AP Calculus AB 1-Month Study Plan

title: "AP Calculus AB 1-Month Study Plan" description: "A complete 4-week AP Calculus AB study plan: weekly topic breakdown, mixed practice, FRQ work, calculator drills, and a final-week timed mock." date: "2026-01-15" examDate: "May AP Exam" topics:

• Limits & Continuity
• Derivatives
• Applications of Derivatives
• Integrals
• Applications of Integrals
• Differential Equations

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.):

1. Numerical derivative (nDeriv).
2. Numerical integral (fnInt).
3. Graph + intersect for area problems.
4. Graph + zero for critical points.
5. 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 →.