Calc AB · Unit 7 Progress Check

AP Calculus AB Unit 7 Progress Check: Differential Equations.

College Board builds the Unit 7 Progress Check from about 15 multiple-choice questions and 3 free-response questions, drawn from differential equations, a unit worth 5–10% of the multiple-choice section of the AP Calculus AB exam. None of the three free-response questions is a shortened version. Explanations only — we never publish AP Classroom answer keys.

Updated September 2026Written by Mahmudul HasanFree · No signup

What is on the Unit 7 Progress Check

College Board publishes the size of this assignment in two places in the Course and Exam Description, and both agree: about 15 multiple-choice questions and 3 free-response questions for AP Calculus AB. The word about is College Board’s, not ours: the count is published as an approximation, so treat 15 as the shape of the assignment rather than a promise.

One detail in that listing is worth pulling out. None of the three free-response questions is flagged as a shortened version, and College Board does use that flag elsewhere in the same document, on the Progress Checks for Units 1, 2 and 3. Its absence here is a signal rather than a silence: all three run at full length.

That share is the fact most study sites get wrong. Unit 7 is 5–10% of the multiple-choice section, not of the whole exam. College Board attaches that qualifier twice on the same page: once in the sentence introducing the table, once in the table’s own heading. For the free-response half of the exam it gives no unit-by-unit share at all. Three of the five study sites we checked publish 6–12% instead, a figure that appears nowhere in the current Course and Exam Description; one of them cites a 2019 edition as its source. College Board also budgets roughly 8 to 9 class periods to the unit.

This is one of every AP Calculus AB unit Progress Check walked through on Curve.

The seven topics AP Calculus AB is responsible for

Unit 7 has nine topics, but two of them, Euler’s method and logistic models, are marked BC only. An AB student is responsible for seven:

7.1 Modeling situations with differential equations

Turning a sentence about how fast something changes into an equation involving a derivative. This is the topic College Board lists first, and the one study guides most often skip.

7.2 Verifying solutions

Substituting a proposed function and its derivative back into the equation. College Board updated this topic’s wording for 2026 to say plainly that a differential equation may have infinitely many solutions.

7.3 Sketching slope fields

Drawing the field. College Board’s definition is deliberately narrow: the field draws the equation only at scattered sample points, never across the whole plane.

7.4 Reasoning using slope fields

Reading the field to describe how solutions behave. College Board scopes this to first-order equations and says solutions come as functions or whole families of them.

7.6 General solutions by separation of variables

Splitting the variables and antidifferentiating. Note College Board’s hedge: some differential equations can be solved this way, not all.

7.7 Particular solutions from initial conditions

Using a given point to pin down the constant. Exactly one solution curve passes through that point, and the answer can carry a restriction on its domain.

7.8 Exponential models

Recognizing the equation you get when a quantity grows in step with how much of it is already there, and knowing its solution without re-deriving it.

The multiple choice: what each question type is testing

Fifteen questions across seven topics leaves roughly two questions per idea, so the set is broad rather than deep. These are the patterns that recur, and what each is really asking.

Match an equation to a field

At any point, the little segment’s slope is whatever the equation gives you there. Test two or three convenient points and eliminate; do not try to read the whole picture at once.

Verify a proposed solution

Differentiate what you are given and check both sides agree. This is topic 7.2: it is a substitution question, not a solving question, and solving from scratch wastes the time the question was designed to save you.

Write the equation from a sentence

Topic 7.1. Growth in step with the amount present becomes a constant times the quantity; growth in step with a gap becomes a constant times a subtraction. The question is finished before any integration starts.

Set up a separation

Every y and dy on one side, every x and dx on the other, before a single integral sign appears. Questions in this family often stop at the setup.

Find the constant

Substitute the initial condition after antidifferentiating, never before. Only one curve in the family passes through the given point.

Read an exponential model

Spot the shape, read off the rate constant, answer. College Board says explicitly that these models can be used and interpreted without performing the derivation.

Use the equation directly

Some questions never want a solution at all. A differential equation is a statement about a rate, so it will answer a question about a slope or a speed on its own.

A scoping note on slope fields

The skill College Board pairs with topic 7.4 sits in Mathematical Practice 4, and that practice is the one College Board states is not assessed in the multiple-choice section. That is a statement about the practice, not about the content: slope-field questions certainly do appear on the multiple choice. What it means is that the drawing-and-communication half of the skill is examined in the free response instead.

The free response: three questions, full length

College Board publishes the count, three questions, and does not publish a breakdown of what each one asks, so any site telling you what the Unit 7 free response “usually” contains is guessing. What can be said is what the unit’s own required content makes examinable, and what College Board says about how free-response work is judged across the course.

The work itself is the answer. On the AP exam, when a result comes from a calculator’s built-in capability, College Board requires the setup written out, whether that is the equation being solved or the integral being evaluated, alongside whatever the calculator returned. A bare number is worth less than the same number with the work shown above it, and since the Progress Check is built from the same question types, it is the place to build that habit.

