Calc AB · Unit 4 Progress Check

AP Calculus AB Unit 4 Progress Check Contextual Applications of Differentiation walkthrough.

AP Calculus AB Unit 4 applies the derivative to real situations — motion, related rates, and approximation — and the Unit 4 Progress Check MCQ is where units and setup start carrying real weight. This walkthrough covers the question types, the traps, and how to work through them. Explanations only — no AP Classroom answer keys.

Updated August 2026Written by Mahmudul HasanFree · No signup

What Unit 4 covers

Unit 4 is Contextual Applications of Differentiation. Roughly 10–15% of the AP Calculus AB exam, and the unit that makes derivatives mean something.

Motion

Position, velocity, and acceleration; speed as the absolute value of velocity.

Rates of change in context

Interpreting f′(t) as a rate with units, in words.

Related rates

Differentiating an equation relating two quantities with respect to time.

Linear approximation

Using the tangent line to estimate a nearby value, and whether it over- or under-estimates.

L’Hôpital’s rule

Resolving 0/0 and ∞/∞ indeterminate forms by differentiating numerator and denominator.

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.

Motion sign reasoning

A particle speeds up when velocity and acceleration share a sign, and slows when they differ.

Related rates setup

Write the relationship first, differentiate with respect to t, and only then substitute the given values.

Interpretation with units

“f′(5) = 3 means…” — the answer must include the rate and the units.

Tangent line approximation

Concavity decides direction: concave up means the tangent underestimates.

L’Hôpital recognition

Confirm the form is genuinely indeterminate before applying the rule.

The Progress Check FRQ

Unit 4 free response often gives a rate in context and asks you to compute and then explain. Points come from correct differentiation, correct substitution at the right moment, and a sentence interpreting the result with units — the interpretation is a separate point from the calculation.

Where students lose the most points

Substituting values before differentiating

In related rates, plugging numbers in early turns variables into constants and destroys the derivative.

Omitting units

A contextual answer without units loses the interpretation point.

Confusing speed and velocity

Speed is the absolute value; a particle can have negative velocity and increasing speed.

Applying L’Hôpital to a determinate form

If substitution gives a number, the rule does not apply.

Forgetting the chain rule in related rates

Every variable changing with time contributes a d/dt factor.

How to work through this unit

In every related-rates problem, write the equation relating the quantities before you differentiate, and keep all values symbolic until after the derivative is taken.

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 4 Progress Check cover?

Contextual applications of differentiation: motion, rates of change with units, related rates, linear approximation, and L’Hôpital’s rule.

What is the most common related-rates mistake?

Substituting the given numerical values before differentiating. Values that change with time must stay as variables until after you differentiate with respect to t.

When does a particle speed up?

When velocity and acceleration have the same sign. If they have opposite signs, the particle is slowing down regardless of direction.

Do you post AP Calculus Unit 4 answers?

No. We publish walkthroughs of the reasoning and setup traps rather than AP Classroom answer keys.