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On the Road

Four vehicles travelled on a road. What can you deduce from the times that they met?

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Parabolic Patterns

The illustration shows the graphs of fifteen functions. Two of them have equations y=x^2 and y=-(x-4)^2. Find the equations of all the other graphs.

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More Parabolic Patterns

The illustration shows the graphs of twelve functions. Three of them have equations y=x^2, x=y^2 and x=-y^2+2. Find the equations of all the other graphs.

Lap Times

Age 14 to 16 Challenge Level:

Two cyclists, practising on a track, pass each other at the starting line and go at constant speeds. If you record the times each takes to complete a lap can you devise a method for finding when and where they will meet? You may like to start by supposing they take 72 seconds and 80 seconds respectively to complete a lap. Notice that with these lap times they meet for the first time at the starting line. When and where do they meet if the lap times are 70 seconds and 85 seconds? Can you find other lap times that are such that the cyclists meet exactly half way round the track.