AP Calculus AB study plan

Evaluate limits graphically, numerically, and algebraically, including one-sided and infinite limits

Identify and classify discontinuities (removable, jump, infinite) from equations and piecewise definitions

State and apply the Intermediate Value Theorem to justify existence of roots

Sketch a function satisfying given limit and continuity conditions

Connect the limit definition of the derivative to difference quotients and estimate derivatives numerically

Compute derivatives of polynomials, exponentials, logs, and trig functions using shortcut rules

Apply the product and quotient rules fluently without sign errors

Relate differentiability to continuity and identify points of non-differentiability

Differentiate composite functions with the chain rule, including nested and trig compositions

Use implicit differentiation to find slopes on curves defined implicitly

Differentiate inverse functions, including inverse trig, using the inverse-function derivative formula

Apply logarithmic differentiation to complicated products and powers

Solve related-rates problems by identifying given and unknown rates and writing a relating equation

Set up and interpret rectilinear motion problems using position, velocity, and acceleration

Use linear approximation and differentials to estimate function values

Apply the Mean Value Theorem and Rolle's Theorem to justify conclusions on intervals

Find critical points and use sign charts to determine intervals of increase and decrease

Apply the first and second derivative tests to classify local extrema

Determine concavity and locate inflection points

Solve applied optimization problems and justify global extrema on closed intervals

Evaluate definite integrals as limits of Riemann sums and interpret them as net accumulation

Apply the Fundamental Theorem of Calculus to evaluate definite integrals exactly

Compute antiderivatives including u-substitution for indefinite and definite integrals

Use properties of integrals and the accumulation function to analyze area and change

Solve separable differential equations and find particular solutions from initial conditions

Interpret slope fields and sketch solution curves qualitatively

Set up and evaluate integrals for area between curves

Apply accumulation to volume of solids of revolution using disk and washer methods

Complete two full-length timed practice exams under test conditions

Classify every missed problem by domain and error type (concept, algebra, setup, time)

Re-solve all missed problems from scratch without notes

Memorize and self-quiz the full formula and theorem sheet