AP Calculus BC Exam

Section I: Multiple choice

45 questions · 105 minutes · 50% of score

Forty-five multiple-choice questions split into two separately timed parts by calculator policy. Questions arrive in every representation the course uses: analytical, graphical, tabular, and verbal. Each question has four answer choices with one correct answer, and there is no penalty for guessing. BC-only material is woven through the section, not quarantined at the end, so series and parametric questions can appear anywhere.

• Part A: 30 questions, 60 minutes, no calculator. Two thirds of the section at a flat 2 minutes per question.
• Part B: 15 questions, 45 minutes, graphing calculator required. Three minutes per question. Only some of these actually need the calculator, but it must be on the desk.
• The section samples all 10 units; the two BC-only units alone account for 10-15% (Unit 9) and 15-20% (Unit 10) of it.

The cumulative unit exams on this site reproduce this format, including the no-calculator and calculator split, so timed practice here feels like the real Section I.

Section II: Free response

6 questions · 90 minutes · 50% of score · 9 points each

Six free-response questions, each scored out of 9 points against a published rubric with partial credit throughout. Like Section I, it splits by calculator policy, but in the opposite proportion: the calculator part comes first and is the smaller one.

• Part A: 2 questions, 30 minutes, graphing calculator required. Fifteen minutes per question.
• Part B: 4 questions, 60 minutes, no calculator. If you finish early you may return to the Part A questions during this time, but without the calculator.
• Show the work that leads to your answer. Readers award points for the setup, the reasoning, and the answer separately; a correct number with no supporting work may earn little where work is requested.

See the full FRQ guide for the recurring question types and how the 9 points are typically distributed.

Calculator policy and reference materials

Required on some parts, banned on others · no formula sheet

• A graphing calculator is required on Section I Part B and Section II Part A, and is not permitted on Section I Part A or Section II Part B. Keep it in radian mode.
• You are expected to use it to graph a function in a window, find zeros and points of intersection, numerically evaluate a derivative at a point, and numerically evaluate a definite integral.
• Avoid rounding intermediate computations. Unless a question says otherwise, report decimal approximations accurate to three places after the decimal point, and store values in the calculator instead of retyping rounded ones.
• No formula sheet is provided on exam day. Every derivative and antiderivative form you need has to come from memory. The reference page collects them for study, but nothing like it appears in the exam booklet.

Multiple choice by unit

The CED's ranges for the BC exam

• Unit 1, Limits and Continuity: 5-10% of the multiple choice section.
• Unit 2, Differentiation: Definition and Fundamental Properties: 5-10% of the multiple choice section.
• Unit 3, Differentiation: Composite, Implicit, and Inverse Functions: 5-10% of the multiple choice section.
• Unit 4, Contextual Applications of Differentiation: 5-10% of the multiple choice section.
• Unit 5, Analytical Applications of Differentiation: 10-15% of the multiple choice section.
• Unit 6, Integration and Accumulation of Change: 15-20% of the multiple choice section.
• Unit 7, Differential Equations: 5-10% of the multiple choice section.
• Unit 8, Applications of Integration: 5-10% of the multiple choice section.
• Unit 9, Parametric Equations, Polar Coordinates, and Vector-Valued Functions: (BC only) 10-15% of the multiple choice section.
• Unit 10, Infinite Sequences and Series: (BC only) 15-20% of the multiple choice section.

Units 6 and 10 are the heaviest at 15-20% each. The BC-only material goes beyond Units 9 and 10: six BC-only topics sit inside Units 6 through 8 (integration by parts, linear partial fractions, improper integrals, Euler's method, logistic models, and arc length), so even the shared units run deeper than their AB versions.

The AB subscore

One exam, two scores

Every AP Calculus BC score report includes an AP Calculus AB subscore, computed from the exam questions covering the AB-overlap material. A BC student's report therefore shows both a BC score on the full course and a 1 to 5 subscore on the AB portion alone, so a rough day on series does not erase what the exam saw of your differentiation and integration.

The overlap is real course structure, not a sample: Units 1 through 8 are shared with AB, and BC compresses them plus two more units into the same school year. The pace, not the exam format, is the main difference in the experience of taking BC.

The four Mathematical Practices

What every question is really testing

• Implementing Mathematical Processes: choosing a procedure and carrying it out accurately: differentiating, antidifferentiating, evaluating a limit, solving for the quantity asked.
• Connecting Representations: moving between a graph, a table, an expression, and a verbal description of the same function, including reading f, f prime, and f double prime against each other.
• Justification: backing a conclusion with the definition or theorem that licenses it: continuity before applying the Intermediate Value Theorem, differentiability before the Mean Value Theorem, a sign change in the derivative before declaring a maximum.
• Communication and Notation: stating answers with correct notation and, in context, correct units. Free-response rubrics regularly reserve points for notation and interpretation alone.