AP Calculus AB & BC

Complete AP Calculus AB and BC guide. Covers limits, derivatives, applications, integrals, applications of integrals, differential equations, and BC-only topics (parametric/polar, sequences and series). Includes worked examples and exam strategy.

Topics Covered

Limits & Continuity

Derivatives

Applications of Derivatives

Integrals

Applications of Integrals

Differential Equations

Parametric & Polar (BC)

Sequences & Series (BC)

What you get

Full topic-by-topic curriculum coverage

Spaced-repetition flashcards for every topic

Multiple-choice quizzes with explanations

Term-matching vocabulary games

Aligned with the College Board CED

Exam technique tips throughout

Key terms & definitions bank

12 months of access from purchase

Free Sample

Unit 1 — Limits & Continuity

THE BIG PICTURE. Unit 1 introduces the single most important concept in calculus — the limit. Every subsequent idea (derivatives, integrals, series) is built on the limit. The unit weighs 10–12% of AB / 4–7% of BC but its conceptual importance is enormous: students who don't internalize limits as the formal way to talk about "approaches" struggle with everything that follows. The MC and FRQ both directly test (1) computing limits, (2) continuity classifications, and (3) the IVT for proving roots exist.

Sample Flashcards

How do you compute $lim_{x \to c} f (x)$ ?

Try in this order: 1) Direct substitution: if $f$ is continuous at $c$ , the limit equals $f (c)$ . 2) Algebraic manipulation if step 1 gives $\frac{0}{0}$ : factor and cancel; rationalize; combine fractions. 3) Special limits: $\frac{sin x}{x} \to 1$ , $\frac{1 - cos x}{x} \to 0$ , $\frac{e ^{x} - 1}{x} \to 1$ as $x \to…

Compute $lim_{x \to 3} \frac{x ^{2} - 9}{x - 3}$ .

Direct substitution gives $\frac{0}{0}$ . Factor numerator: $x^{2} - 9 = (x - 3) (x + 3)$ . Cancel $(x - 3)$ : limit becomes $lim_{x \to 3} (x + 3) = 6$ . The original function had a removable discontinuity (a hole) at $x = 3$ .

Sample Key Terms

Limit

The value $f (x)$ approaches as $x$ approaches $c$ . Notation: $lim_{x \to c} f (x) = L$ . The function need not be defined at $c$ for the limit to exist.

One-Sided Limit

$lim_{x \to c^{-}} f (x)$ considers $x$ approaching $c$ from values less than $c$ ; $lim_{x \to c^{+}} f (x)$ from values greater than $c$ . The two-sided limit exists iff both one-sided limits exist and are equal.

Continuity

$f$ is continuous at $c$ if $f (c)$ is defined, the limit exists, and $lim_{x \to c} f (x) = f (c)$ . Continuous on an interval means continuous at every point.

What's Covered

Unit 1 — Limits & Continuity
Unit 2 — Differentiation: Definition & Fundamental Properties
Unit 3 — Differentiation: Composite, Implicit & Inverse Functions
Unit 4 — Contextual Applications of Differentiation
Unit 5 — Analytical Applications of Differentiation
Unit 6 — Integration & Accumulation of Change
Unit 7 — Differential Equations
Unit 8 — Applications of Integration
Unit 9 (BC) — Parametric, Polar & Vector Functions
Unit 10 (BC) — Sequences & Series

10 topics · 125+ flashcards · quizzes & matching games included

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