AP Calculus guides
Free, clear guides to AP Calculus: topics, equations, exam technique and revision plans.
- AP Calculus AB vs BC: which should you take?AP Calculus AB vs BC compared: what each course covers, how the exams work, how hard BC is and how to choose.
- AP Calculus AB units, explainedAll eight AP Calculus AB units explained in plain English, plus the two extra units in AP Calculus BC and how to study each one.
- AP Calculus formula sheet: what to memoriseThere is no formula sheet in the AP Calculus AB or BC exam. Here are the derivatives, integrals, theorems and BC formulas to memorise.
- AP Calculus AB review and study planAn AP Calculus AB review plan: what to revise in each unit, free-response tips, calculator skills and a plan for the final weeks.
- AP Calculus BC units, explainedAll ten AP Calculus BC units explained, including the BC-only topics, what to focus on and how to prepare for the exam.
- AP Calculus BC series, made clearAP Calculus BC series made clear: sequences, convergence tests, Taylor and Maclaurin series, radius of convergence and error bounds.
- Related rates in AP CalculusRelated rates in AP Calculus made clear: a step-by-step method, worked examples with ladders and cones, and the mistakes to avoid.
- AP Calculus derivative rulesEvery derivative rule you need for AP Calculus AB and BC: power, product, quotient and chain rules, trig, exponential, log and inverse functions.
- Arc length, explained with examplesArc length explained for AP Calculus BC: the formula for y = f(x) and parametric curves, speed and total distance, worked examples and practice with answers.
- The chain rule, explained with examplesThe chain rule explained step by step: the formula, spotting the inner and outer function, examples with powers, trig, exponentials and logs, plus practice.
- Euler's method, explained with examplesEuler's method explained for AP Calculus BC: the formula, a step-by-step table, over- or underestimates from concavity, and step size, with practice.
- Derivatives of exponentials and logarithmsDerivatives of e^x, ln x, a^x and log base b explained: proofs, chain rule cases like ln(f(x)) and logarithmic differentiation, with practice and answers.
- The fundamental theorem of calculus, explainedThe fundamental theorem of calculus explained: Part 1 and Part 2, derivatives of accumulation functions, net change and AP-style questions, with practice.
- Implicit differentiation, explained with examplesImplicit differentiation explained: why it works, a four-step method, examples with circles, products and trig, tangent lines and second derivatives.
- Improper integrals, explained with examplesImproper integrals explained for AP Calculus BC: infinite limits and discontinuities, convergence and divergence, the p-integral rule, with worked examples.
- Critical points, inflection points and the derivative testsInflection points, concavity and the first and second derivative tests explained for AP Calculus, with absolute extrema, justifications and practice.
- Integration by parts, explained with examplesIntegration by parts explained: the formula, choosing u with LIATE, worked examples with ln x and e^x sin x, definite integrals and the tabular method.
- The intermediate value theorem, explainedThe intermediate value theorem explained for AP Calculus: what it says, why continuity matters, showing a root exists, and writing a full-credit justification.
- L'Hôpital's rule, explained with examplesL'Hôpital's rule explained: the conditions, 0/0 and ∞/∞ limits, other indeterminate forms, and how to justify it on AP free-response, with practice.
- Limits in calculus, explained with examplesLimits explained for AP Calculus: one-sided limits, substitution, factoring, rationalising, limits at infinity, the squeeze theorem and continuity.
- Linear approximation, explained with examplesLinear approximation explained for AP Calculus: local linearity, the tangent line formula, estimates, over- or underestimates and differentials, with practice.
- Logistic growth, explained with examplesLogistic growth explained for AP Calculus BC: the logistic differential equation, carrying capacity, fastest growth at L/2 and the solution, with practice.
- The mean value theorem, explained with examplesThe mean value theorem explained: what it says, the conditions, Rolle's theorem, how it compares with the IVT and EVT, and AP-style examples with answers.
- Polar coordinates, explained for AP Calculus BCPolar coordinates explained for AP Calculus BC: converting to Cartesian, common polar curves, dy/dx, and area inside and between polar curves, with practice.
- The product rule and quotient rule, explainedThe product rule and quotient rule explained: the formulas, where they come from, when to rewrite instead, combining with the chain rule, with practice.
- Riemann sums, explained with examplesRiemann sums explained for AP Calculus: left, right and midpoint sums, the trapezoidal rule, over- and underestimates and sums from tables, with practice.
- U-substitution, explained with examplesU-substitution explained for AP Calculus and A level Maths: when to use it, choosing u, the step-by-step method and changing limits, with practice.
- Volumes of revolution, explained with examplesVolumes of revolution explained for AP Calculus: disc and washer methods, rotating about any axis, known cross-sections and setting up the integral.