Calc AB · Unit 7 Progress Check

AP Calculus AB Unit 7 Progress Check Differential Equations walkthrough.

AP Calculus AB Unit 7 is differential equations, and the Unit 7 Progress Check MCQ covers slope fields, separation of variables, and exponential models. This walkthrough covers what each question type tests, the traps, and how to work through them. Explanations only — we never publish AP Classroom answer keys.

Updated August 2026Written by Mahmudul HasanFree · No signup

What Unit 7 covers

Unit 7 is Differential Equations. Differential equations is roughly 6–12% of the AP Calculus AB exam and a reliable free-response topic.

Slope fields

Sketching and reading a slope field, and matching it to a differential equation.

Solutions to differential equations

Verifying a function satisfies dy/dx, and distinguishing general from particular solutions.

Separation of variables

The standard technique: separate y and x, integrate both sides, then solve for the constant.

Initial conditions

Using a given point to find C and produce a particular solution.

Exponential growth and decay

dy/dt = ky, whose solution is y = y0·e^(kt).

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.

Match a slope field

At each point the segment slope equals dy/dx there. Test a couple of points to eliminate options.

Verify a solution

Differentiate the proposed function and check it satisfies the equation — do not try to solve from scratch.

Separation setup

Get all y terms with dy and all x terms with dx before integrating.

Find the constant

Substitute the initial condition after integrating, not before.

Exponential model reasoning

Recognise dy/dt = ky as exponential and read off the rate constant.

The Progress Check FRQ

Unit 7 free response usually asks you to solve a differential equation by separation of variables with a given initial condition, or to interpret a slope field. Points come from correctly separating, integrating both sides with +C, applying the initial condition to find C, and solving explicitly for y.

Where students lose the most points

Forgetting +C on integration

And then never finding the particular solution — two lost points from one omission.

Applying the initial condition too early

Integrate first, then substitute the point to solve for C.

Not separating fully

Every y must be on the dy side and every x on the dx side before you integrate.

Leaving the answer implicit

If the question asks for y = f(x), solve for y explicitly.

Misreading a slope field

The segments show dy/dx, not the solution curve itself.

How to work through this unit

For separation problems, work in a fixed order: separate, integrate both sides with one +C, substitute the initial condition to find C, then solve for y. Each step is a rubric point.

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

Frequently asked questions

Quick answers — written by humans, not a chatbot.

What does the AP Calculus AB Unit 7 Progress Check cover?

Differential equations: slope fields, verifying solutions, separation of variables, initial conditions and particular solutions, and exponential growth and decay.

How do I solve a differential equation by separation of variables?

Separate all y terms with dy and all x terms with dx, integrate both sides adding one constant, then use the initial condition to find the constant and solve explicitly for y.

What does a slope field show?

At each point it shows the slope dy/dx given by the differential equation, not the solution curve. Solution curves follow the direction of the segments.

Do you post AP Calculus Unit 7 answers?

No. AP Classroom work is graded as your own, so we publish walkthroughs of the reasoning instead.