Content created by Newcastle University

Questions on matrix arithmetic.

Solve a linear programming problem, and perform sensitivity analysis.

Find the first few terms of the Maclaurin and Taylor series of given functions.

Questions about the limits of sequences from a first year pure maths course.

Find the integral of an improper fraction.

Find an integral by choosing a suitable substitution.

Questions which rely on knowledge of standard integrals.

Determine the optimal frequency and size of orders given information about demand and prices.

Questions on Kruskal-Wallis and Friedman tests.

Apply the Kruskal-Wallis test on some data to determine if a measurement differs between groups.

Integrate the product of two functions by the method of integration by parts.

Integrate various functions by rewriting them as partial fractions.

Find $\frac{\mathrm{d}y}{\mathrm{d}x}$ by differentiating an implicit equation.

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Use the quotient rule to differentiate various functions.

Given linear programming problems in standard form, write down the dual problem.

Use the product rule to differentiate various functions.

Use the chain rule to differentiate various functions.

Questions on differentiation from first principles, and continuity and differentiability.

For given optimisation problems, determine maximin, maximax, and minimax regret actions, expected value criteria, expected value of perfect information.

Questions on Pearson and Spearman correlation coefficients.

Questions about complex arithmetic; argument and modulus of complex numbers; complex roots of polynomials; de Moivre's theorem.