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Loch Ness

Draw graphs of the sine and modulus functions and explain the humps.

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The family of graphs of x^n + y^n =1 (for even n) includes the circle. Why do the graphs look more and more square as n increases?

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Complex Countdown

Play a more cerebral countdown using complex numbers.


Stage: 5 Challenge Level: Challenge Level:1

Why do this problem?
It requires an understanding of how to handle functions that are defined differently on different parts of their domains and how to interpret the situation when the derivative takes different values close to point but on opposite sides of the point.

Possible approach
A short problem that can be used as a lesson starter.

Key questions
What can you say about the function when $x< 0$?

What can you say about the function when $x> 0$?