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

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

Give the cartesian coordinates of a point $P$, find the equivalent polar coordinates

Drag points on an axis to plot a linear graph (integer gradient and intercept only)

Calculate the length of a line segment given two points

Find the gradient of the line that passes through the points 

Drag points on an axis to plot a linear graph (rational gradient and intercept)

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

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

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

Finding the stationary point of a function of the form $\frac{a \ln(x)}{x}$ and determining its nature.

Calculate the functional value at a point.

Construct a line through two points in a GeoGebra worksheet. Change the line by setting the positions of the two points when the worksheet is embedded into the question.

Use two points on a line graph to calculate the gradient and $y$-intercept and hence the equation of the straight line running through both points.

The answer box for the third part plots the function which allows the student to check their answer against the graph before submitting.

This particular example has a positive gradient.

A question testing the application of the Cosine Rule when given two sides and an angle. In this question, the triangle is always obtuse and both of the given side lengths are adjacent to the given angle (which is the obtuse angle).

Find the equation of a straight line which has a given gradient $m$ and passes through the given point $(a,b)$.

Find the shear, normal force and bending moment at a point in a beam supporting a uniformly distributed load.

Homework set.  Find internal shear force, normal force, and bending moment at a designated point in a rigid body.

Calculate the moment of a force about three points using the definition of a Moment.  All forces and points are in the same plane.

Calculate the distance between two points along the surface of a sphere using the cosine rule of spherical trigonometry. Context is two places on the surface of the Earth, using latitude and longitude.

The question is randomised so that the numerical values for Latitude for A and B will be positive and different (10-25 and 40-70 degrees). As will the values for Longitude (5-25 and 50-75). The question statement specifies both points are North in latitude, but one East and one West longitude, This means that students need to deal with angles across the prime meridian, but not the equator.

Students first calculate the side of the spherical triangle in degrees, then in part b they convert the degrees to kilometers. Part a will be marked as correct if in the range true answer +-1degree, as long as the answer is given to 4 decimal places. This allows for students to make the mistake of rounding too much during the calculation steps.

Students are given an exponential equation and asked to evaluate it at two points.

The constants in the exponential are randomised.

Given one point and the gradient determine the equation of the line.

Used for LANTITE preparation (Australia). MG = Measurement & Geometry strand. NC = Non Calculator. The start time for Period 1 (randomised) and the end time for Period 2 (randomised) are given, and students are asked to find the middle of those two times. 

This question defines an otherwise-pointless pre-submit task of "wait for a while" before marking the student's answer, in order to demonstrate how to use the pre-submit tasks feature.

Use two points on a line graph to calculate the gradient and $y$-intercept and hence the equation of the straight line running through both points.

The answer box for the third part plots the function which allows the student to check their answer against the graph before submitting.

This particular example has a positive gradient.

Implicit differentiation.

Given $x^2+y^2+dxy +ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$.

Also find two points on the curve where $x=0$ and find the equation of the tangent at those points.

Students are given an exponential equation and asked to evaluate it at two points.

The constants in the exponential are randomised.

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

Missing: Application with bacteria, turning points, difficult chain rule