AP Calculus AB Unit 1: Limits and Continuity

Unit 1 covers limits and continuity: evaluating limits algebraically and graphically, one-sided limits, and the three conditions a function must meet to be continuous at a point. Everything later in AB is defined in terms of a limit.

40 questions3 CED topics100% with a figure
How this unit behaves

What 40 questions on it look like

With only 3 topics, this unit is narrow enough to master completely — an unusual opportunity in a course this size.

100% of the questions come with a figure — a graph, diagram or data display. Reading the figure correctly is most of the work before any content knowledge applies.

Exploring Types of Discontinuities20
Confirming Continuity over an Interval10
Estimating Limit Values from Graphs and Tables10

Questions per CED topic.

From the bank

Three real limits and continuity questions

Drawn from the practice pool, not from the mock papers.

Exploring Types of Discontinuities · Connecting Representations · with figure

Use Figure 1. Which statement about lim as x approaches -2 of f(x) is true?

  1. AThe limit is 1.
  2. BThe two-sided limit does not exist because the one-sided limits are different.correct
  3. CThe limit is -1.
  4. DThe limit is 0.
Why B is correct

The left-hand limit is 1, while the right-hand limit is -1. Since they are unequal, the two-sided limit does not exist.

Confirming Continuity over an Interval · Connecting Representations · with figure

Use Figure 1. Is t continuous at x=-2?

  1. ANo, because the left-hand limit does not exist.
  2. BNo, because the right-hand limit does not exist.
  3. CNo, because t(c) is different from the limit.
  4. DYes, because the two-sided limit equals t(c).correct
Why D is correct

The graph approaches y=2 from both sides and the filled point is also at y=2, so t is continuous at x=-2.

Exploring Types of Discontinuities · Connecting Representations · with figure

Use Figure 1. Which statement about lim as x approaches -1 of f(x) is true?

  1. AThe limit is 2.
  2. BThe limit is -2.
  3. CThe two-sided limit does not exist because the one-sided limits are different.correct
  4. DThe limit is 0.
Why C is correct

The left-hand limit is 2, while the right-hand limit is -2. Since they are unequal, the two-sided limit does not exist.

40 questions on this unit, free to start.

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FAQ

Limits and Continuity questions

What are the conditions for continuity?

The function is defined at the point, the limit exists there, and the two are equal. Most questions fail exactly one of the three.

How do I handle a 0/0 limit?

Factor and cancel, rationalise, or use a known special limit. 0/0 is indeterminate, not undefined — it means more work, not no answer.
Last reviewed 2026-08-28. Unit and topic names follow the College Board course framework. Question counts describe the PrepScore practice bank, not the exam.

Practise limits and continuity until the reasoning is automatic.

Real AP questions with a full explanation on every answer, and a mistake bank that only clears when you get it right.