Calc AB · Unit 6 Progress Check

AP Calculus AB Unit 6 Progress Check: Integration and Accumulation of Change walkthrough.

AP Calculus AB Unit 6 is Integration and Accumulation of Change, and the Unit 6 Progress Check MCQ covers Riemann sums, both parts of the Fundamental Theorem, u-substitution and choosing an antidifferentiation technique. Below is what each question type is really asking, the traps that cost the most points, and how to get College Board’s own explanation of every question you missed. Explanations only. We do not publish AP Classroom answer keys, here or on any of the other ap calculus ab progress check answers walkthroughs.

Updated September 2026Written by Mahmudul HasanFree · No signup

What Unit 6 covers

Unit 6 is Integration and Accumulation of Change. In College Board’s Course and Exam Description it is worth 15–20% of the multiple-choice section, which ties it with Unit 5 for the heaviest weighting of the eight Calculus AB units. College Board does not publish a unit-by-unit weighting for the free-response section at all. You will see 17–20% quoted in a lot of places, including some large study sites. That figure is not College Board’s.

Riemann sums

Left, right, midpoint and trapezoidal approximations, and whether each one over- or underestimates. Includes reading the summation and definite-integral notation these are written in.

The definite integral

Area under a curve, including signed area below the axis.

Properties of definite integrals

Splitting an integral at an interior point, reversing the limits to flip the sign, and pulling constants out. These turn into questions you can answer without computing anything.

Fundamental Theorem, Part 1

Differentiating an accumulation function, with the chain rule when the upper limit is a function.

Fundamental Theorem, Part 2

Evaluating a definite integral using an antiderivative.

Antiderivatives and indefinite integrals

The basic rules and the notation for them, including the constant of integration.

u-substitution

Reversing the chain rule, and handling the limits when the integral is definite.

Long division and completing the square

Two rewrites that turn an integral you cannot do into one you can. Easy to miss because the work happens before any integrating starts.

Choosing a technique

Looking at an unfamiliar integrand and deciding which method it wants. College Board lists this as its own topic, and it is the skill the multiple-choice section leans on hardest.

Accumulation in context

Reading a definite integral of a rate as a net change, with units.

The Progress Check MCQ: what each question type tests

These are the question patterns that recur on this Progress Check, and what each one is really asking.

Over- and underestimates

On an increasing function a left Riemann sum sits under the curve and a right sum sits over it; on a decreasing function it is the other way round. Sketching one strip settles it faster than reasoning about it.

FTC Part 1 with a variable bound

Differentiating an accumulation function whose lower limit is a constant and whose upper limit is g(x) gives f(g(x)) times g′(x), where f is the integrand. The chain-rule factor is the usual casualty.

u-substitution execution

Pick u, compute du, and then either convert both limits to u-values or back-substitute to x before evaluating. Both are correct; doing neither is the error.

Technique selection

You are shown an integrand and asked which method applies, rather than asked to evaluate it. Look at the structure: an inner function with its derivative alongside means substitution, a top-heavy rational function means division first.

Definite-integral properties

Given the value of an integral over two adjacent intervals, produce the value over the whole. No antiderivative is needed, which is exactly why it is asked.

Net change interpretation

The integral of a rate gives the net change over the interval, carrying the rate’s units multiplied by the units of the input.

Signed area

Regions below the axis contribute negatively. Total area needs the absolute value.

Left and right Riemann sums on an increasing function. The relationship reverses when the function is decreasing.

One thing worth knowing before you start: Unit 6 sits on both sides of the calculator line. On the real exam, College Board splits the multiple-choice section into a 29-question Part A where a graphing calculator is not permitted and a 13-question Part B where one is required, and splits the free-response section the other way round, with 2 calculator questions and 4 without. That is why the Progress Check has a Part A and a Part B too. A definite integral you may evaluate numerically and one you have to antidifferentiate by hand are not the same question. You can check the current format on College Board’s AP Calculus AB exam page.

