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Can you deduce which Olympic athletics events are represented by the graphs?

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.

Can you find sets of sloping lines that enclose a square?

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its vertical and horizontal movement at each stage.

On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?

Can you find the area between this graph and the x-axis, between x=3 and x=7?

Can you solve the clues to find out who's who on the friendship graph?

Can you draw the graph of $y=x$ after it has been rotated $90$ degrees clockwise about $(1,1)$?

Who's closest to the correct number of sweets in a jar - an individual guess or the average of many individuals' guesses? Which average?

Which of these graphs could be the graph showing the circumference of a circle in terms of its diameter ?

Can you sketch graphs to show how the height of water changes in different containers as they are filled?

How could you use this graph to work out the weight of a single sheet of paper?

The graph represents a salesman’s area of activity with the shops that the salesman must visit each day. What route around the shops has the minimum total distance?

Make your own pinhole camera for safe observation of the sun, and find out how it works.

The water is being drained from a pool. After how long will the depth of the pool be 144 cm?

A Hamiltonian circuit is a continuous path in a graph that passes through each of the vertices exactly once and returns to the start. How many Hamiltonian circuits can you find in these graphs?

What proportion of people make 90% confident guesses which actually contain the correct answer?

This task requires learners to explain and help others, asking and answering questions.

Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.

This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.

You may like to read the article on Morse code before attempting this question. Morse's letter analysis was done over 150 years ago, so might there be a better allocation of symbols today?