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##### Age 14 to 18 Challenge Level:

Learn how solving inverse problems can save lives in this article from Plus Magazine.

##### Age 14 to 18 Challenge Level:

Learn about algorithms for solving optimisation problems in this article from Plus Magazine.

##### Age 16 to 18 Challenge Level:

What happens to areas under the graph of $\frac{1}{x}$ when they are stretched?

##### Age 16 to 18 Challenge Level:

What different ways can you find to calculate these integrals?

##### Age 16 to 18 Challenge Level:

Can you find the gradient function of $\sin 3x$. How did you convince yourself?

##### Age 16 to 18 Challenge Level:

Can you find the definite integral of a transformed function?

##### Age 16 to 18 Challenge Level:

Can you work out the equation of the function from its graph?

##### Age 16 to 18 Challenge Level:

By considering a point on a unit circle, can you use geometry to find the derivatives of $\sin x$ and $\cos x$?

##### Age 16 to 18 Challenge Level:

How are $\sin x$, $\cos x$ and $\tan x$ related to each other? Can you make sense of the the 'slices'?

##### Age 14 to 18 Challenge Level:

Can you prove an algebraic statement using geometric reasoning?

##### Age 16 to 18 Challenge Level:

Which of the sketches matches the function given?

##### Age 16 to 18 Challenge Level:

Can you match all the different trig functions to their graphs?

##### Age 16 to 18 Challenge Level:

Can you sketch the graphs of these two reciprocal functions? What are the links between them?

##### Age 16 to 18 Challenge Level:

What happens when you combine functions? Can you sketch the results?

##### Age 7 to 14 Challenge Level:

Can you beat the clock to the midnight hour?

##### Age 5 to 14 Challenge Level:

Can you always reach the exit first and escape the vortex?

##### Age 5 to 14 Challenge Level:

Try this slightly more challenging version of Driplets and see if you can find a winning strategy.

##### Age 5 to 11 Challenge Level:

This game follows on from Last Bead. Can you find a way to take the last drip or drips?

##### Age 5 to 11 Challenge Level:

Take turns to remove a bead from the string. Can you find a way to play so that you will always win?

##### Age 5 to 11 Challenge Level:

Can you be the player to take the last counter?

##### Age 16 to 18 Challenge Level:

Can you fill in all the missing values and trig functions to make the tables complete?

##### Age 16 to 18 Challenge Level:

Can you compose four functions to create the set of functions given?

##### Age 16 to 18 Challenge Level:

Can you find functions with the desired properties to fill in the table?