Content created by Newcastle University

Factorise $\displaystyle{ax ^ 2 + bx + c}$ into linear factors. 

No description given

Compute tables of Hamming distances in given codes, then determine which codes are equivalent.

Using a given list of four complex numbers, find by inspection the one that is a root of a given cubic real polynomial and hence find the other roots.

Find $\displaystyle \frac{a} {b + \frac{c}{d}}$ as a single fraction in the form $\displaystyle \frac{p}{q}$ for integers $p$ and $q$.

Student is given a set of constraints for a linear program. Asked to enter the constraints as inequalities, and then to identify the optimal solution.

Problem with solving the simultaneous equations gven by the constraints - too unwieldy and not given enough marks for doing so. Best if the point of intersection is given graphically by putting the mouse over the intersection.

Multiple response question (4 correct out of 8) covering properties of convergent and divergent sequences and boundedness of sets. Selection of questions from a pool.

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

Given random set of data (between 13 and 23 numbers all less than 100), find their stem-and-leaf plot.
This version of the question asks for 10 fields to be filled rather than the full 25, although the question statement asks for 25. I am sure that the first version asked for all 25.

When are vectors $\boldsymbol{v,\;w}$ orthogonal?

Part b) is not answered in Advice, the given solution is for a different question.

Find angle between plane $\Pi_1$, given by three points, and the plane $\Pi_2$ given in Cartesian form.

The calculation of $cos(\alpha)$ at the end of Advice has fractionNumbers switched on and so the result is presented as a fraction, which can be misleading. Best if calculation is followed through without using fractionNumbers.

Gradient of $f(x,y,z)$.

Should include a warning to insert * between multiplied terms

A plane goes through three given non-collinear points in 3-space. Find the Cartesian equation of the plane in the form $ax+by+cz=d$.

There is a problem in that this equation can be multiplied by a constant and be correct. Perhaps d can be given as this makes a,b and c unique and the method of the question will give the correct solution.

Find the Cartesian form $ax+by+cz=d$ of the equation of the plane $\boldsymbol{r=r_0+\lambda a+\mu b}$.

The solution is not unique. The constant on right hand side could be given to ensure that the left hand side is unique.

Find minimum distance between a point and a line in 3-space. The line goes through a given point in the direction of a given vector.

The correct solution is given, however the accuracy of 0.001  is not enough as in some cases answers near to the correct solution are also marked as correct.

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.

No description given

Find the cosine of the angle between two pairs of 3D and 4D vectors.

The calculations and answers are correct, however the Advice should display the interim calculations of the lengths of vectors and their products to say 6dps. At present the student may be mislead into using 2dps at each stage - the instruction at the start of Advice is somewhat confusing.

A collection of true/false questions aiming to reveal misconceptions about concepts encountered in a first year pure maths course.

No description given

Cartesian form of the parametric representation of a surface, normal vector, and magnitude.

Accuracy for part c) should be made more stringent as can be marked correct for an incorrect answer. Use a different sample range rather than 0 to 1 would help as would setting accuracy to something less than 0.001.

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.

Determine the correct parametric representation of a given curve.  Curve is randomly chosen from a set of 20.

The graph of the curve was not displayed on my machine.

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.

Find a unit vector orthogonal to two others.

Uses $\wedge$ for the cross product. The interim calculations should all be displayed to enough dps, not 3,  to ensure accuracy to 3 dps. If the cross product has a negative x component then it is not explained that the negative of the cross product is taken for the unit vector.

Curl of a vector field.

Should warn that multiplied terms need * to denote multiplication.

Find all points for which the gradient of a scalar field is orthogonal to the $z$-axis.

Should warn that multiplied terms need * to denote multiplication.

Gradient of $f(x,y,z)$.

Should warn that multiplied terms need * to denote multiplication.

No description given