# AP Calculus AB exam guide > All eight AP Calculus AB units with published exam weightings, from limits through applications of integration. - Canonical page: https://www.arcadesacademy.com/exams/ap-calculus-ab - Markdown source: https://www.arcadesacademy.com/exams/ap-calculus-ab/llms.txt - Exam family: AP exams - Governing body: College Board - Official exam information: https://apstudents.collegeboard.org/courses/ap-calculus-ab - Who takes it: High school students taking a first calculus course for college credit or placement, typically after precalculus. - Follows the fall 2020 course and exam description, from 3 May 2021 - Guide structure last checked against official sources: August 30, 2026 ## Overview AP Calculus AB covers the material of a first-semester college calculus course: limits and continuity, differentiation and its applications, and integration and its applications, including separable differential equations. The Course and Exam Description organizes that content into eight units, each with a published weighting range, and pairs it with mathematical practices that emphasize justification and communication. The published weightings put integration and the analytical applications of differentiation at the top, which reflects how the free-response section is written: accumulation functions, related rates, optimization, and the Fundamental Theorem of Calculus appear year after year. The exam also insists on notation and justification, so a correct answer with no supporting reasoning routinely loses points. Arcade Academy is an independent study workspace. Use the official Course and Exam Description as the authoritative content list and the official exam page for current format details, and use the unit pages below to organize problem practice and timed free-response work. ## Exam format - **Total time:** 3 hours 10 minutes - **Section I:** 42 multiple-choice questions in 1 hour 40 minutes, 50% of the exam score - **Section I detail:** Part A is 29 questions in 62 minutes with no calculator; Part B is 13 questions in 38 minutes with a graphing calculator required - **Section II:** 6 free-response questions in 1 hour 30 minutes, 50% of the exam score - **Section II detail:** Part A is 2 questions in 30 minutes with a graphing calculator required; Part B is 4 questions in 60 minutes with no calculator - **Format update:** The multiple-choice count and section timing changed beginning with the May 2027 exam; confirm the current numbers on the official exam page - **Delivery:** Hybrid digital: multiple-choice questions are answered and free-response prompts are read in College Board's Bluebook app, and free-response answers are handwritten in a paper booklet - **Score scale:** 1 to 5 ## Scoring The multiple-choice and free-response sections each contribute half of a composite score, which College Board converts to the reported 1 to 5 scale using cut points set for that year's exam. Colleges set their own credit and placement policies, and many treat AB and BC scores differently, so check the specific institution. ## Units AP Calculus AB is organized into 8 units. Each one below lists its published weighting where the governing body publishes one, the topics it covers, and study tips specific to it. ### 1. Unit 1: Limits and Continuity - Position: 1 of 8 - Published weighting: 10–12% - Page: https://www.arcadesacademy.com/exams/ap-calculus-ab/unit-1-limits-and-continuity Unit 1 introduces the limit as the idea that makes calculus work, then defines continuity in terms of it. Algebraic, graphical, and numerical approaches to limits are all expected, along with the squeeze theorem, asymptotic behavior, and the Intermediate Value Theorem. Correct limit notation established here is required for the rest of the course. #### Topics - **Defining and estimating limits** — Reading limits from graphs and tables, and understanding one-sided limits and when a limit fails to exist. - **Determining limits algebraically** — Direct substitution, factoring, rationalizing, and using algebraic manipulation on indeterminate forms. - **Squeeze theorem and special limits** — Bounding a function between two others, and the standard trigonometric limits used repeatedly later. - **Continuity** — The three-part definition of continuity at a point, classifying discontinuities, and removable versus jump behavior. - **Asymptotes and infinite limits** — Connecting vertical and horizontal asymptotes to infinite limits and limits at infinity. - **Intermediate Value Theorem** — Stating the hypotheses and using the theorem to justify the existence of a solution on an interval. #### Study tips - Write limit notation correctly on every problem; the free-response section deducts for notation even when the value is right. - Practice stating theorem hypotheses before conclusions, since the exam asks for justification rather than assertion. - Work limits from graphs and tables as well as algebraically, because