Section II is six free-response questions worth 9 points each, half of the exam score, in 90 minutes. Part A (Questions 1 and 2, 30 minutes) requires a graphing calculator; Part B (Questions 3 through 6, 60 minutes) allows none. Unlike AP Precalculus, the questions are not officially named task types, but the same handful of archetypes returns year after year, and every question is scored by a rubric that pays for setups, justifications, and interpretations as much as for final numbers. For the section-by-section format of the whole exam, see the exam guide.
Questions
6
9 points each
Time
90 min
30 + 60 by part
Weighting
50%
of the exam score
Calculator
Part A only
required on Questions 1-2
The recurring archetypes
Five setups that keep coming back
1
Contextual rate and accumulation
Units 4, 6, 8 · Real-world context · Either part
A rate of change in a real setting: water flowing into a tank, people joining a line, sand arriving on a beach. The question asks for the accumulated change over an interval, an average value, and what a definite integral of the rate means in the story's own units.
Write the integral before computing anything: the setup ∫ab r(t) dt earns its points even when the arithmetic never finishes.
Interpret with units: "the amount of water, in gallons, that enters the tank from t = 0 to t = 8" is worth a point; a bare number is not.
Net change needs a starting value: the amount at time b is the amount at time a plus the integral of the rate, not the integral alone.
2
Particle motion
Units 4, 6, 8 · Straight-line motion
A particle moves along a line with velocity v(t). Position, displacement, total distance, and whether the speed is increasing all come from reading v and its derivative correctly, and every claim needs a sign-based justification.
Speed increases when v and a share a sign. Justify with the signs of both velocity and acceleration, never with two speed values.
Displacement integrates v(t); total distance integrates |v(t)|. They differ whenever the particle turns around.
A direction change is a sign change of v, not merely a zero of v; check that v actually crosses.
3
Area and volume
Unit 8 · Region bounded by curves
A region bounded by curves: its area, the volume of the solid formed by revolving it about a line, or the volume of a solid whose cross sections are built on it. Nearly every year this is a full question.
Find the intersection points first, and on the calculator part store them to full precision instead of retyping rounded values.
Area is top minus bottom (or right minus left) across the whole interval; check whether the curves trade places partway.
Washers subtract squared radii: π times the integral of R2 - r2, never of (R - r)2.
4
Table and graph analysis
Units 2, 5, 6 · Values, not formulas
The function arrives as a table of values or as the graph of its derivative, so every estimate and every conclusion must come from what is given: Riemann or trapezoidal sums from the table, average rates of change, and reasoning about f from the graph of f′.
A Riemann sum from a table uses the table's subintervals, which are rarely equal width; show the sum term by term.
State the hypotheses before MVT or IVT: f is continuous on [a, b], and differentiable on (a, b) when the Mean Value Theorem is the tool.
On a graph of f′, heights are slopes of f and areas are changes in f: f increases where f′ is positive, and extrema of f sit where f′ changes sign.
5
Differential equations
Unit 7 · Slope fields and separation
A differential equation with a slope field or an initial condition. Sketch or match solution curves, verify that a proposed function satisfies the equation, and solve by separation of variables for the particular solution.
Separate completely before integrating: every y on one side, every x on the other, then write + C on one side immediately.
Use the initial condition to find C before solving for y, and keep the branch (sign or domain) the initial condition selects.
Verifying a solution means substituting into both sides of the equation, not re-solving it from scratch.
Earning the points
What the rubric rewards
Show the setup. Each question is scored out of 9 by a rubric that pays for the pieces: the correct integral or derivative expression earns its points even when the final number is wrong or missing. Write the expression first, always.
Interpret in context, with units. When a question asks what a value means, the answer is a sentence naming the quantity, its units, and the interval, read back into the situation. A number with no units earns no interpretation point.
Justify from the hypotheses. Before applying the Intermediate Value Theorem, the Mean Value Theorem, or the Extreme Value Theorem, state that the conditions hold: "f is continuous on [a, b]" is the line the rubric looks for.
Three decimal places. Where a calculator value is expected, report answers accurate to three places after the decimal point, and store intermediate values in the calculator instead of retyping rounded ones.
Never leave a bare number where reasoning is asked. "Justify your answer" and "explain" attach the point to the reasoning; the number alone earns nothing there, even when it is right.
Stay in radian mode on the calculator questions. Degree mode quietly wrecks every trigonometric evaluation, and no rubric forgives it.
The fastest way to stop losing FRQ points
Most lost points trace to a small set of documented misconceptions: subtracting radii before squaring in a washer, reporting displacement where total distance was asked, dropping the constant of integration, or applying a theorem whose hypotheses were never checked. Diagnose which ones are costing you, then drill exactly those in Unit 4, Unit 6, Unit 7, and Unit 8.
College Board publishes decades of past free response questions with scoring guidelines, sample student responses, and chief reader commentary. Scoring your own attempts against the real rubrics is the single best way to learn where the points actually sit. Find them on the AP Calculus AB exam page, along with the Course and Exam Description behind the whole framework. For how Section II fits into the full exam day, see the exam guide.
Common questions
FAQ
How many free response questions are on AP Calculus AB?
Six, each scored out of 9 points by rubric, for 50 percent of the exam score. Part A is Questions 1 and 2 in 30 minutes with a required graphing calculator; Part B is Questions 3 through 6 in 60 minutes with no calculator.
Which AP Calculus AB FRQs allow a calculator?
Part A, which is Questions 1 and 2, requires a graphing calculator and runs 30 minutes. Part B, which is Questions 3 through 6, allows no calculator and runs 60 minutes. Keep the calculator in radian mode.
Are the AP Calculus AB FRQs fixed task types?
No. Unlike AP Precalculus, the calculus questions carry no official names. The same archetypes recur, though: contextual rate and accumulation, particle motion, area and volume, table and graph analysis, and differential equations.
How precise do calculator answers need to be?
Unless a question says otherwise, report decimal answers accurate to three places after the decimal point, and avoid rounding intermediate values; store them in the calculator instead of retyping rounded copies.
Do I lose points for a right answer with no work?
You can. The 9 points on each question sit on a rubric that pays for setups, justifications, and interpretations as well as answers. Where work or reasoning is requested, an unsupported answer may earn nothing.
