Given three vectors with integer components, find the corresponding magnitude and direction.

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Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Find the determinant and inverse of three $2 \times 2$ invertible matrices.

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

Find the integral of an improper fraction.

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

5 questions on using substitution to find indefinite integrals.

Implicit differentiation including finding tangents

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

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

Find the modulus and argument of complex numbers.

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

5 questions on definite integrals - integrate polynomials, trig functions and exponentials; find the area under a graph; find volumes of revolution.

5 questions on finding local and global maxima and minima on compact intervals and on the real line for differentiable functions.

5 questions on using substitution to find indefinite integrals.

Use a given factor of a polynomial to find the full factorisation of the polynomial through long division.

Given a factor of a cubic polynomial, factorise it fully by first dividing by the given factor, then factorising the remaining quadratic.

Finding the lengths and angles within a right-angled triangle using: pythagoras theorem, SOHCAHTOA and principle of angles adding up to 180 degrees.

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This question tests the student's knowledge of the remainder theorem and the ways in which it can be applied.

Finding x and y values for straight line graphs

Given the graph of the line determine the equation of the line.

Find the lowest common multiple and highest common factors of given numbers. Also a question on identifying prime numbers.

Curl and divergence of a vector field.  Determine whether the vector field is irrotational or solenoidal.

Find the solution of a first order separable differential equation of the form $axyy'=b+y^2$.

Find the common ratio of a given geometric sequence, write down the formula for the nth term and use it to calculate a given term in the sequence.

Find the equation of a straight line which has a given slope or gradient $m$ and passes through the given point $(a,b)$.

There is a video in Show steps which goes through a similar example.

Using trig identities to find solutions to equations