AP Calculus AB 1-Month Study Plan

A month of focused, structured prep is more than enough to earn a 4 or 5 on the AP Calculus AB exam — even if your in-class grade is shaky. This plan assumes ~1 hour per weekday and ~2-3 hours on each weekend day.

If you need to compress: see our 7-day cram plan or 3-day cram plan.

Week 1: Limits, Continuity, and Derivative Foundations

Goal: Walk into Week 2 with derivative rules on autopilot.

Day	Focus	Output
Mon	Diagnose: take 20-question MCQ pretest	List your 5 weakest topics
Tue	Limits: algebra, conjugates, indeterminate forms	15 problems
Wed	Limits at infinity, asymptotes, IVT	15 problems
Thu	Continuity, the derivative as a limit	10 problems
Fri	Power, product, quotient, and chain rules	25 derivative problems
Sat	Trig, exponential, log, and inverse trig derivatives	20 problems + flashcards
Sun	Implicit differentiation + 1 free-response question	10 problems + 1 FRQ

Internal link: AP Calculus AB topic library →.

Week 2: Applications of Derivatives

Goal: Master the FRQ-heavy topics that account for ~18% of the exam.

Day	Focus	Output
Mon	Critical points, sign charts, increasing/decreasing	10 problems
Tue	Concavity, inflection points, Second Derivative Test	10 problems
Wed	Curve sketching from $f$ , $f'$ , or $f''$	Analyze 5 graphs
Thu	Optimization	8 word problems
Fri	Related rates	8 problems
Sat	Mean Value Theorem, linearization, L'Hôpital's Rule	12 problems + 1 FRQ
Sun	Mixed-topic FRQ practice	2 timed FRQs

💡 Justification language: Memorize the wording the rubric wants. " $f$ has an absolute max at $x = 3$ because $f'(3) = 0$ and $f''(3) < 0$ ." Practice writing this verbatim.

Week 3: Integrals and FTC

Goal: Make antiderivatives and u-substitution second nature.

Day	Focus	Output
Mon	Antiderivative table + u-substitution	25 problems
Tue	Definite integrals, properties, geometric meaning	15 problems
Wed	Riemann sums (LRAM, RRAM, MRAM, Trapezoidal) — algebraic and from tables	10 problems
Thu	Fundamental Theorem of Calculus, both parts	12 problems
Fri	Accumulation functions: $g(x) = \int_a^x f(t) \, dt$	8 problems
Sat	Area between curves + average value	10 problems + 1 FRQ
Sun	Volume by disks, washers, and cross sections	8 problems + 1 FRQ

⚠️ FTC chain rule trap: $\frac{d}{dx} \int_a^{x^2} f(t) \, dt = f(x^2) \cdot 2x$ — always apply the chain rule to the upper limit.

Week 4: Applications, DEs, Mock Exam, and Polish

Goal: Lock in particle motion, differential equations, and exam stamina.

Day	Focus	Output
Mon	Particle motion: position, velocity, displacement vs distance	10 problems
Tue	Slope fields + separation of variables	10 problems
Wed	Exponential growth/decay + logistic models (BC bonus, AB skim)	8 problems
Thu	Mixed multiple-choice mock: 45 questions, timed	Score and review
Fri	Full timed FRQ section: 6 questions in 90 min	Score with rubric
Sat	Full timed mock exam (entire 3h 15min)	Honest score
Sun	Targeted review of weakest mock topics + light FRQ work	Don't cram new material

Daily habits throughout the month

Spaced repetition flashcards for derivative and integral rules — 5 min/day.
One FRQ per week minimum from a past College Board exam — score with the rubric.
Track missed problems in a single notebook by topic. Review weekly.

Calculator routine (build into Week 2 onward)

Become fluent with these on your specific calculator (TI-84, TI-Nspire, etc.):

Numerical derivative (nDeriv).
Numerical integral (fnInt).
Graph + intersect for area problems.
Graph + zero for critical points.
nSolve for equations like $f(x) = k$ .

The night before & morning of

Skim the last-minute review checklist.
Review the FRQ template phrasings.
Sleep 8+ hours.
Eat breakfast with protein and slow carbs.
Pack: 2 sharpened #2 pencils, blue/black pens, approved calculator, fresh batteries, photo ID.

Final word

A 4-week plan rewards consistency more than intensity. Show up every day, even if it's just 30 minutes. The students who score 5s aren't the ones who pull all-nighters — they're the ones who logged 25 quiet sessions in a row.

Start now: browse AP Calculus AB topics →.