AP Calculus AB — Stewart Early Transcendentals 5e Teaching Map

The headline

Your reading order is: 1 → 2 → 3 → 4 → 5 → 6 → 9.

Chapters 7, 8, 10, 11 and everything after do not exist for AB purposes, with one surgical exception: §7.7 contains the Trapezoidal Rule, which is tested. Pull that out and fold it into Chapter 5, then close the book on Chapter 7.

Note that Stewart puts Differential Equations (Ch 9) after two chapters you're skipping entirely. Jump straight from Ch 6 to Ch 9.

Chapter 1 — Functions and Models

Prerequisite review. Diagnose, don't teach.

§	Title	AB status
1.1–1.3	Representing functions; models; new functions from old	Review only as needed
1.4	Graphing Calculators and Computers	Do it — calculator fluency is graded
1.5	Exponential Functions	Required background
1.6	Inverse Functions and Logarithms	Required background — 5e moved inverse trig here from the appendix, and he needs it for Ch 3

Give this a week at most. If he's solid on trig, logs, and piecewise functions, move on.

Chapter 2 — Limits and Derivatives

→ AB Unit 1 (10–12%) and the front of Unit 2 (10–12%)

§	Title	AB status
2.1	The Tangent and Velocity Problems	Cover
2.2	The Limit of a Function	Cover — includes infinite limits, vertical asymptotes
2.3	Calculating Limits Using the Limit Laws	Cover — Squeeze Theorem lives here
2.4	The Precise Definition of a Limit	SKIP — epsilon-delta is not tested
2.5	Continuity	Cover — the Intermediate Value Theorem is here
2.6	Limits at Infinity; Horizontal Asymptotes	Cover
2.7	Tangents, Velocities, Rates of Change	Cover
2.8	Derivatives	Cover — definition of the derivative
2.9	The Derivative as a Function	Cover — What Does f′ Say About f? gets real in Ch 4

Supplement: estimating limits and derivatives from tables of values. Stewart is thin here and the AP is not.

Chapter 3 — Differentiation Rules

→ AB Units 2, 3 (9–13%), and part of Unit 4

Listed by title — check your TOC for numbers.

§	Section title	AB status
3.1	Derivatives of Polynomials and Exponential Functions	Cover — power rule, eˣ
3.2	The Product and Quotient Rules	Cover
3.3	Rates of Change in the Natural and Social Sciences	Cover, and don't rush it. This is your best in-book source for interpreting derivatives in context with units, plus particle motion. It maps to a third of AB Unit 4
3.4	Derivatives of Trigonometric Functions	Cover — all six
3.5	The Chain Rule	Cover
3.6	Implicit Differentiation	Cover — derivatives of inverse trig functions are derived here
3.7	Higher Derivatives	Cover — brief
3.8	Derivatives of Logarithmic Functions	Cover ln x. Logarithmic differentiation is optional — not a CED topic
3.9	Hyperbolic Functions	SKIP
3.10	Related Rates	Cover thoroughly — reliable FRQ material
3.11	Linear Approximations and Differentials	Cover the linear approximation half. The dy = f′(x)dx formalism is optional

Chapter 4 — Applications of Differentiation

→ AB Unit 5 (15–18%, heaviest differentiation unit) plus one piece of Unit 4

§	Title	AB status
4.1	Maximum and Minimum Values	Cover — Extreme Value Theorem, critical points, Candidates Test
4.2	The Mean Value Theorem	Cover thoroughly — he must state the hypotheses aloud
4.3	How Derivatives Affect the Shape of a Graph	Cover thoroughly — First and Second Derivative Tests, concavity, inflection. Densest AB section in the book
4.4	Indeterminate Forms and L'Hospital's Rule	Cover 0/0 and ∞/∞ only — skip the exotic forms
4.5	Summary of Curve Sketching	Cover
4.6	Graphing with Calculus and Calculators	Light pass
4.7	Optimization Problems	Cover thoroughly
4.8	Applications to Business and Economics	SKIP — marginal cost/revenue is not on AB
4.9	Newton's Method	SKIP
4.10	Antiderivatives	Cover — your bridge into Ch 5

Chapter 5 — Integrals

→ AB Unit 6 (17–20%, single heaviest unit on the exam)

§	Title	AB status
5.1	Areas and Distances	Cover — left, right, and midpoint Riemann sums
5.2	The Definite Integral	Cover — notation and properties
5.3	The Fundamental Theorem of Calculus	Cover very thoroughly — both parts, and accumulation functions
5.4	Indefinite Integrals and the Net Change Theorem	Cover
5.5	The Substitution Rule	Cover — the only integration technique AB tests
5.6	The Logarithm Defined as an Integral	SKIP — theoretical

Insert here: the Trapezoidal Rule from §7.7. Do the trapezoidal material and nothing else from that section — Simpson's Rule and error bounds are not tested.

Supplement: two CED topics Stewart doesn't give a home to.

Rewriting integrands by long division and completing the square (the long-division technique appears as a preliminary in §7.4; take it without taking partial fractions).
Riemann sums from tables with unequal subinterval widths. Extremely common on the exam, essentially absent from Stewart.

