AP Calculus AB Unit 8 Progress Check: Applications of Integration.
AP Calculus AB Unit 8 is Applications of Integration, and College Board publishes what its Progress Check holds: about 30 multiple-choice questions and three free-response questions, none of them shortened. Explanations only — we never publish AP Classroom answer keys.
What is on the AP Calculus AB Unit 8 Progress Check
College Board publishes the shape of this assessment on two agreeing surfaces in the AP Calculus AB and BC Course and Exam Description: the Course at a Glance and the Unit 8 opener. Both give the same figures for Progress Check 8 — about 30 multiple-choice questions and three free-response questions. College Board writes the count with a tilde, as ~30, so treat it as an approximation rather than an exact number.
The three free-response questions run at full length. College Board labels shortened Progress Check free response as partial, and it uses that label elsewhere in the same document, on Progress Checks 1, 2 and 3. Unit 8 carries no such marker, so its absence is evidence rather than silence.
What College Board does not publish is how AP Classroom divides those questions. If your teacher assigned a Part A and a Part B, that split is not described on any College Board surface, and neither is the content of either part. The totals above are what is actually published. You can compare this unit with the rest of the course in our all eight AP Calculus AB Progress Checks hub.
The twelve topics it is drawn from
College Board lists thirteen topics in Unit 8, and the last one is BC only, so an AB Progress Check is drawn from twelve. Topic 8.13, the arc length of a smooth planar curve and distance traveled, is marked BC only in the course framework and is not AB content.
College Board writes disc rather than disk in its own topic titles, which is why the spelling above may not match your textbook. The two mean the same method.
What Unit 8 is actually worth
Unit 8 carries 10–15%, and the qualifier matters more than the number. College Board states it twice on one page: the weightings are given for the multiple-choice section, and the table itself is titled the exam weighting for the multiple-choice section. It is not 10–15% of the whole exam, which is how several of the largest study guides report it. College Board attaches no unit weightings to the free-response section whatsoever.
The exam those weightings belong to is three hours and ten minutes long. Section I is 42 multiple-choice questions worth half the exam. Part A holds 29 of them across 62 minutes and bars the calculator; Part B holds the remaining 13 across 38 minutes and requires a graphing one. Section II carries the other half in six free-response questions: a 30-minute pair that expects a calculator, then a 60-minute set of four that does not. The exam is a hybrid digital one: you answer the multiple choice and read the free-response questions in Bluebook, then handwrite your answers in a paper booklet. It is scheduled for Monday, May 10, 2027.
Those multiple-choice figures are new. College Board changed Part A from 30 questions to 29 and its timing from 60 minutes to 62, and Part B from 15 questions to 13 and its timing from 45 minutes to 38, effective with the May 2027 exams. That is why a slightly older guide will tell you the section has 45 questions rather than 42.
The multiple-choice questions: what each pattern is asking
College Board does not publish the individual Progress Check questions, so what follows is the set of patterns this unit’s topics can produce, and what each one is really testing.
The three free-response questions
College Board publishes the count and the length and nothing further: three questions, none of them shortened. It does not publish their content, so any guide that tells you exactly what Unit 8 free response will ask is describing a pattern it has inferred, not a published fact.
What is published is the skill each topic is paired with, and that is the better guide. Across Unit 8 College Board pairs its topics with applying a rule or procedure, identifying the right procedure for the relationship in front of you, applying a definition or theorem, using correct notation, identifying mathematical information from a graph or table, connecting representations, and applying appropriate rounding. Notation and rounding are worth noticing, because both are skills College Board names for this unit and neither is about setting the integral up.
Where students lose points
What College Board does not give you
There is no formula sheet for AP Calculus AB. The course and exam description contains no equation sheet, no reference information and no appendix of formulas, and no College Board page offers one. AP Biology, Chemistry, Physics and Statistics students are handed printed reference material on exam day; Calculus students are not. Everything in the topic list above has to come from memory, which is the real reason this unit rewards understanding the slice rather than memorizing six separate formulas. Our AP Calculus AB equation sheet gathers what has to be in your head, to learn beforehand rather than to consult on the day.
