Given the coordinates of three 2-dimensional points $A$, $B$ and $C$, find the vectors $\vec{AB}$, $\vec{AC}$ and $\vec{CB}$.

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

Calculating a section of a sector of a circle when given the arc length and angle of the sector of the circle. This question requires the use of the formulas to find the area of a sector of a circle and to find the area of a triangle. 

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

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

Evaluating a modulus function of the form $f(x)=ax+b|x|$ for a given value of $x$.

Evaluating a modulus function of the form $f(x)=x^2+m|x|$ for a given value of $x$.

Evaluating a modulus function of the form $f(x)=c-m|x|$ for a given value of $x$.

Evaluating a modulus function of the form $f(x)=m|x|+c$ for a given value of $x$.

Evaluating a cubic function for a given value of $x$.

Evaluating a quadratic function for a given value of $t$.

Evaluating a linear function for a given value of $x$.

Evaluating composite functions involving a linear function and a modulus function of the form $f(x)=|x|+c$, for a given value of $x$.

Given an equation of the form $m=m_0 e^{-kt}$ to model the mass of a radioactive material, calculate the decay constant $k$ and the time taken for the material to reach a certain percentage of its initial mass. 

Given an equation of the form $T=T_0 e^{kt}$ to model temperature, calculate the temperature after a given time, the time taken to reach a certain temperature, and the time taken for the temperature to double.

Rewriting $\log_{10}\left(\frac{\sqrt{x}}{y}\right)$ in terms of $\log_{10}(a)$ and $\log_{10}(b)$, where $a$, $b$, $x$ and $y$ are given.

Rewriting $\log_{10}(\sqrt{x})$ in terms of $\log_{10}(a)$ and $\log_{10}(b)$, where $a$, $b$ and $x$ are given.

Rewriting $\log_{10}\left(\frac{x}{y}\right)$ in terms of $\log_{10}(a)$ and $\log_{10}(b)$, where $a$, $b$, $x$ and $y$ are given.

Given the polar coordinates of a point $P$, calculate the equivalent cartesian coordinates

Given a randomised log function select the possible ways of writing the domain of the function.

Independent events in probability. Choose whether given three given pairs of events are independent or not.

Round numbers to a given number of decimal places.

Round numbers to a given number of significant figures.

Calculate the length of a line segment given two points

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Calculating the area enclosed between a cosine function and a quadratic function by integration. The limits (points of intersection) are given in the question.

Example of an explore mode question. Student is given a 2x2 matrix and is asked to find the characteristic polynomial and eigenvalues, and then eigenvectors for each eigenvalue. The part asking for eigenvectors can be repeated as often as the student wants, to be used for different eigenvalues.

Assessed: calculating characteristic polynomial and eigenvectors.

Feature: any correct eigenvector is recognised by the marking algorithm, also multiples of the "obvious" one(s) (given the reduced row echelon form that we use to calculate them).

Randomisation: a random true/false for invertibility is created, and the eigenvalues a and b are randomised (condition: two different evalues, and a=0 iff invertibility is false), and a random invertible 2x2 matrix with determinant 1 or -1 is created (via random elementary row operations) to change base from diag(a,b) to the matrix for the question. Determinant 1 or -1 ensures that we keep integer entries.

The implementation uses linear algebra functions such as "find reduced echelon form" or "find kernel of a reduced echelon form", from the extension "linalg2".

Solving a pair of simultaneous equations of the form $y=mx+c_1$ and $y=ax^2+kx+c_2$ to find the possible values for the unknown coefficient $k$, when given the values of $m$, $a$, $c_1$ and $c_2$.