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On the Road

Four vehicles travelled on a road with constant velocities. The car overtook the scooter at 12 o'clock, then met the bike at 14.00 and the motorcycle at 16.00. The motorcycle met the scooter at 17.00 then it overtook the bike at 18.00. At what time did the bike and the scooter meet?

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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.

Alison's Mapping

Stage: 4 Challenge Level: Challenge Level:1

Before starting to explore Alison's mapping, you might want to watch a short video explaining how to use the NRICH Number Plumber.

This text is usually replaced by the Flash movie.

Alison has created a mapping which you can access by clicking on the picture below. The initial challenge is to figure out what Alison's mappings do. You can drop some numbers into the mappings, and see what comes out.

Test your ideas by predicting the outputs for some different inputs.
Only reveal the hidden parts of the mapping once you are certain you know what is going on.
Can you find an input which gives the same output for both mappings?

Click on the picture to explore Alison's mappings.

As you explore Alison's mappings, you will notice points appearing on the graph. The input number is the x coordinate, and the output number is the y coordinate.
Create some other function machines using the NRICH Number Plumber, and observe the outcomes on the graph.

Mathematicians like to ask themselves questions about what they notice.
What possible questions could you ask?

These questions may lead you to make conjectures - something which you believe to be true but need to investigate further in order to convince yourself.