Calc AB · Unit 1 Progress Check

AP Calculus AB Unit 1 Progress Check Limits and Continuity walkthrough.

AP Calculus AB Unit 1 is limits and continuity, and the Unit 1 Progress Check MCQ Part A is where you find out whether you can evaluate a limit algebraically rather than by guessing from a graph. 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 1 covers

Unit 1 is Limits and Continuity. Roughly 10–12% of the AP Calculus AB exam, and the foundation the derivative is defined on.

Limit notation and meaning

What a limit describes, and why it can exist where the function value does not.

One-sided limits

Left and right limits, and the rule that a two-sided limit exists only when they agree.

Algebraic techniques

Factoring, rationalising, and simplifying to resolve 0/0 indeterminate forms.

Squeeze theorem

Bounding a function between two others that share a limit.

Continuity

The three-part definition, and classifying removable, jump, and infinite discontinuities.

Asymptotes

Vertical asymptotes from limits, horizontal asymptotes from limits at infinity.

Intermediate Value Theorem

Guaranteeing a value is attained on a closed interval where the function is continuous.

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.

Evaluate an algebraic limit

If direct substitution gives 0/0, factor or rationalise first — never conclude the limit does not exist.

Graph-based limits

Read left and right behaviour separately. An open circle does not stop a limit from existing.

Classify a discontinuity

Removable means the gap can be filled; jump means the one-sided limits differ; infinite means an asymptote.

Limits at infinity

Compare degrees of numerator and denominator to find the horizontal asymptote.

IVT application

Confirm continuity on the closed interval first, then argue the value must be attained.

The Progress Check FRQ

Unit 1 free response usually asks you to justify continuity at a point or apply the Intermediate Value Theorem. Points come from explicitly checking all three conditions for continuity — the function is defined, the limit exists, and they are equal — and from naming the theorem you are invoking.

Where students lose the most points

Substituting before simplifying

0/0 is not an answer. It is a signal to factor or rationalise.

Saying a limit does not exist too quickly

It fails only when the one-sided limits disagree or the function grows without bound.

Confusing the limit with the function value

They differ at a removable discontinuity — that is the whole point of the concept.

Forgetting to check continuity before the IVT

The theorem requires continuity on the closed interval; without it the argument earns nothing.

Mixing up vertical and horizontal asymptotes

Vertical comes from limits at a point; horizontal comes from limits at infinity.

How to work through this unit

When substitution gives 0/0, that is information, not failure — it tells you a common factor is hiding. Factor, cancel, then substitute again.

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 1 Progress Check cover?

Limits and continuity: limit notation, one-sided limits, algebraic techniques for indeterminate forms, the squeeze theorem, continuity and discontinuity types, asymptotes, and the Intermediate Value Theorem.

What do I do when a limit gives 0/0?

That is an indeterminate form, not an answer. Factor, cancel, or rationalise to simplify the expression, then substitute again.

What are the three conditions for continuity at a point?

The function must be defined there, the limit must exist there, and the limit must equal the function value.

Do you publish Unit 1 Progress Check answers for AP Calculus?

No. We publish walkthroughs of the reasoning and the common traps instead of answer keys.