AP Calculus BC exam guide 2027

The exam at a glance

The AP Calculus BC exam is on Monday 10 May 2027 in the morning session (College Board’s Session 1, typically the morning; your school confirms the exact start time). It is a hybrid digital exam: you answer the multiple-choice questions in the Bluebook app, and you see the free-response questions in Bluebook but write your answers by hand in a paper booklet. The whole exam lasts 3 hours 10 minutes: 42 multiple-choice questions in 1 hour 40 minutes (50%) and 6 free-response questions in 1 hour 30 minutes (50%).

The BC exam has the same structure as AB, and the two are in the same exam slot. BC covers all of AB plus Units 9 and 10 and a few extra topics inside Units 6, 7 and 8, so the unit weightings differ.

How free-response answers are scored

College Board’s course description weights the free-response section heavily towards reasoning: Justification (Mathematical Practice 3) is 35–60% of the free-response score and Communication and Notation (Practice 4) is 10–25%. On multiple choice, Justification is only 10–20% and Communication and Notation is not assessed at all. So the way you write an answer matters as much as the number at the end.

• Write the setup for every calculator result. If you use the calculator to solve an equation, find a derivative at a point or evaluate a definite integral, write the equation, derivative or integral you are evaluating and then the result. “\( \int_0^4 v(t)\,dt = 7.392 \)” shows exactly what you did; a bare 7.392 does not.
• Give units when the question has a context. A rate of change of water in a tank is in litres per hour; an accumulated amount is in litres. Read the units off the question and attach them to your final answer.
• Justify with the condition, not the conclusion. Write “\( f \) has a relative maximum at \( x = 3 \) because \( f'(x) \) changes from positive to negative at \( x = 3 \)”, not “because it goes up then down”. Name the function you mean (\( f \), \( f’ \) or \( f” \)) and never write “it”.
• Check the hypotheses of a theorem out loud. Before using the Mean Value Theorem, Intermediate Value Theorem or Extreme Value Theorem, state that the function is continuous (and differentiable, for the MVT) on the interval, then state the conclusion.
• Use the task verb. College Board’s free-response task verbs include approximate, calculate, determine, estimate, evaluate, explain, identify, interpret, justify, represent and verify. “Justify” and “explain” need a sentence of reasoning; “interpret” needs the meaning in context, with units.
• Keep your notation correct. Write \( \dfrac{dy}{dx} \), the limits on a definite integral and \( +C \) on an antiderivative. Sloppy notation such as dropping the \( dx \) or writing equals signs between unequal expressions can cost the communication point.

Free-response questions

College Board states that the AB and BC exams share three common free-response questions on AB content, that the free-response questions mix procedural and conceptual tasks roughly equally, and that at least two of them use a real-world context. Beyond that it does not fix the question types. Common patterns in past papers include a rate in context given by a table of values (Riemann sums, average value, and interpretation with units); particle motion along a line (velocity, acceleration, speeding up or slowing down, total distance); reading the graph of \( f’ \) to analyse \( f \) (increasing, concavity, extrema, accumulation functions); a differential equation with a slope field and separation of variables; and area or volume of a region; and, on BC, a parametric, vector or polar question and a series question (Taylor polynomials and error bounds). Treat these as patterns to practise, not as a guarantee of what will appear.

10-week revision plan