AP Calculus BC 1-Month Study Plan

title: "AP Calculus BC 1-Month Study Plan" description: "A full month of AP Calculus BC prep with weekly breakdowns: 4 weeks of focused review, mixed practice, and cumulative mock exams. Build mastery, not panic." date: "2026-01-15" examDate: "May AP Exam" topics:

• 4-Week Schedule
• Weekly Breakdowns
• Cumulative Practice

You have four weeks to prepare. This plan builds cumulatively: Week 1 solidifies AB foundations, Week 2 adds BC techniques, Week 3 emphasizes series and convergence, and Week 4 refines with full-length exams and final review.

Aim for 60-90 minutes per weekday, 2-3 hours on weekends. Consistency beats cramming.

Week 1: AB Foundations (Limits through Integrals)

| Day | Topics | MCQ | Practice | Notes | |---|---|---|---|---| | Mon | Limits, continuity, IVT | 10 | 2 IVT problem setups | Single-sided limits; when IVT applies | | Tue | Derivative rules, chain rule | 12 | Chain rule on 5 composite functions | Speed over accuracy initially | | Wed | Implicit differentiation, related rates | 8 | 2 related-rates FRQ setups | Identify the changing quantities | | Thu | Optimization (application of derivatives) | 10 | 1 full optimization FRQ | Must cite First Derivative Test | | Fri | Antiderivatives, basic integration | 12 | $u$-substitution on 6 integrals | Memorize $\int e^{kx}$, $\int \frac{1}{x}$, etc. | | Sat | Area between curves, volume (disks) | 8 | 1 area FRQ + 1 volume FRQ | Units! Always include units. | | Sun | Review + Week 1 practice set | 15 MCQ | 2 mixed FRQ (any AB topic) | 90 min review total |

Week 2: AB Applications + BC Foundations (Integrals & Parametric)

| Day | Topics | MCQ | Practice | Notes | |---|---|---|---|---| | Mon | Integration by parts | 10 | 5 IBP drills; LIATE priority | Use $u = x$ on $\int x e^x dx$; $u = e^x$ on $\int e^x \cos x dx$ | | Tue | Partial fractions, improper integrals | 12 | 2 partial fraction decompositions | Check: does $\int_a^{\infty}$ converge? | | Wed | Parametric functions (intro) | 10 | Find $dy/dx$ on 4 parametric curves | Template: $\frac{dy/dt}{dx/dt}$ | | Thu | Parametric motion, speed, acceleration | 8 | 2 speed/acceleration problems | $\text{speed} = \sqrt{(dx/dt)^2 + (dy/dt)^2}$ | | Fri | Polar curves (intro) | 12 | Sketch 3 polar curves; identify symmetry | Rose curves, limaçons, spirals | | Sat | Polar area, area between curves | 8 | 2 polar area FRQ setups | $A = \frac{1}{2} \int r^2 d\theta$ | | Sun | Review + Week 2 practice set (mixed) | 20 MCQ | 2 FRQ (1 AB, 1 parametric/polar) | 90 min; assess weak topics |

Week 3: Series & Convergence (BC Specialty)

| Day | Topics | MCQ | Practice | Notes | |---|---|---|---|---| | Mon | Geometric & $p$-series | 12 | Classify 8 series (geo vs $p$ vs other) | $\sum ar^n$ vs $\sum \frac{1}{n^p}$ | | Tue | Ratio test, comparison tests | 10 | 5 series; state test + conclusion | Must name the test on FRQ | | Wed | Alternating series, error bounds | 12 | Alternating series error on 3 series | $\|R_n\| \leq a_{n+1}$ for alternating | | Thu | Maclaurin series (intro) | 10 | Write Taylor formula from derivatives | $f(x) = \sum \frac{f^{(n)}(a)}{n!}(x-a)^n$ | | Fri | Memorized Maclaurin series | 14 | Match functions to series ($e^x$, $\sin x$, etc.) | Flashcard: 5 series by heart | | Sat | Lagrange error & interval of convergence | 12 | 2 IOC problems with endpoint testing | Must test endpoints! | | Sun | Review + Week 3 practice set (series-heavy) | 22 MCQ | 2 FRQ (Taylor polynomial + IOC) | 100 min review |

Week 4: Refinement + Full Mock Exams

| Day | Topics | MCQ | Practice | Notes | |---|---|---|---|---| | Mon | Arc length (parametric & polar) | 10 | 1 parametric arc length; 1 polar arc | Often combined with area problems | | Tue | Differential equations (logistic, Euler) | 8 | Recognize logistic model; 3 Euler's method steps | Minor topic; 1-2 points max | | Wed | Catch-up day | 0 | Review flagged topics from Weeks 1-3 | Focus on your weakest area | | Thu | Full mock exam (Part A: no calc) | 28 | 90 min, 28 non-calc MCQ + 3 FRQ | Strict timing; realistic conditions | | Fri | Mock debrief + weak-topic drills | 0 | Rework 3-4 problems from Thursday | Understand why you missed them | | Sat | Full mock exam (Part B: calculator) | 17 | 50 min, 17 calc MCQ + 3 FRQ | Back-to-back with Friday prep | | Sun | Final review + night-before checklist | 0 | Skim last-minute review → | Sleep 8 hours. Rest. Trust your work. |

Weekly milestone targets

• Week 1 end: 85%+ on AB MCQ (limits, derivatives, basic integrals).
• Week 2 end: 80%+ on mixed AB + parametric/polar MCQ.
• Week 3 end: 75%+ on series/convergence MCQ (this is the hardest topic).
• Week 4, Thu-Sat: Full mock scoring 70+ (out of 108).

Common patterns to lock in by Week 2

1. FTC with chain rule: $\frac{d}{dx} \int_a^{g(x)} f(t) \, dt = f(g(x)) \cdot g'(x)$.
2. Parametric $dy/dx$: Always $\frac{dy/dt}{dx/dt}$, never $\frac{dy}{dx}$.
3. Polar area: Always $\frac{1}{2} \int r^2 \, d\theta$, not $\int r^2 \, d\theta$.
4. Speed formula: $\sqrt{(dx/dt)^2 + (dy/dt)^2}$, not $(dx/dt) + (dy/dt)$.

Common patterns to lock in by Week 4

1. Series convergence: Ratio test for $a^n$ or $n!$ in denominator; $p$-test for $\frac{1}{n^p}$; alternating test for $(-1)^n a_n$.
2. IOC endpoint testing: Every exam tests endpoints. Test them separately; convergence can differ at endpoints.
3. Lagrange error: $|R_n| \leq \frac{M|x-a|^{n+1}}{(n+1)!}$. Find $M$ on the interval, then compute the bound.
4. Integration by parts: LIATE (Logs, Inverse trig, Algebraic, Trig, Exponential). Choose $u$ as the priority item.

Feeling stuck? Browse worked examples by topic → or review FRQ templates →. You've got this. 🎯