Given 3 vectors $\mathbf a$, $\mathbf b$ and $\mathbf c$, find the constants $p$, $q$ and $k$ such that $ p\mathbf a + q \mathbf b = \mathbf c$, where $k$ is an unknown component of $\mathbf c$ .

Given 3 vectors $\mathbf v$, $\mathbf a$ and $\mathbf b$, find the constants $c_1$ and $c_2$ such that $\mathbf v = c_1 \mathbf a + c_2 \mathbf b$ .

Rounding integers and decimals to a specific number of sig figs.

Inequality involving a single absolute value, question solution uses the piecewise nature of the absolute value function.

Solving inequalities that involve a quadratic and where the right-hand side is 0.

Solving inequalities that involve a quadratic and where the right-hand side is not 0. 

Randomly chooses one of the following

a) Divide numerical fractions. Simplifying is discussed in the advice but not required to get full marks.

b) Divide a negative whole number by a fraction. Simplifying is discussed in the advice but not required to get full marks.

Randomly chooses one of the following

a) Multiply numerical fractions. Simplifying is discussed in the advice but not required to get full marks.

b) Multiply a negative fraction by a whole number. Simplifying is discussed in the advice but not required to get full marks.

Fractions already have a common denominator. Addition and subtraction 50:50 split, when subtracting, the answer is negative half the time. Students shouldn't have to worry about reducing fractions by design.

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Find the number of people with heights greater then mean plus two times the standard deviation.

This question uses a Geogebra applet to solve a linear program with two variables using the graphical method. It contains three steps:

1. Construct the feasible area (polygon) by adding the constraints one by one. The students can see what happens when the constraints are added.
2. Add the objective function, and the level set of the objective value is shown, as well as its (normalised) gradient.
3. Compute the optimal solution by moving the level set of the objective around.

The full list of questions to choose from to build a bespoke Skills Audit for Maths and Stats

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Skills Audit for Maths and Stats for MAS156 Aerospace Engineering, Electrical and Eletronic Engineering, and Electronics and Computing Engineering students. 

Skills Audit for Maths and Stats for MAS156 Aerospace Engineering students. 

Skills Audit for Maths and Stats for MAS153 Materials Science students.

Skills Audit for Maths and Stats for MAS156 Aerospace Engineering students. 

Skills Audit for Maths and Stats for MAS140 Chemical and Biological Engineering.

Skills Audit for Maths and Stats for CIV109 Civil and Structural Engineering.