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. 

Calculate a speed in m/s given distance and time taken, then convert that to km/hour

A graph shows both the speed and acceleration of a car. Identify which line corresponds to which measurement, and calculate the acceleration during a portion of time.