all three representations appear. ### 2. Unit 2: Differentiation: Definition and Fundamental Properties - Position: 2 of 8 - Published weighting: 10–12% - Page: https://www.arcadesacademy.com/exams/ap-calculus-ab/unit-2-differentiation-definition-and-fundamental-properties Unit 2 defines the derivative as a limit of difference quotients, then builds the basic rules that make computation practical. The connection between differentiability and continuity, and the standard derivatives of power, exponential, logarithmic, and trigonometric functions, are established here. #### Topics - **Defining the derivative** — Average rate of change, the difference quotient, and the derivative as the limit of that quotient. - **Derivative as a function** — Estimating derivative values from graphs and tables, and sketching a derivative from a function graph. - **Differentiability and continuity** — Why differentiability implies continuity, and the corners, cusps, and vertical tangents where it fails. - **Basic derivative rules** — Power, constant multiple, sum and difference rules applied to polynomial and radical functions. - **Derivatives of transcendental functions** — Derivatives of sine, cosine, the exponential function, and the natural logarithm. - **Product and quotient rules** — Applying both rules cleanly, including recognizing when algebraic simplification first is faster. #### Study tips - Compute a derivative from the limit definition a few times each week; the exam asks for it directly. - Practice sketching the derivative graph from a function graph and vice versa until the shape relationships are automatic. - Keep a short list of the functions where differentiability fails and be able to name the reason. ### 3. Unit 3: Differentiation: Composite, Implicit, and Inverse Functions - Position: 3 of 8 - Published weighting: 9–13% - Page: https://www.arcadesacademy.com/exams/ap-calculus-ab/unit-3-differentiation-composite-implicit-and-inverse-functions Unit 3 extends differentiation to the cases that matter most in applications. The chain rule enables everything that follows, implicit differentiation handles relations that are not solved for a variable, and the inverse function rule covers inverse trigonometric and logarithmic derivatives. Higher-order derivatives are introduced here as well. #### Topics - **The chain rule** — Differentiating composite functions, including nested compositions and combinations with other rules. - **Implicit differentiation** — Differentiating relations term by term and solving for the derivative, including tangent lines to curves. - **Derivatives of inverse functions** — Using the inverse function relationship to find a derivative without an explicit formula. - **Inverse trigonometric derivatives** — Derivatives of arcsine, arccosine, and arctangent and their use in composite expressions. - **Higher-order derivatives** — Second and higher derivatives, their notation, and their interpretation in motion problems. - **Selecting procedures for derivatives** — Recognizing which rule or combination of rules a given expression requires before differentiating. #### Study tips - Identify the outer and inner functions explicitly before applying the chain rule until the recognition is automatic. - Practice implicit differentiation on curves where the tangent is vertical or horizontal, a common exam prompt. - Do mixed derivative drills where the rule is not announced; procedure selection is itself a tested skill. ### 4. Unit 4: Contextual Applications of Differentiation - Position: 4 of 8 - Published weighting: 10–15% - Page: https://www.arcadesacademy.com/exams/ap-calculus-ab/unit-4-contextual-applications-of-differentiation Unit 4 puts derivatives to work in applied settings. Motion along a line, related rates, linear approximation, and L'Hospital's rule are the core techniques, and interpreting a derivative with correct units and meaning is a persistent requirement. Related rates problems appear on the free-response section regularly. #### Topics - **Interpreting the derivative in context** — Explaining what a rate of change means in a situation, with correct units. - **Straight-line motion** — Position, velocity, acceleration, speed, and determining when an object changes direction. - **Rates of change in applied contexts** — Modeling change in non-motion situations such as volume, temperature, or population. - **Related rates** — Relating changing quantities through an equation and differentiating with respect to time. - **Linear approximation** — Using the tangent line to approximate function values, and determining whether the estimate is over or under. - **L'Hospital's rule** — Evaluating indeterminate quotient limits after verifying the hypotheses. #### Study tips - Write units in every contextual answer; the free-response rubrics award points for correct interpretation with units. - For related rates, set up the geometric relationship before differentiating, and