The assessment has been designed to take no more than 2 hours to complete. You must submit the test by 10:00 am (UK time) on 13th May. Once you start the test, it has to be completed by 2 hours.

When answering the exam you should observe normal exam conditions and must not communicate/collude with other students taking the paper. The work that you submit must be your own work. Should you encounter IT difficulties that significantly affect your ability to complete this exam or when uploading your answer(s) you may submit a PEC detailing these. 

Solve the equation  5x - 8 = 32

Multiplication and division of upper and lower bounds.

Linear combinations of $2 \times 2$ matrices. Three examples.

AEP Y1 - Engineering Mathematics Assessment 1(i)

Note that part(i) counts 20% towards the final Y1 Engineering Mathematics module grade.

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

Multiplication of $2 \times 2$ matrices.

AEP Y1 - Engineering Mathematics Assessment 1(i)

Note that part(i) counts 20% towards the final Y1 Engineering Mathematics module grade.

Q1. True/false questions about basic facts.

Q2 and Q3. Velocity-time graphs are given with areas underneath them shaded. The area of the shaded regions are given. From this, definite integrals of v ar eto be determined.

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

$A,\;B$ $2 \times 2$ matrices. Find eigenvalues and eigenvectors of both. Hence or otherwise, find $B^n$ for largish $n$.

Find the determinant of a $4 \times 4$ matrix.

Find the determinant of a $3 \times 3$ matrix.

Q1. True/false questions about basic facts.

Q2 and Q3. Velocity-time graphs are given with areas underneath them shaded. The area of the shaded regions are given. From this, changes in position, distances are to be calculated.

A randomly generated list of numbers is shown to the student. They must tick every occurrence of the lowest number. The number of occurrences isn't always the same - sometimes the minimum is unique and sometimes it is repeated. The map function makes it easy to construct a marking matrix.

A mathematical expression part whose answer is the product of two matrices, $X \times Y$.

By setting the "variable value generator" option for $X$ and $Y$ to produce random matrices, we can ensure that the order of the factors in the student's answer matters: $X \times Y \neq Y \times X$.

List all vectors in a spanning set.

(repeated 3 times)

Three 3 dim vectors, one with a parameter $\lambda$ in the third coordinate. Find value of $\lambda$ ensuring vectors coplanar. Scalar triple product.

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

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 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.

Paired t-test to see if there is a difference between times take in a task.

Arrivals given by exponential distribution, parameter $\theta$ and $Y$, sample mean on inter-arrival times. Find and calculate unbiased estimator for $\theta$.

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

Multiplication of $2 \times 2$ matrices.

Using simple substitution to find $\lim_{x \to a} bx+c$, $\lim_{x \to a} bx^2+cx+d$ and $\displaystyle \lim_{x \to a} \frac{bx+c}{dx+f}$ where $d\times a+f \neq 0$.

$A$ a $3 \times 3$ matrix. Using row operations on the augmented matrix $\left(A | I_3\right)$ reduce to $\left(I_3 | A^{-1}\right)$.

Evaluate $\int_1^{\,m}(ax ^ 2 + b x + c)^2\;dx$, $\int_0^{p}\frac{1}{x+d}\;dx,\;\int_0^\pi x \sin(qx) \;dx$, $\int_0^{r}x ^ {2}e^{t x}\;dx$

Given two sets of data, sample mean and sample standard deviation, on performance on the same task, make a decision as to whether or not the mean times differ. Population variance not given, so the t test has to be used in conjunction with the pooled sample standard deviation.

Link to use of t tables and p-values in Show steps.

Question on the exponential distribution involving a time intervals and arrivals application, finding expectation and variance. Also finding the probability that a time interval between arrivals is less than a given period. All parameters and times randomised.