The Progress Check FRQ

Unit 6 free response is often a rate-in, rate-out problem: given a rate function, find an accumulated amount, a maximum, or a net change. AP Calculus free response is generally marked on the work rather than the final number, so the things that earn credit are a correct integral set up with its limits, correct use of the Fundamental Theorem, and a sentence interpreting the answer in context with units. College Board weights communication and notation at 10–25% of the free-response section, which is why the sentence is not optional.

Where students lose the most points

Forgetting +C on indefinite integrals

The tell is an answer with no constant when the question never gave you limits. If there are no numbers on the integral sign, the answer is a family of functions, not one function.

Not changing limits after u-substitution

Catch it by checking that your limits and your variable agree. If the integral now reads in u but the limits are still the original x-values, you have mixed two methods together.

Dropping the chain rule in FTC Part 1

A variable upper limit that is a function of x contributes its own derivative. If your answer is just the integrand with the bound substituted in, and the bound was anything other than plain x, a factor is missing.

Confusing net change with total distance

Signed area gives net change. Total distance needs the absolute value of the rate. If a question says total distance travelled and your integrand has no absolute value in it, stop.

Misreading which endpoint the sum uses

Left versus right changes the answer, and so does whether the function is increasing or decreasing. Read both facts off the question before you decide whether the estimate is high or low.

How to see your own Unit 6 Progress Check answers

This is the part most pages leave out. You do not need anyone to post a key, because College Board has already written an explanation for every question on the Progress Check, and it is sitting in AP Classroom attached to your own attempt.

College Board’s own description of Progress Checks is that the multiple-choice questions come with rationales explaining the correct and the incorrect answers, and the free-response questions come with scoring information. Its published guidance to teachers is to give students that question-level feedback through those answer rationales, and it states that students can view their own progress in AP Classroom.

So the explanation you are looking for exists, it is written by the people who wrote the question, and it is specific to the answer you actually chose. Your teacher is the one who turns it on. Ask them to make the rationales visible for Unit 6, or to go through the ones the class got wrong together. That is a normal request, it is what College Board tells teachers to do, and it is worth more than a scraped answer key, which gives you a letter and no reason.

A scoring guide someone uploaded to a document-sharing site cannot do any of that. It is tied to one version of the question set, it goes stale when College Board rotates items, and it never tells you why the answer you picked was wrong.

How to work through this unit

For every accumulation problem, write the sentence “the integral of this rate gives me …” with units before you compute anything. It forces you to name what the integral means, which is the same thing the free-response section asks you to write down, and it catches a wrong setup before you have spent time evaluating it.

If the technique choice is what is slowing you down, work through the integrals on our ap calc ab cheat sheet by naming the method before solving any of them. Recognition is a separate skill from execution, and it is the one Unit 6 tests.

Once you have finished the Progress Check, put your raw score into our AP AB calc score calculator to see roughly where that pace puts you on the 1–5 scale. For the full exam format and a study plan, use the AP Calculus AB Review.

Frequently asked questions

Quick answers, checked against College Board.

Does the Unit 6 Progress Check count toward my AP score?

No. Progress Checks are formative: College Board describes them as feedback that shows students where they need to focus. Only the May exam produces your 1 to 5. Your teacher may still put the score in the gradebook, but that is a school decision, not College Board’s.

Is there a formula sheet for AP Calculus AB?

No. College Board provides reference information for nine exams, including Biology, Chemistry, Physics and Statistics, and Calculus is not one of them. Nothing is handed to you, so the antiderivative rules in Unit 6 have to be memorised rather than looked up.

Is Unit 6 the same on the AP Calculus BC exam?

It is the same unit, and it carries the same 15 to 20 percent of the multiple-choice section on Calc AB and Calc BC alike. BC adds three topics AB does not have: integration by parts, linear partial fractions and improper integrals.

What is the difference between Unit 6 and Unit 8?

Unit 6 teaches you how to integrate. Unit 8 is what you do with the integral once you can: area between curves, volumes, average value and motion problems. Unit 8 assumes everything in Unit 6, which is why it is worth fixing Unit 6 first.

Do you post AP Classroom Unit 6 answers?

No. Those questions are College Board’s assessment material, and a leaked key would only tell you which letter to pick on a question you will never see again. You also do not need one: AP Classroom already holds College Board’s own explanation of every question you got wrong, and your teacher can make it visible.