Understand the concept of a limit, evaluate limits analytically, numerically and graphically, and determine the continuity of functions.
Learn the derivative as the instantaneous rate of change and slope of a tangent line, apply differentiation rules, and solve problems involving motion, optimization, and related rates.
Master product, quotient, and chain rules; differentiate
polynomial, rational, trigonometric, exponential, and logarithmic functions.
Analyze graphs using first and second derivatives,
identify local and absolute extrema, and explore concavity and inflection points.
Understand definite and indefinite integrals,
antiderivatives, and the Fundamental Theorem of Calculus.
Apply substitution, integration by parts (as appropriate for
AB), and numerical approximation methods such as Riemann sums and trapezoidal
sums.
Calculate areas between curves, volumes of solids of revolution, average value of functions, and solve accumulation problems.
Solve basic separable differential equations and interpret slope fields.
Apply calculus concepts to real-world problems, interpret results, and justify conclusions.
Practice AP-style multiple-choice and free-response
questions with an emphasis on problem-solving strategies and clear mathematical
communication.
Learn limits, continuity, derivatives, and integrals with analytical, graphical, and numerical approaches.
Master differentiation, integration, and apply them to motion, optimization, graph analysis, and real-world problems.
Solve differential equations, use calculus in modeling, and prepare effectively for AP exam questions.
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