AP Calculus AB 7-Day Cram Plan

A full week is enough time to rebuild fluency in every major AP Calculus AB topic and walk into the exam confident on every question type. This plan is roughly 3-4 hours per day with a final timed mock on Day 7.

If you only have 3 days, jump to our 3-day cram plan instead.

Day 1: Limits, Continuity, and the Derivative Definition (3 hrs)

Why it matters: A solid grasp of limits is the foundation for every later topic. Don't skip it because it feels easy.

Day 2: Derivative Rules and Implicit Differentiation (3 hrs)

• Power, product, quotient, and chain rules — drill until automatic.
• Derivatives of trig, inverse trig, exponential, and logarithmic functions.
• Implicit differentiation (a near-guaranteed FRQ topic).
• Higher-order derivatives.

Practice: 30 derivative MCQs + 1 implicit differentiation FRQ.

Day 3: Applications of Derivatives, Part 1 (4 hrs)

This is one of the two highest-weight units on the exam (~15-18% of points).

• Critical points, increasing/decreasing intervals, concavity, inflection points.
• Sign charts and justification language — practice writing it out.
• Local vs. absolute extrema (Closed Interval Method).
• Curve sketching from $f$, $f'$, or $f''$.

Practice: 1 full FRQ analyzing a function from its derivative graph.

💡 Score booster: Memorize this sentence: "$f$ has a relative maximum at $x = c$ because $f'$ changes from positive to negative at $c$." Adapt it for every justification.

Day 4: Applications of Derivatives, Part 2 + MVT (3 hrs)

• Optimization (real-world max/min) — set up, derive, solve, justify.
• Related rates — draw the picture, write the equation, differentiate, plug in last.
• Mean Value Theorem — recite the hypotheses verbatim and apply.
• Linearization and tangent line approximations.

Practice: 1 optimization FRQ + 1 related rates FRQ.

Day 5: Integrals, Antiderivatives, and FTC (4 hrs)

The other heavyweight unit (~17-20% of the exam).

• Antiderivatives of all basic functions — memorize the table.
• u-substitution — drill 15 problems until it's reflexive.
• Definite integrals: properties, evaluating, geometric interpretation.
• Riemann sums (left, right, midpoint, trapezoidal) — both algebraic and from a table of values.
• Fundamental Theorem of Calculus, both parts. Especially $\frac{d}{dx} \int_a^{g(x)} f(t) \, dt = f(g(x)) \cdot g'(x)$ — chain rule applied to FTC.

Practice: 25 integration MCQs + 1 Riemann-sum FRQ from a table.

Day 6: Applications of Integrals + Differential Equations (4 hrs)

• Area between curves (set up integrals with respect to $x$ and $y$).
• Volume by disks, washers, and known cross sections.
• Average value of a function: $\frac{1}{b-a} \int_a^b f(x) \, dx$.
• Particle motion: position, velocity, displacement vs. distance traveled.
• Accumulation functions and rate-in/rate-out problems.
• Slope fields, separation of variables, exponential growth/decay.

Practice: 1 particle-motion FRQ + 1 area/volume FRQ + 1 differential equation FRQ.

⚠️ Common trap: Distance traveled = $\int_a^b |v(t)| \, dt$, not $\int_a^b v(t) \, dt$. The latter is displacement. This trips students up every year.

Day 7: Full Timed Mock + Targeted Review (3-4 hrs)

• Take an official released exam under timed conditions:
  • Section I, Part A: 30 MCQ in 60 min, no calculator.
  • Section I, Part B: 15 MCQ in 45 min, calculator.
  • Section II, Part A: 2 FRQ in 30 min, calculator.
  • Section II, Part B: 4 FRQ in 60 min, no calculator.
• Score it honestly. Use the official scoring rubrics for FRQs.
• Spend the remaining time reviewing missed topics from the mock — not learning new material.

Calculator drills (do throughout the week)

Practice these until they're muscle memory:

1. nDeriv for derivatives at a point.
2. fnInt for definite integrals.
3. Graph + intersect for area problems.
4. Graph + zero for critical points.
5. nSolve (or numerical solver) for finding $x$ given $f(x) = k$.

What to do the night before

Open the last-minute review → for a one-page formula and trap checklist. Sleep 8 hours. Eat breakfast.

Recap: one week to peak

• 2 days on derivatives and their applications.
• 2 days on integrals and their applications.
• 1 day on differential equations and motion.
• 1 day on a full timed mock.
• Limits / continuity / FTC sprinkled throughout.

Start now: browse AP Calculus AB topics →.