 10–12% |
| 3 | Differentiation: composite, implicit and inverse | 9–13% |
| 4 | Contextual applications of differentiation | 10–15% |
| 5 | Analytical applications of differentiation | 15–18% |
| 6 | Integration and accumulation of change | 17–20% |
| 7 | Differential equations | 6–12% |
| 8 | Applications of integration | 10–15% |
The two heaviest-weighted units are integration and accumulation of change (Unit 6) at 17 to 20 percent and analytical applications of differentiation (Unit 5) at 15 to 18 percent. Between them they carry roughly a third of the multiple-choice weight. Differential equations (Unit 7) is the lightest by MCQ weight but frequently claims a full FRQ, so its weight on your final score can be higher than the MCQ percentage suggests.
Unit 1: Limits and continuity
Enduring understandings: The concept of a limit underlies calculus; limits describe function behavior at points and at infinity; a function is continuous where the limit equals the function value.
Most commonly tested: evaluating limits algebraically (factoring, rationalizing, using the squeeze theorem), one-sided limits, limits at infinity, continuity conditions and the intermediate value theorem. L'Hopital's rule is formally introduced later, in Unit 4.
Where students under-prepare: the formal three-part definition of continuity. FRQs sometimes ask 'is f continuous at x = a', expecting the student to verify that f(a) exists, the limit exists, and they're equal; eyeballing a graph isn't enough.
Units 2 and 3: Differentiation
Unit 2 covers the definition of the derivative, power rule, product rule, quotient rule, chain rule and derivatives of basic functions. Unit 3 extends to composite functions, implicit differentiation, and derivatives of inverse functions (including inverse trig).
Most commonly tested: chain rule applied through multiple layers of composition, implicit differentiation on curves that mix x and y, derivatives of inverse trig functions.
Where students under-prepare: implicit differentiation. The technique itself is straightforward, but recognizing when a curve is defined implicitly (any equation that isn't already solved for y) and remembering to apply the chain rule to every y term catches students out under time pressure.
Unit 4: Contextual applications of differentiation
This is the physics-flavored unit: rates of change in real-world settings, related rates, and linear approximation.
Most commonly tested: related rates problems (ladder sliding down a wall, water draining from a cone, balloon inflating), and interpreting the derivative in context ('the rate at which the tank is filling at t = 3 is 2.5 liters per minute').
Where students under-prepare: setting up related rates from a verbal description. The equation itself is often standard geometry (Pythagorean, volume of a cone, area of a circle), but translating the words into a labeled diagram with named variables and known rates trips people up.
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Unit 5: Analytical applications of differentiation
The heaviest analytical unit: first and second derivative tests, extrema, inflection points, concavity, and optimization.
Most commonly tested: finding local and absolute extrema on an interval, classifying critical points with the first or second derivative test, analyzing concavity, solving an optimization problem.
Where students under-prepare: the justification step. When an FRQ asks 'is f increasing at x = 2', the rubric wants you to reference the sign of f prime at x = 2, not just assert 'yes' and move on. This 'implementing procedures' vs 'communicating and reasoning' distinction is where MCQ-strong students often bleed FRQ points.
Unit 6: Integration and accumulation of change
The heaviest unit by MCQ weight: Riemann sums, the fundamental theorem of calculus, antiderivatives, techniques of integration (u-substitution primarily), and integrals defined as accumulation functions.
Most commonly tested: Riemann sums from tables (trapezoidal, left, right, midpoint), the FTC in both forms (evaluating a definite integral, differentiating an integral function), u-substitution, and interpreting an integral function g(x) defined as the integral from 0 to x of f(t).
Where students under-prepare: the exact statement of the second FTC. When g(x) is defined as an integral, g prime is the integrand, but if the upper limit is a composite function (h(x) instead of just x), the chain rule kicks in and g prime becomes f(h(x)) times h prime of x.
Unit 7: Differential equations
Slope fields, separable differential equations, and exponential growth and decay models.
Most commonly tested: sketching a slope field from a given dy/dx, solving a separable equation, applying an initial condition to find the particular solution.
Where students under-prepare: the constant of integration. After separating and integrating both sides, students frequently forget to apply the initial condition to find C, or apply it before exponentiating (giving the wrong form of the general solution). Working with implicit solutions when the algebra to solve for y is messy is another common trap.
Unit 8: Applications of integration
Area between curves, volumes of solids of revolution (disc and washer), volumes with known cross-sections, average value, and applications like particle motion (position from velocity).
Most commonly tested: area between two curves, volume of revolution about a horizontal or vertical line (potentially shifted, requiring adjusted radii), volume with cross-sections of a specified shape (square, semicircle, equilateral triangle).
Where students under-prepare: rotation about a shifted axis. When the axis of rotation is y = -2 rather than the x-axis, the outer and inner radii both shift by 2, and forgetting the shift is a common way to zero out the volume calculation.
Read every FRQ prompt for the mathematical practice being tested. 'Compute' or 'evaluate' is procedures. 'Explain' or 'justify' is communicating and reasoning; the rubric wants the reference to a theorem or a sign of a derivative, not just the numerical answer.
Practice AP Calculus AB with our past papers
Every recent released AP Calc AB paper grouped by year, with worked solutions that show the setup, computation and justification for every FRQ part.
