Finding equivalent fractions, and expressing fractions in other equivalent forms.

Find centroidal moments of inertia and radius of gyration for a beam composed of  two angle sections forming a box beam.

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Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

Solving a pair of simultaneous equations of the form $a_1x+b_1y=c_1$ and $a_2 x^2+b_2y^2=c_2$ by forming a quadratic equation.

Solving a pair of simultaneous equations of the form $a_1x+y=c_1$ and $a_2x^2+b_2xy=c_2$ by forming a quadratic equation.

Solving a pair of simultaneous equations of the form $a_1xy=c_1$ and $a_2x+b_2y=c_2$ by forming a quadratic equation.

Calculate reactions and shear and bending moment at a point for an overhanging beam with a constant or uniformly varying distributed load.

Given the following three vectors $\textbf{v}_1,\;\textbf{v}_2,\;\textbf{v}_3$ Find out whether they are a linearly independent set are not. Also if linearly dependent find the relationship $\textbf{v}_{r}=p\textbf{v}_{s}+q\textbf{v}_{t}$ for suitable $r,\;s,\;t$ and integers $p,\;q$.

Given $5$ vectors in $\mathbb{R^4}$ determine if a spanning set for $\mathbb{R^4}$ or not by looking for any simple dependencies between the vectors.

Choose which of 5 matrices are in a) row echelon form but not reduced b) reduced row echelon form c) neither.

Given a 3x3 matrix with very big elements, perform row operations to find a matrix with single-digit elements. Then reduce that to an upper triangular matrix, and hence find the determinant.

Use this as a template to create Shear and Bending Moment diagram problems.   Supports concentrated forces and moments, uniformly distributed loads, and uniformly varying loads.

Some basic tasks involving vectors, including converting to/from component form, scalar product, resultant vectors.

Algebra:  Quadratic Factorisation.

              Coefficient of squared term is 1.

Straight line graph formula

Shows how to use the lpad function to format a time in HH:MM format so that leading zeros are used for numbers less than 10.

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Calculating the derivative of a function of the form $ax^n \ln(bx)$ using the product rule.

Calculating the derivative of a function of the form $\frac{(x-a)^2}{bx}$, finding its stationary points and determining their nature.

Find the derivative of a function of the form $y=a \sin(bx+c)$ using a table of derivatives.

Recoginising different forms of calculus notation.

Calculate the magnitude of a 3-dimensional vector $\mathbf v$, where $\mathbf v$ is written in the form $v_1 \mathbf i+v_2 \mathbf j + v_3 \mathbf k$.

Calculate the magnitude of a 3-dimensional vector, where $\mathbf v$ is written in the form $\pmatrix{v_1\\v_2\\v_3}$.

Calculate the magnitude of a 2-dimensional vector $\mathbf v$, where $\mathbf v$ is written in the form $v_1 \mathbf i+v_2 \mathbf j$.

Calculate the magnitude of a 2-dimensional vector, where $\mathbf v$ is written in the form $\pmatrix{v1\\v2}$.

Given the position vectors of three 2-dimensional points $A$, $B$ and $C$, find the coordinates of a fourth point $D$ such that $ABCD$ forms a parallelogram. 

Rewriting expressions of the form $n\log(a)\pm m\log(b)$ as a single logarithm.

The student is shown a circuit diagram with three logic gates. It's always in the form (a OP b) OP (b OP c).

They have to fill in a truth table for the circuit. There is a step which expands the truth table, adding a column for each of the first two gates.

Calculating the derivative of a function of the form $(ax+b)^n$ using the chain rule.