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AP Calculus practice exam generator (AB & BC)

ExamTeX generates printable AP Calculus mock exams in the College Board's style. The real exam has Section I with 45 multiple-choice questions (1h 45m, 50% of score, split into calculator and no-calculator parts) and Section II with 6 free-response questions (1h 30m, 50% of score); one ExamTeX exam holds up to 35 multiple-choice questions, so practice Section I in parts. Upload your AB or BC unit notes, pick the AP Calculus style, and questions use College Board phrasing — distractors built from common errors, "Justify your answer" reasoning — with a point-by-point scoring guideline for every question. Because exams compile through LaTeX, every integral, limit, and derivative prints exactly like the real paper.

Section I — Multiple Choice

Part A: 30 questions, no calculator (60 min). Part B: 15 questions, graphing calculator required (45 min). Covers limits, derivatives, integrals, and (BC) series.

Marks: 45 questionsTime: 1h 45mWeight: 50% of score

Section II — Free Response

Part A: 2 questions with calculator (30 min). Part B: 4 questions without (60 min). Each FRQ scored out of 9 points with partial credit for setup and justification.

Marks: 6 questions × 9 ptsTime: 1h 30mWeight: 50% of score

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Sample question with mark scheme

FRQ (no calculator): Let RR be the region enclosed by the graphs of f(x)=x2f(x) = x^2 and g(x)=2xg(x) = 2x. (a) Find the area of RR. (b) Find the volume of the solid generated when RR is revolved about the xx-axis. (c) The region RR is the base of a solid whose cross-sections perpendicular to the xx-axis are squares. Find the volume of this solid.
Show mark scheme
(a) 3 pts: intersection points x = 0, 2 (1 pt); integrand 2x − x² (1 pt); area = ∫₀²(2x − x²)dx = 4/3 (1 pt). (b) 3 pts: washer setup π∫₀²[(2x)² − (x²)²]dx (2 pts: outer/inner radii correct); evaluation 64π/15 (1 pt). (c) 3 pts: cross-section area (2x − x²)² (1 pt); integral setup (1 pt); evaluation 16/15 (1 pt).

Every generated paper includes a full mark scheme with worked solutions.

Common mistakes AP Calc students make

  • Dropping the constant of integration on indefinite integrals — a reliably lost point on FRQs.
  • Justifying a maximum with "the derivative is zero" instead of the required sign-change or second-derivative argument — AP readers award justification points only for calculus-based reasoning.
  • Rounding intermediate values: final answers must be correct to three decimal places, and early rounding propagates.
  • On calculator questions, writing only the numeric answer without showing the setup (the integral or equation being solved) — setup carries its own points.

Frequently Asked Questions

Does ExamTeX cover both AP Calculus AB and BC?

Yes. There is one AP Calculus style, and questions come from the notes you upload — upload BC material (series, parametric, polar, vectors) for BC practice or AB material for AB, and name your course in the instructions box. You can also generate topic-targeted drills, such as a Unit 6 integration set.

Are the FRQs scored like real AP Calculus questions?

Each generated free-response question includes a scoring guideline split across the parts, showing the setup, computation, and justification steps AP scorers award points for, so you can self-grade realistically. Point values are editable if you want the real exam's 9-point totals.

Does the math print properly?

Yes — exams compile through LaTeX, so limits, integrals, Riemann sums, and series notation render in print quality, the way the real exam paper looks. This matters for practicing under genuine exam conditions.

Can I practice just the no-calculator section?

Yes. Generate a multiple-choice-only set for timed drilling and ask for no-calculator questions in the instructions box, or a free-response-only set for Section II. You control question counts and the time limit.

How is this different from AP Classroom?

AP Classroom has the College Board's fixed question bank — use it. ExamTeX complements it with unlimited fresh papers generated from your own notes, so when you have exhausted the official questions you can keep sitting timed, properly typeset mocks targeted at your weak units.

Or generate other study materials

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