AP Calculus BC 1-Month Study Plan

A structured 4-week plan that builds mastery without burning out.

⏱️ ~60 hours total over 4 weeks∬ AP Calculus BC

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

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

Common patterns to lock in by Week 4

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

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