Students are shown 4 exponential equations, and 4 graphs and asked to match them.

Students explore the relationship between length and area of a rectangle.

The perimeter of the rectangle is randomised. Students are given 11 different lengths, and asked to compute rectangle width and area for each. They are then asked to graph the function, identify it as a parabola, and estimate the maximum value.

Students are asked to find either the initial production cost, or a gradient, or the break even point from a graph.
They are then asked to determine the profit or loss from the graph for the production of a particular number of units. This number is randomised.

Students are shown a graph with 6 vertices and asked to find the length of the shortest path from A to a random vertex.

There is only one graph, but all of the weights are randomised.

They can find the length any way they wish. In the advice, the steps of Dijkstra's algorithm used in solving this problem are displayed. It is not a complete worked solution but it should be sufficient to figure out the shortest path used to reach each vertex.

Students are shown one of a disconnected graph, a tree, and a graph containing cycles. They are asked the yes/no question: "Is this a connected graph?"

This question displays one of 6 graphs and asks the yes/no question, "Does this graph contain a cycle"?

This question displays one of 10 graphs. It asks the student to either 

(a) count the vertices, or

(b) count the edges, or

(c) state how many vertices a spanning tree would contain, or

(d) state how many edges a spanning tree would contain, or

(e) state the degree of a selected (randomly chosen) vertex.

Students are shown a line graph and asked to write the line equation.

The line is drawn in geogebra. m and b are randomised. 

The line equation is given as a fill-in-the-gaps, y = <gap>x + <gap>

Students are shown a graph of the value of a machine over time. The line equation is randomised.

They are asked to evaluate value at a given time, and the time at which a given value is reached. They are asked when the machine has no value, and the range of times over which the model is valid. They are also asked to explain the physical meaning of the gradient.

Students are shown an exponential graph and asked to identify the equation from a selection of 4.

Students are shown an exponential graph and asked to identify its equation from 4 choices.

The graph is randomised.

Students are given a hyperbolic graph and asked to select the correct equation from 4 choices.

Student is shown a graph with a parabola and asked to identify the correct equation. Multiple choice question.

Students are shown a parabola and asked to identify its graph from a selection of choices.

Students are given 4 parabola equations and their respective graphs and asked to match them.

Students are given equations for a line, a parabola, a hyperbola and an exponential, and their respective graphs and are asked to match them.

Students are given 4 equations for hyperbolas and 4 graphs and asked to match them.

Students are given the equation of a hyperbola and asked to identify the hyperbolic graph out of a set of 4 graphs.

The student is shown an exponential graph and asked to evaluate the function at some given value.

They are also asked whether or not the model is valid for all real inputs, but they only give a yes/no response. The reasoning is explained in the advice but is not required from students.

Students are shown an exponential function formula and asked to identify the correct graph, given an exponential, a hyperbola, a parabola and a line.

Students are shown an exponential graph and asked to choose the correct formula for the graph.

Shows an exponential graph displaying the value of an investment under compound interest. Students have to identify the type of graph and answer 3 questions about the value of the investment from the graph.

Data from a compound interest are shown in a table. Students are asked to compute the value of an investment, and to identify the type of graph.

A question to practise the following skills in the context of Earth Sciences:

• using a data set to deduce a linear relationship
• using the graph to make predictions

A graph is drawn. A student is to identify the derivative of this graph from four other graphs. There are four such questions.

Calculating the area enclosed between a linear function and a quadratic function by integration. The limits (points of intersection) are not given in the question and must be calculated.

Given random graph of cirlce, write locus in complex form. centre in 1st quadrant

Used for LANTITE preparation (Australia). NA = Number & Algebra strand. Students are shown an infographic, and need to calculate a percentage from the information supplied. There are 7 different versions of this question.

Used for LANTITE preparation (Australia). SP = Statistics & Probability strand. Students are shown an infographic, given the details of one man and asked how many routine screenings they should have. There are seven possible questions.

This question demonstrates a few ways of interacting with a Venn diagram drawn using JSXGraph.