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Real(ly) Numbers

If x, y and z are real numbers such that: x + y + z = 5 and xy + yz + zx = 3. What is the largest value that any of the numbers can have?

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How Many Solutions?

Find all the solutions to the this equation.

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On the Road

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

More Parabolic Patterns

Stage: 4 and 5 Challenge Level: Challenge Level:1

This is another inverse problem. If you were given the equations and asked to draw the graphs then graphing software would do the work for you. This challenge is posed the opposite way round. You have to use mathematical reasoning to deduce the equations of the graphs in the illustration. Then you can use graphing software to check to see if your reasoning was correct.


You can read about one teacher's experience of using this task in the classroom.