For a separable equation, four things have to be visible on the page: the variables split, both sides antidifferentiated with a constant of integration, that constant determined from the initial condition, and the expression rearranged into whatever form was asked for. Leave any of the four implicit and it is not there to be credited. For the full picture of how the exam’s free-response section is structured and timed, see the AP Calculus AB Review.

Where College Board says students lose points

Most pages about this unit offer a list of plausible mistakes. College Board names its own, in the Course and Exam Description’s preparation notes for Unit 7, and two of the three are blunt about the cost.

Not separating the variables

College Board says this severely limits how many points are available, not that it costs a point. If a y is still sitting on the dx side when you integrate, the rest of the question cannot recover.

Leaving out the constant of integration

Named in the same sentence, with the same consequence. Without the constant there is nothing for the initial condition to determine, so one omission takes the particular solution with it.

Assuming a fraction means a logarithm

College Board’s third named error, and the one almost nobody publishes: students meet a fraction while antidifferentiating and reach for a logarithm because some of these problems genuinely produce one. Check what is actually in the denominator first.

Three more that follow from the required content

These are not on College Board’s list, but they are direct consequences of what the unit says students must know, so they are worth the same attention.

Applying the initial condition too early

Antidifferentiate first. Substituting the point before you have a constant to solve for does nothing.

Ignoring the domain

The required content says outright that solutions can be subject to domain restrictions. If you divided by something that could be zero, the answer does not hold everywhere.

Reading a slope field as a solution curve

The segments show the rate, not the path. A solution curve is the one you draw by following them.

How to work through this unit

College Board describes the solution strategy for a contextual separable equation as something that should become routine, and routine is the right word: the same four steps in the same order every time, until the order is automatic. Separate, antidifferentiate both sides with one constant, use the initial condition to find it, rearrange into the form the question asked for.

The step before all four of those, turning a sentence into an equation, is the one that is easiest to skip, because it produces no calculation to drill. Topic 7.1 exists for it, and College Board lists it first. College Board’s own example for the unit asks how you would model the number of computers infected by a virus given only how fast the infection is spreading. If you can write that equation, the rest of the unit is procedure.

Once you have finished the Progress Check, the obvious next move depends on where it went wrong. Separation of variables is antidifferentiation wearing a different hat, so if the integrals are the slow part, the AP Calculus AB Unit 6 Progress Check covers the material sitting underneath this one. For a one-screen summary of every unit at once, the AP Calculus AB cram chart condenses each to an idea, a tool and a trap. A raw score from the assignment can also go into the AP Calc AB curve calculator, which estimates what a similar rate would be worth on the exam itself.

About “answers” for this Progress Check

Most of what ranks for this query is a reposted answer key. Curve does not publish one and does not link to one, for a reason that is practical as much as principled: AP Classroom work is graded as your own, and a key gives you the letter without the reasoning the question was built to test.

There is a legitimate route to the answers, and it is the one the tool was designed around. Once your teacher releases the Progress Check results in AP Classroom, every question comes back with College Board’s own rationale for the correct option and for each distractor. That is a better artifact than any key, because it tells you why the wrong answer was tempting. If your teacher has not released it, asking is the whole of the process.

Sources: College Board, AP Calculus AB and BC Course and Exam Description (effective Fall 2020, with the clarifications implemented for Fall 2026) and the AP Central AP Calculus AB exam page. Written by Mahmudul Hasan.

Frequently asked questions

Quick answers, checked against College Board.

How many questions are on the AP Calculus AB Unit 7 Progress Check?

College Board publishes about 15 multiple-choice questions and 3 free-response questions for AB, on two agreeing pages of the Course and Exam Description. The count is written as an approximation, so treat 15 as the size of the assignment rather than an exact number.

How much of the AP Calculus AB exam is Unit 7?

5 to 10 percent of the multiple-choice section. That qualifier is College Board’s own, and it matters: for the free-response half of the exam no unit-by-unit share is given at all. A larger range you may have seen elsewhere traces back to a superseded edition of the framework.

Is Euler's method on the AP Calculus AB Unit 7 Progress Check?

No. Topic 7.5, Euler’s method, and topic 7.9, logistic models, are both marked BC only. An AB student is responsible for the other seven topics in the unit.

Do I have to memorize the exponential growth formula?

Yes. AP Calculus is one of the courses where College Board supplies no reference sheet on exam day, so anything you want on paper has to be in your head first.

What does a slope field show?

The value of the derivative, drawn only at scattered sample points rather than everywhere. The segments are rates, and a solution curve is the path you get by following them; a first-order equation has a whole family of those.

Do you post AP Calculus Unit 7 answers?

No. Ask your teacher to release the Progress Check in AP Classroom instead, which returns College Board’s own rationale for every option, including the wrong ones.