Given vectors $\boldsymbol{A,\;B}$, find $\boldsymbol{A\times B}$

Given a pair of 3D position vectors, find the vector equation of the line through both.  Find two such lines and their point of intersection.

Given two 3 dim vectors, find vector equation of line through one vector in the direction of another. Find two such lines and their point of intersection.

Find the stationary points of the function: $f(x,y)=a x ^ 3 + b x ^ 2 y + c y ^ 2 x + dy$ by choosing from a list of points.

Inputting the values given into the partial derivatives to see if 0 is obtained is tedious! Could ask for the factorisation of equation 1 as the solution uses this. However there is a problem in asking for the input of the stationary points - order of input and also giving that there is two stationary points.

Find all words with given Hamming distance from a given codeword.

Given a set of vectors, find a basis which generates their span as a subspace of $\mathbb{Z}_n$.

Given a matrix in the field $\mathbb{Z}_n$. By reducing it to row-echelon form (or otherwise), find a basis for the row space of the matrix, as a list of vectors.

Given a set of codewords generating a code, write down a generator matrix, encode three data vectors, and decode one codeword.

Given a set of codewords generating a code, give a generating matrix, encode three data vectors, and decode one codeword.

Given a set of codewords generating a code, give a generating matrix, encode three data vectors, and decode one codeword.

Compute the minimum distance between codewords of a code, given a parity check matrix.

Unit normal vector to a surface, given in Cartesian form.

Intersection points, tangent vectors, angles between pairs of curves, given in parametric form.

Find the unit vector parallel to a given vector.

Interim calculations in Advice should be presented in enough accuracy to ensure that the final calculations are to 3dps.

Although the statement has 4 power stations and 3 pits, when the question is run sometimes 3 power stations are given and sometimes 4 pits.

Minitab was used to fit both an AR(1) model and an AR(2) to a stationary series. A  table is given summarising the results obtained from Minitab. Choose the most appropriate model and make a forecast based on that model.

Approximating integral of a quadratic by Riemann sums . Includes an interactive graph in Advice showing the approximations given by the upper and lower sums and how they vary as we increase the number of intervals.

Approximating integral of a quadratic by Riemann sums . Will include an interactive graph in Advice showing the approximations given by the upper and lower sums and how they vary as we increase the number of intervals.

Find a regression equation given 12 months data on temperature and sales of a drink. 

No description given

Given mean and sd of 1000 sample returns on a scale of 1 to 7 together with a given score, find the z-score.

Also find the 95% confidence interval for the population mean.

Minitab was used to fit an AR(1) model to a stationary time series. Given the output answer the following questions about the model and use the model to make forecasts.

Given data on population mean and population standard deviation and three sampling sizes, calculate the probabilities that the sample means are within a specified distance from the population mean.

A graphical approach to aiding students in writing down a formal proof of discontinuity of a function at a given point.

Uses JSXgraph to sketch the graphs and involves some interaction/experimentation by students in finding appropriate intervals.

For a sample of size n from a normal distribution and given the mean of the sample and the standard deviation of the distribution, find the MLE for the mean. Also the expected information and a confidence interval for the mean.

For a sample of size n from a Poisson distribution $\operatorname{Poisson}(\lambda)$ and given the mean of the sample, find the MLE for $\lambda$. Also find the expected information and a confidence interval for $\lambda$.

For a sample of size n from an Exponential distribution $\operatorname{Exponential}(\lambda)$  and given the mean of the sample, find the MLE for $\lambda$. Also find the expected information and a confidence interval for $\lambda$.

For a sample of size n from a normal distribution, given mean of the sample mean and the standard deviation , find the t-statistic corresponding to a null hypothesis $\mu=m$ and a given confidence level. Check if the result is significant at this level.

Given a linear combination $Y$ of three independent random variables with given means and variances, find the mean of variance of $Y$.

Given a discrete random variable $X$ find the expectation of $1/X$ and $e^X$.