Calculators are permitted, but not everywhere. On the exam a graphing calculator is required for Part B of the multiple choice and for Part A of the free response, and is not permitted in the other two parts. College Board adds that for Calculus AB the built-in Desmos calculator is only available in the calculator-required parts, because these exams keep sections where no calculator is allowed.
How to see your own Unit 8 Progress Check answers
The Progress Check returns its own explanations. College Board says it hands back a rationale for every multiple-choice option, the wrong ones as well as the right one, plus scoring detail on the free response. Those rationales are the answer key, written by the people who set the questions, and they are worth more than anything reposted elsewhere.
They are released by your teacher rather than automatically. If you cannot see them after submitting, ask your teacher to release the results for Unit 8; teachers can do this for the whole class or for an individual student. That is the route this page points you to. We do not publish AP Classroom answer keys, and we do not link to the copies that circulate on document-sharing sites. The rationales your teacher can release are the real ones, and they are better than anything reposted second-hand.
How to work through this unit
Sketch the region and draw one representative slice before writing anything. The slice tells you the variable, the limits, and whether you need a disc or a washer. College Board makes the same point in its own guidance for this unit, noting that focusing on orientation, horizontal or vertical, is what tells you whether the thickness is measured in x or in y.
College Board also supplies the idea that ties the unit together. Every area and every volume here is what you get by adding up thinner and thinner rectangles or slabs and pushing that process to its limit, which is the Riemann sum idea from Unit 6 wearing a different hat. Read the unit that way and the formulas above stop being separate things to remember; they are one method applied to different slices. College Board also flags the words to watch for in a prompt, since terms like accumulation and net change point at the structure the question wants.
Unit 8 asks the same interpretation skill that Unit 4 does, and College Board says so directly in its guidance for this unit, so our AP Calculus AB Unit 4 Progress Check walkthrough is worth a second pass if contextual problems are where you lose time. When the Progress Check is behind you, the Calc AB AP score calculator will translate a raw total into the 1–5 band it corresponds to, and the AP Calculus AB Review sets out the rest of the course.
Frequently asked questions
Quick answers, checked against College Board.
What does the AP Calculus AB Unit 8 Progress Check cover?
Applications of integration. College Board draws it from twelve AB topics: average value, particle motion, accumulation in context, area between curves in x and in y, area where curves cross more than twice, volumes with square, rectangular, triangular and semicircular cross sections, and volumes by the disc and washer methods.
How many questions are on the Unit 8 Progress Check?
College Board publishes about 30 multiple-choice questions and three free-response questions. It writes the multiple-choice count as an approximation, and it does not publish how AP Classroom splits those questions into parts.
Are the Unit 8 free-response questions shortened?
No. College Board labels shortened Progress Check free response as partial, and uses that label on Progress Checks 1, 2 and 3. Unit 8 carries no such label, so all three run full length.
What is the difference between the disc and washer method?
Use the disc method when the region touches the axis of rotation, so the solid has no hole. Use the washer method when a gap sits between the region and the axis, subtracting the inner radius squared from the outer radius squared.
How do I find total distance traveled from velocity?
Integrate the absolute value of velocity. Integrating velocity alone gives displacement, which can be smaller than the distance traveled or even zero.
Is a formula sheet provided for AP Calculus AB?
No. The course and exam description contains no equation sheet or reference information, and no College Board page offers one. Unlike Biology, Chemistry, Physics and Statistics, Calculus students are given no printed reference material on exam day.
Do you post AP Calculus Unit 8 answers?
No. What this page explains is the reasoning and the setup traps, never an AP Classroom key. Ask your teacher to release the Progress Check results, which carry College Board’s own rationale for every question.