Quick reference

Every chapter's objectives in one place. Use it to find where you are: scan for the first row you cannot honestly claim, and start there.

limits

Chapter	You should be able to	Standard
What a limit is	State what it means for a limit to exist Distinguish the limit at a point from the value at that point Use one-sided limits to show a limit does not exist Read a limit off a graph and off a table	`none`
Computing limits	Evaluate a limit by direct substitution and say when that is legal Resolve a 0/0 form by factoring or by rationalising Recognise the standard limits that no algebra will produce Choose the right technique from the shape of the expression	`none`
Continuity	State the three conditions for continuity at a point Classify a discontinuity as removable, jump, or infinite Choose a constant that makes a piecewise function continuous Apply the Intermediate Value Theorem, and say what it does not promise	`none`
Limits at infinity	Evaluate a limit as x grows without bound Find horizontal asymptotes by comparing degrees Distinguish a vertical asymptote from a hole Rank the growth rates that decide every such limit	`none`

differentiation

Chapter	You should be able to	Standard
The derivative	Write the difference quotient for a function at a point Explain why the limit is needed and what goes wrong without it Compute a derivative from the definition, not the rules Say where a function fails to be differentiable, and why	`none`
The rules	Differentiate powers, including negative and fractional exponents Apply the product and quotient rules correctly Recognise when a rule does not apply Differentiate the standard functions from memory	`none`
Chain rule	Identify the outer and inner function in a composition Differentiate nested compositions correctly Explain why the inner derivative appears as a factor Recognise a composition disguised as something simpler	`none`

applications-of-derivatives

Chapter	You should be able to	Standard
Related rates	Set up a related-rates problem from a geometric relationship Differentiate an equation implicitly with respect to time Know why numbers must be substituted only after differentiating Interpret the sign of a rate	`none`
Implicit	Differentiate an equation implicitly and solve for dy/dx Explain why every y produces a dy/dx factor Find the tangent line to an implicitly defined curve Derive the derivative of an inverse function	`none`

contextual-applications

Chapter	You should be able to	Standard
Motion and rates	Interpret a derivative in context, with units Analyse rectilinear motion from a position function Distinguish displacement from total distance Apply L'Hôpital's rule and know when it does not apply	`none`

analytical-applications

Chapter	You should be able to	Standard
Extrema and shape	Find critical points and classify them Use the first and second derivative tests, and know when each fails Locate inflection points and relate them to concavity Apply the Extreme Value Theorem on a closed interval	`none`

integration

Chapter	You should be able to	Standard
The definite integral	Express an area as a Riemann sum and then as an integral Compare left, right, midpoint and trapezoid approximations Say which rules over- and under-estimate, and why Interpret a definite integral as accumulated change	`none`
The FTC	State both parts of the Fundamental Theorem Evaluate a definite integral using an antiderivative Differentiate a function defined by an integral, including with the chain rule Explain why the theorem is true, not just what it says	`none`
Substitution	Recognise an integrand that is a chain rule derivative Carry out a u-substitution, including changing the limits Choose u when several candidates present themselves Say why a substitution sometimes fails	`none`

differential-equations

Chapter	You should be able to	Standard
Differential equations	Verify that a function solves a differential equation Solve a separable equation and apply an initial condition Model exponential and logistic growth Read a solution curve off a slope field	`none`

applications-of-integration

Chapter	You should be able to	Standard
Area and volume	Find the area between two curves Compute a volume by discs, washers, or known cross-sections Choose the variable of integration deliberately Recognise the one procedure underneath all of them	`none`

parametric-and-polar

Chapter	You should be able to	Standard
Parametric and polar	Find dy/dx for a parametric curve Compute arc length and speed from a parametrisation Convert between polar and Cartesian, and find polar area Treat a vector-valued function as a position over time	`none`

series

Chapter	You should be able to	Standard
Convergence	Distinguish a sequence from a series Apply the nth-term test and say what it cannot do Recognise and sum a geometric series Choose an appropriate convergence test	`none`
Taylor series	Construct a Taylor polynomial from derivatives at a point Recognise the four standard Maclaurin series Explain what the radius of convergence means Use a series to evaluate an otherwise impossible integral	`none`