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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. 

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

Given two angles and a side-length of a triangle, use the sine rule to calculate an unknown side-length.

Rewriting a trigonometric expression of the form $A\sin(\theta)+B\cos(\theta)$ to $R\cos(\theta-\alpha)$ by calculating $R$ and $\alpha$.

Using given information to complete the equation $c= A \cos{ \left( \frac{2 \pi}{P} \left( t-H \right) \right) }+V $ that describes the concentration, $c$, of perscribed drug in a patient's drug over time, $t$. Calculating the maximum concentration and the concentration at a specific time. 

Translating prefixes into orders of magnitude, e.g. kilo = 10^(3)

Convert speeds from m/s to km/h

Using the given information to complete the equation $y= A \cos{ \left( \frac{2 \pi}{P} x  \right) }+V $ that describes an electromagnetic wave and calculating the smallest angle, $x$, for which $y=y_0$.

Simple exercise in collecting terms in different powers of \(x\)