label which rate is given and which is wanted. - Distinguish speed from velocity carefully; questions about speeding up and slowing down turn on the sign comparison. ### 5. Unit 5: Analytical Applications of Differentiation - Position: 5 of 8 - Published weighting: 15–18% - Page: https://www.arcadesacademy.com/exams/ap-calculus-ab/unit-5-analytical-applications-of-differentiation Unit 5 carries one of the largest published weightings in AB. It covers the Mean Value Theorem and Extreme Value Theorem, the first and second derivative tests, concavity and points of inflection, curve sketching, and optimization. Justification language matters more here than anywhere else in the course. #### Topics - **Mean Value and Extreme Value Theorems** — Stating hypotheses correctly and applying each theorem to guarantee a value on an interval. - **Increasing and decreasing behavior** — Using the sign of the first derivative to describe intervals of increase and decrease. - **First and second derivative tests** — Classifying critical points as local maxima, minima, or neither, and knowing when each test applies. - **Concavity and points of inflection** — Using the second derivative to determine concavity and to locate where it changes. - **Curve sketching** — Assembling derivative information into a complete graph, including asymptotes and endpoints. - **Optimization** — Setting up a model, reducing it to one variable, and justifying that a candidate is the extremum. #### Study tips - Memorize the exact justification phrasing for each test; the rubric wants the derivative sign change stated explicitly. - Work optimization problems all the way through the justification step, not just to the candidate value. - Practice reconstructing a function's behavior from a derivative graph, which is a recurring multiple-choice pattern. ### 6. Unit 6: Integration and Accumulation of Change - Position: 6 of 8 - Published weighting: 17–20% - Page: https://www.arcadesacademy.com/exams/ap-calculus-ab/unit-6-integration-and-accumulation-of-change Unit 6 carries the largest published weighting in the course. Riemann sums lead to the definite integral, the Fundamental Theorem of Calculus links integration to differentiation, and accumulation functions formalize the idea of total change. Antiderivative techniques at the AB level include substitution. #### Topics - **Riemann sums and definite integrals** — Left, right, midpoint, and trapezoidal approximations, and the limit that defines the definite integral. - **Accumulation functions** — Interpreting an integral with a variable upper limit, and reading its behavior from the integrand's graph. - **Fundamental Theorem of Calculus** — Both parts of the theorem: evaluating definite integrals and differentiating an accumulation function. - **Properties of definite integrals** — Additivity over intervals, reversing limits, and using symmetry to simplify evaluation. - **Antiderivatives and indefinite integrals** — Reversing the basic derivative rules, including the transcendental functions. - **Integration by substitution** — Recognizing a composite integrand and changing variables, including adjusting the limits. #### Study tips - Practice both parts of the Fundamental Theorem separately until the second part, differentiating an accumulation function, is instant. - Do Riemann sum estimates from tables of values and state whether the estimate is an overestimate or underestimate, with a reason. - Give this unit the most practice time; its published weighting is the highest of the eight. ### 7. Unit 7: Differential Equations - Position: 7 of 8 - Published weighting: 6–12% - Page: https://www.arcadesacademy.com/exams/ap-calculus-ab/unit-7-differential-equations Unit 7 covers modeling with differential equations at the AB level: interpreting and sketching slope fields, verifying solutions, and solving separable equations with an initial condition. Exponential growth and decay is the standard applied model. Correct treatment of the constant of integration and the domain of the solution is expected. #### Topics - **Modeling situations with differential equations** — Translating a described rate of change into an equation relating a function and its derivative. - **Verifying solutions** — Confirming that a proposed function satisfies a given differential equation and initial condition. - **Slope fields** — Sketching and interpreting slope fields, and matching them to differential equations. - **Separation of variables** — Separating and integrating both sides, then applying the initial condition to determine the constant. - **Exponential growth and decay** — Recognizing the model in which the rate is proportional to the amount, and using it in context. #### Study tips - Apply the initial condition immediately after integrating, before simplifying, which avoids sign and constant errors. - Practice sketching a particular solution through a given point on a slope field. - State the domain of the solution when the problem context requires it; the rubric sometimes awards a point for it. ### 8. Unit 8: Applications of Integration - Position: 8 of 8 - Published weighting: 10–15% - Page: https://www.arcadesacademy.com/exams/ap-calculus-ab/unit-8-applications-of-integration Unit 8 uses the definite integral to compute quantities: average value, area between curves, accumulated change in motion problems, and volumes by cross sections and by revolution. Setting up the correct integral, with the right integrand and limits, carries most of the credit even before the arithmetic. #### Topics - **Average value of a function** — The integral definition of average value and its interpretation in context. - **Accumulated change and motion** — Position from velocity, total distance from speed, and net change from a rate function. - **Area between curves** — Setting up integrals with respect to x or y, including regions requiring more than one integral. - **Volumes with known cross sections** — Integrating the area of square, rectangular, triangular, or semicircular cross sections. - **Volumes of revolution: disk and washer** — Revolving a region about a horizontal or vertical line, including axes other than the coordinate axes. #### Study tips - Sketch the region and a representative slice before writing any volume or area integral. - Distinguish displacement from total distance every time; the difference is a standard free-response trap. - Practice revolution about lines that are not the axes, since those setups appear regularly. ## Study strategies - Weight practice by the published unit percentages, giving integration and the analytical applications of differentiation the largest share of sessions. - Practice writing justifications in the exact language the rubrics use, because on the free-response section a correct answer with no reasoning frequently earns partial or no credit. - Split practice between calculator and no-calculator conditions, since both sections of the exam have a part of each and the skills differ. - Work the recurring free-response formats deliberately: a rate-in and rate-out accumulation problem, a table-of-values problem, a particle motion problem, and an area or volume problem. - Keep derivative and antiderivative rules on a spaced-repetition schedule so recall stays automatic while your time goes to problem setup. - Take at least one full timed exam; the exam is more than three hours long and pacing across four separately timed parts is its own skill. ## Frequently asked questions ### How is the AP Calculus AB Exam structured? The exam runs 3 hours 10 minutes. Section I is 42 multiple-choice questions in 1 hour 40 minutes for 50% of the score, split into a 29-question no-calculator part and a 13-question calculator part. Section II is 6 free-response questions in 1 hour 30 minutes for the other 50%, split into a 2-question calculator part and a 4-question no-calculator part. Confirm current numbers on the official exam page, since the format changed beginning with the May 2027 exam. ### Which AP Calculus AB units are hardest? College Board does not rank difficulty. Students most often report that the justification requirements in Unit 5 and the setup work in Unit 8 volumes take the most practice, and that related rates in Unit 4 is a common sticking point. Practice results should determine where you spend time. ### How is the exam scored? Both sections contribute equally to a composite score that is converted to the reported 1 to 5 scale using cut points set each year. Colleges publish their own credit and placement policies, and many distinguish between AB and BC scores, so check each institution. ### Should I take AB or BC? AB covers roughly a first-semester college calculus course, while BC adds parametric, polar, and vector-valued functions and infinite series and moves faster. Students choose based on pacing preference, schedule, and the sequence their school offers, not on any assumption that one score is easier to earn. ### What is the calculator policy, and how is the exam delivered? A graphing calculator is required for one part of each section and prohibited on the other part. AP Calculus AB is a hybrid digital exam: multiple-choice questions are answered in College Board's Bluebook app and free-response answers are handwritten in a paper booklet. Confirm current policy on the official exam page. ### Is Arcade Academy affiliated with College Board? No. AP® is a registered trademark of College Board, which was not involved in the production of, and does not endorse, this site. 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Arcade Academy is an independent educational resource. Confirm current exam format, dates, and policies with College Board directly. AP® is a registered trademark of College Board, which was not involved in the production of, and does not endorse, this site. Arcade Academy is an independent educational resource.