AP Calculus AB 3-Day Cram Plan

You have three days until the AP Calculus AB exam. This is not the time to learn new material from scratch — it's time to drill the highest-frequency topics and lock in the FRQ patterns the College Board reuses every single year.

This plan assumes ~4 focused hours per day. Skip nothing on the checklist; if you're short on time, shorten the practice sets, not the topic coverage.

Day 1: The Big 3 — Limits, Derivatives, and Their Rules (4 hrs)

The first 30+ multiple-choice questions on the exam lean heavily on these foundations. Get them automatic.

What to review (90 min)

• Limits: limits at infinity (compare degrees), one-sided limits, limits from a graph, $\lim_{x \to a} \frac{f(x)}{g(x)}$ when both are 0 (algebraic manipulation, factoring, conjugates).
• Continuity: 3-part definition, Intermediate Value Theorem (IVT) — know how to cite it on FRQs.
• Derivative rules: product, quotient, chain — fast and clean.
• Implicit differentiation: don't lose easy points here.
• Derivatives of inverse trig and $\ln$, $e^x$: memorize the table cold.

What to practice (2.5 hrs)

• 20 mixed multiple-choice questions on derivatives (calc and no-calc).
• 1 full FRQ on a function defined piecewise — these test continuity, differentiability, and IVT in one question.

💡 Highest leverage: Implicit differentiation appears almost every year on at least one FRQ. Drill 5 problems tonight.

Day 2: Applications of Derivatives + Integrals Setup (4 hrs)

These two areas account for nearly half of all AP Calc AB points.

What to review (90 min)

• Critical points, increasing/decreasing intervals, concavity: be able to justify with a sign chart.
• Optimization: define variables, write the constraint, write the objective, take derivative, solve, and justify it's a max/min.
• Related rates: the standard moving-shadow / expanding-balloon / sliding-ladder setups.
• Mean Value Theorem: state both hypotheses (continuous on $[a,b]$, differentiable on $(a,b)$) — every FRQ scoring rubric demands the wording.
• Antiderivatives + u-substitution: rapid-fire. Know $\int \sec^2 x \, dx$, $\int \frac{1}{x} dx$, $\int e^{kx} dx$ instantly.

What to practice (2.5 hrs)

• 1 timed optimization FRQ.
• 1 related-rates FRQ.
• 15 no-calculator integration MCQs.

⚠️ FRQ trap: When asked to justify a max or min, you MUST cite either the First Derivative Test (sign change of $f'$) or the Second Derivative Test ($f''(c) < 0$). "Looks like a max from the graph" earns zero justification points.

Day 3: Integrals Applications + Full FRQ Practice (4 hrs)

What to review (90 min)

• Definite integrals: properties, $\int_a^a f = 0$, $\int_a^b = -\int_b^a$.
• Fundamental Theorem of Calculus (both parts): $\frac{d}{dx} \int_a^{x} f(t) \, dt = f(x)$, and $\int_a^b f'(x) \, dx = f(b) - f(a)$.
• Area between curves, volume by disks/washers, average value of a function $\frac{1}{b-a} \int_a^b f(x) \, dx$.
• Particle motion: position from velocity, velocity from acceleration, displacement vs distance traveled.
• Accumulation function problems: interpret $g(x) = \int_a^x f(t) \, dt$ from a graph.

What to practice (2.5 hrs — full timed set)

• 1 full FRQ on particle motion (every year).
• 1 full FRQ on accumulation/area-under-curve.
• 25 mixed multiple-choice (calculator + non-calculator), strictly timed.

The night before

Skim our last-minute review checklist. Get 8 hours of sleep — short-term memory consolidation is real, and a tired brain misreads $\int$ vs $\sum$.

Calculator must-knows

On the calculator section, these four functions earn easy points:

1. nDeriv(f(x), x, a) — numerical derivative at a point.
2. fnInt(f(x), x, a, b) — definite integral.
3. Graph + intersect — find where $f(x) = g(x)$ for area problems.
4. Graph + zero — find roots for critical points.

Practice these with the actual buttons tonight, not for the first time on exam day.

Common point-leaks

• Forgetting "+ C" on indefinite integrals.
• Skipping units on related-rates and accumulation problems.
• Writing the chain rule but forgetting the inner derivative.
• Using "increasing because $f' > 0$" without naming the interval.
• Failing to state MVT/IVT hypotheses verbatim on FRQs.

What this 3-day plan deliberately skips

You will not fully relearn slope fields, separation of variables, or differential equations in 3 days. If you're shaky there: skim the formulas, do 3 example problems, and accept you may lose 4-6 points on those questions. Spend the saved time mastering integrals and derivative applications instead.

Ready to start?

Open the AP Calculus AB topic library → and start with whichever Day 1 topic you're weakest on. Mix in 3-5 practice problems per topic from the worked examples. Good luck — you've got this.