Use the chain rule to differentiate various functions.

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

Integrate various functions by rewriting them as partial fractions.

Questions which rely on knowledge of standard integrals.

Find the integral of an improper fraction.

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

Questions on matrix arithmetic.

Approximate the integral of a function by Riemann sums.

Questions on vector arithmetic and vector operations, including dot and cross product, as well as the vector equations of planes and lines.

Solve a system of linear equations using Gaussian elimination.

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4 questions on integrating by parts.

5 questions on using substitution to find indefinite integrals.

Implicit differentiation including finding tangents

Find eigenvalues and eigenvectors of a $2 \times 2$ matrix.

5 questions on vectors. Scalar product, angle between vectors, cross product, when are vectors perpendicular, combinations of vectors defined or not.

Find the determinants of three $2 \times 2$ invertible matrices.

Two questions on solving systems of simultaneous equations.

6 questions on standard statistical distributions.

Binomial, Poisson, Normal, Uniform, Exponential.

Find the modulus and argument of complex numbers.

Find the inverses of three $2 \times 2$ invertible matrices.

Three questions on linear combinations and products of matrices.

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