AP Calculus BC study plan

Compute definite integrals from the limit definition of a Riemann sum for polynomial and simple transcendental integrands

Apply the Fundamental Theorem of Calculus (both parts) to evaluate integrals and differentiate accumulation functions with variable limits

Build a one-page reference of antiderivative rules and verify each rule by differentiating it

Estimate definite integrals numerically using left, right, midpoint, and trapezoidal sums and compare error behavior

Evaluate integrals by substitution, including changing limits of integration for definite integrals

Decompose rational integrands with partial fractions and select u-substitution versus algebraic manipulation

Determine convergence of improper integrals using limit comparisons and p-integral benchmarks

Classify sequences as convergent or divergent and justify with limit laws, squeeze theorem, or growth-rate comparison

Apply all convergence tests (nth-term, geometric, p-series, integral, comparison, limit comparison, alternating, ratio, root) and state the correct hypothesis for each

Determine absolute versus conditional convergence and estimate alternating series error with the remainder bound

Construct power series for functions via differentiation, integration, and geometric-series manipulation

Compute Taylor and Maclaurin polynomials and bound the remainder with the Lagrange error term

Find intervals of convergence and radii of convergence for power series using the ratio and root tests

Represent functions as Taylor series and evaluate series at specific points to approximate function values

Apply the Mean Value Theorem and Rolle's Theorem to justify existence of values satisfying given conditions

Use the first and second derivative tests to classify critical points and locate inflection points

Sketch accurate graphs of functions from sign charts of the first and second derivatives, including asymptotes and end behavior

Solve optimization problems by constructing objective functions and verifying extrema on closed or open intervals

Set up and solve related-rates problems by differentiating constraint equations with respect to time

Apply L'Hopital's rule to indeterminate forms and connect linear approximation to local linearity

Evaluate limits algebraically, graphically, and with one-sided and infinite-limit techniques, and identify removable versus nonremovable discontinuities

State the three conditions of continuity and apply the Intermediate Value Theorem to prove existence of solutions

Differentiate from the limit definition and use derivative rules (product, quotient, chain) fluently

Differentiate implicitly and invert derivatives for inverse trigonometric and general inverse functions

Differentiate and integrate parametric equations, including arc length and slope in parametric form

Convert between polar and rectangular coordinates and compute area and arc length in polar form

Differentiate and integrate vector-valued functions and interpret velocity, speed, and acceleration vectors

Set up and evaluate area between curves, volumes of revolution (disk, washer, shell), and average value integrals

Solve separable differential equations with initial conditions and interpret slope fields qualitatively

Model exponential growth and decay and logistic growth, and solve for constants from given data

Execute a full-length timed practice exam under AP conditions and self-score using official rubrics

Target the three lowest-scoring domains from the practice exam with focused re-drilling and error analysis