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

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. 

Finding the resistance in a simple parallel RL circuit.

Finding the inductance in a simple series RL circuit.

Finding the inductive current in a simple parallel RL circuit.

Finding the current in a simple parallel RL circuit.

Finding the resistive voltage in a simple series RL circuit.

Finding the zero of a non-polynomial function

Find principal stresses by finding the eigenvalues of the matrix

Finding the arc length of a sector of a circle when given the radius of the circle and angle of the sector.

Finding the arc length of a sector of a circle when given the radius of the circle and angle of the sector.

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Homework set.  Problems require finding centroid, then Moment of Inertia about a centroidal axis.

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Collecting like terms, expanding a bracket (distributive law), substitution of values, finding factors, simplifying algebraic fractions.

Finding the area of a circle when given the diameter of the circle.

Finding the stationary points of a cubic equation and determining their nature.

Finding $x$ from a logarithmic equation of the form $\log_ax = b$, where $a$ and $b$ are positive integers.

Finding composite functions of 2 linear functions.

Finding the inverse of a function of the form $f(x)=\frac{mx+c}{x+a},\,x\neq-a$.

Calculating gradient and finding intercept from a geogebra graph.

Use Pythagoras' Theorem to find the length of a side on a right-angled triangle.

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Find a second solution to an ODE by first finding the Wronskian.

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

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix.