Calculus (Advanced · AP Calculus AB)

Find limits from graphs and tables, evaluate one-sided limits, determine when limits exist or don't, and apply the Squeeze Theorem.

Apply limit laws (sum, product, quotient), resolve indeterminate forms by factoring or rationalizing, evaluate trig limits (sinx/x), and use L'Hôpital's Rule.

Define continuity at a point and on an interval, classify discontinuities (removable, jump, infinite), and apply the Intermediate Value Theorem.

Evaluate limits as x→±∞, determine horizontal asymptotes, compare growth rates of polynomials, exponentials, and logarithms.

Understand the derivative as a limit of difference quotients, find equations of tangent lines, and determine where functions are differentiable.

Apply all differentiation rules fluently — power rule, product/quotient rules, chain rule, and derivatives of trigonometric, exponential, and logarithmic functions.

Differentiate implicitly for curves not expressed as y=f(x), solve related rates problems, and find derivatives of inverse trigonometric functions.

Find critical points, apply the Mean Value Theorem, use first/second derivative tests, sketch curves, and solve optimization problems.

Find antiderivatives, approximate area using left/right/midpoint Riemann sums and trapezoidal rule, and evaluate definite integrals.

Apply FTC Part 1 (derivative of an integral) and Part 2 (evaluating definite integrals using antiderivatives) to compute areas and accumulations.

Master u-substitution for indefinite and definite integrals, integrate by parts, and decompose rational functions using partial fractions.

Find area between curves, calculate volumes of solids of revolution (disk, washer, shell methods), and interpret integrals as accumulated quantities.

Sketch and interpret slope fields, solve separable differential equations, and model exponential growth/decay and logistic growth.