AP Calculus AB 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, including functions defined only by a graph or a table of values. Each question has four answer choices with one correct answer, and there is no penalty for guessing.

• 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 8 units; see the weighting table below for how much each contributes.

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 AB exam

• Unit 1, Limits and Continuity: 10-15% of the multiple choice section.
• Unit 2, Differentiation: Definition and Fundamental Properties: 10-15% 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: 10-15% of the multiple choice section.
• Unit 5, Analytical Applications of Differentiation: 15-20% 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: 10-15% of the multiple choice section.

Units 5 and 6 carry the largest ranges at 15-20% each: the analytical applications of the derivative, and integration and accumulation. Between them sits most of what the free response section asks about too, so they repay the deepest practice.

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.