AP Calculus AB · Study Hub | Free AP Calc Study Guides

UNITSChoose a Unit

Each guide is a self-contained, interactive HTML file — works offline, tracks progress in your browser, and has a print mode. There is no formula sheet on the AP Calculus exam, so every formula here must become automatic. Every unit carries a 50-question MCQ bank and 12 nine-point FRQs, revealed in batches as you practice.

Unit 1 Limits & Continuity Exam weight 10–12% The idea the whole course is built on — where a function is heading, whether it arrives, and what the IVT guarantees. 30vocab21theorems50MCQs41FRQ parts Unit 2 Definition & Basic Derivative Rules Exam weight 10–12% The derivative as a limit, differentiability vs continuity, and the power, product, and quotient rules that make it fast. 31vocab20theorems50MCQs46FRQ parts Unit 3 Composite, Implicit & Inverse Functions Exam weight 9–13% The chain rule and its disguises — implicit curves, inverse functions, inverse trig, and second derivatives. 30vocab20theorems50MCQs46FRQ parts Unit 4 Contextual Applications of Differentiation Exam weight 10–15% Particle motion, related rates, linearization, and L’Hospital — derivatives as rates with units and meaning. 30vocab20theorems50MCQs44FRQ parts Unit 5 Analytical Applications of Differentiation Exam weight 15–18% MVT, extrema, concavity, curve analysis, and optimization — the second-heaviest unit, where justification language decides the score. 30vocab20theorems50MCQs47FRQ parts Unit 6 Integration & Accumulation of Change Exam weight 17–20% Riemann sums, the Fundamental Theorem, accumulation functions, and u-substitution — the heaviest-weighted unit on the exam. 31vocab19theorems50MCQs48FRQ parts Unit 7 Differential Equations Exam weight 6–12% Slope fields, separation of variables, and exponential models — the FRQ ritual where +C placement decides points. 29vocab19theorems50MCQs42FRQ parts Unit 8 Applications of Integration Exam weight 10–15% Average value, motion, rate in/rate out, areas, and volumes — slice, write one slice’s contribution, integrate. 30vocab18theorems50MCQs47FRQ parts

TOTALSBy the Numbers

Everything across all 8 units, mapped to the actual AP exam: 45 MCQs (50%) and six 9-point FRQs (50%).

241

Vocabulary Flashcards

157

Theorem & Definition Cards

157

Formulas & Rules

Learning Objectives

400

MCQs (50% of exam)

361

FRQ Parts (50% of exam)

Worked-Problem Steps

Justification Drills

Problem Archetypes

Common Pitfalls

COVERAGEUnit-by-Unit Breakdown

Unit	Vocab	Theorems	Formulas	MCQs	FRQ parts	Worked steps	Justify	Archetypes	Pitfalls
1. Limits & Continuity	30	21	20	50	41	5	2	8	10
2. Basic Derivative Rules	31	20	20	50	46	5	2	7	10
3. Composite & Implicit	30	20	21	50	46	5	2	7	10
4. Contextual Applications	30	20	20	50	44	5	2	7	10
5. Analytical Applications	30	20	18	50	47	5	2	7	10
6. Integration & Accumulation	31	19	20	50	48	5	2	8	10
7. Differential Equations	29	19	18	50	42	5	2	7	10
8. Applications of Integration	30	18	20	50	47	5	2	7	10
Total	241	157	157	400	361	40	16	58	80

STRATEGYHow to Use These Guides

Formulas Until Automatic

There is no formula sheet on AP Calculus. Drill the Formulas & Rules section of each unit until every derivative and antiderivative is instant.

Theorems With Hypotheses

IVT, MVT, and EVT questions are really hypothesis checks. Learn each theorem’s conditions — the exam plants answer choices that skip them.

Respect the Calculator Split

30 of 45 MCQs and 4 of 6 FRQs are no-calculator. Practice each question in its labeled mode — fluency without the calculator is most of the exam.

Write FRQs Before Revealing

Each FRQ is scored out of 9 points. Write your full response first, then compare with the model and scoring notes to see exactly where points are earned and lost.

Steal the Justification Language

“f has a relative maximum at x = 2 because f′ changes sign from positive to negative” — the Justification Bootcamp in every unit gives you the exact sentences readers credit.

Learn the Archetypes

The AP recycles problem skeletons: the tank problem, the f′-graph inquest, the region R triple-ask. Recognize the archetype and the attack plan is already decided.