Chapter 6 — Applications of Integration

→ AB Unit 8 (10–15%)

§	Title	AB status
6.1	Areas between Curves	Cover — including integrating with respect to y, and curves crossing more than twice
6.2	Volumes	Cover thoroughly — discs, washers, and known cross-sections. Rotating about lines other than the axes
6.3	Volumes by Cylindrical Shells	SKIP — the single most over-taught topic for AB
6.4	Work	SKIP
6.5	Average Value of a Function	Cover — small section, reliably tested

Chapter 7 — Techniques of Integration

SKIP THE ENTIRE CHAPTER, except as noted.

§	Title	Why
7.1	Integration by Parts	BC only
7.2	Trigonometric Integrals	Neither exam
7.3	Trigonometric Substitution	Neither exam
7.4	Partial Fractions	BC only — but borrow the long-division setup for AB topic 6.10
7.5	Strategy for Integration	Not needed with one technique
7.6	Tables and CAS	No
7.7	Approximate Integration	Trapezoidal Rule only. Skip Simpson's and error bounds
7.8	Improper Integrals	BC only

Chapter 8 — Further Applications of Integration

SKIP ENTIRELY. Arc length is BC. Surface area, physics and engineering applications, economics and biology, and probability are on neither exam.

Chapter 9 — Differential Equations

→ AB Unit 7 (6–12%)

§	Title	AB status
9.1	Modeling with Differential Equations	Cover — including verifying a proposed solution
9.2	Direction Fields and Euler's Method	Cover the direction fields half only. Stewart's "direction fields" are the AP's "slope fields," and sketching and interpreting them is tested. Euler's method is BC — skip it
9.3	Separable Equations	Cover thoroughly — general and particular solutions from an initial condition
9.4	Exponential Growth and Decay	Cover
9.5	The Logistic Equation	SKIP — BC only
9.6	Linear Equations	SKIP — integrating factors are on neither exam
9.7	Predator-Prey Systems	SKIP

Low weight, but it shows up reliably in free response. Don't let the percentage fool you into skimping.

Chapters 10 and beyond

SKIP ENTIRELY. Parametric and polar (Ch 10) and infinite sequences and series (Ch 11) are BC. Everything from Ch 12 on is multivariable.

That's roughly 40% of your book you never open.

What Stewart won't give him

These are AP-specific and no calculus text emphasizes them enough. This is where points are actually lost.

1. Units and interpretation. "Using correct units, explain the meaning of ∫₀⁸ r(t) dt in the context of this problem." Nearly every FRQ set has one. Needs a unit and a full sentence. §3.3 (Rates of Change in the Natural and Social Sciences) is your best in-book launching point.

2. Tables of values. Estimating derivatives from a table. Riemann sums from table data with unequal widths. Common on the exam, nearly absent from Stewart.

3. Accumulation functions. Given a graph of f, reason about g(x) = ∫ₐˣ f(t) dt — where g increases, its extrema, its concavity. §5.3 states the theorem and moves on; the AP builds whole problems here.

4. Justification language. Rubric points go to naming the theorem and stating its hypotheses. "f is continuous on [a,b] and differentiable on (a,b), so by the Mean Value Theorem…" Right reasoning, wrong words, zero points. Learnable in an afternoon and worth doing early.

5. Reading f′ to describe f. Graph of the derivative, questions about the original function. Constant AP theme, and Stewart approaches it from the opposite direction.

6. Particle motion vocabulary. Speed vs. velocity. "Is the speed increasing?" — velocity and acceleration share a sign. Total distance vs. displacement.

7. Calculator skills. On calculator-active sections he needs exactly four operations: graph in a window, find zeros, numerical derivative at a point, numerical definite integral. He should be able to set up an integral and report the value without producing an antiderivative. That earns full credit.

Exam format

Multiple choice — 45 questions, 105 minutes, 50%

Part A: 30 questions, 60 minutes, no calculator
Part B: 15 questions, 45 minutes, calculator

Free response — 6 questions, 90 minutes, 50%

Part A: 2 questions, 30 minutes, calculator
Part B: 4 questions, 60 minutes, no calculator

Pacing, late August to early May

Window	Stewart	AB units	Share of exam
Sept	Ch 1 review, Ch 2	Units 1–2	~20–24%
Oct–Nov	Ch 3	Units 2–3, part of 4	~15–20%
Nov–Dec	Ch 4	Units 4–5	~25–33%
Jan–Feb	Ch 5 (+ trapezoid from 7.7)	Unit 6	~17–20%
Feb–Mar	Ch 6, then Ch 9	Units 8, 7	~16–27%
April	Review, FRQ drilling, two timed full-length exams	—	—

Front-loading leaves March and April as real buffer. You'll want it.

Practice materials

Released free-response questions on AP Central, back to 1998, with scoring guidelines and chief reader reports. Free. The scoring guidelines are the most valuable document in AP prep — they show exactly which words earn which points.
AP Classroom, once the FCPS coordinator issues his join code. Exam-only enrollees get partial access; some resources require a teacher to assign them.
The CED itself, with sample questions and commentary.

Begin released FRQs on completed units in January. Not as review — as how he learns what a correct answer looks like.