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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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### Summing geometric progressions

Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?

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### Expenses

What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?

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### Why 24?

Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.

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### Areas of parallelograms

Can you find the area of a parallelogram defined by two vectors?

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### Tangled Trig Graphs

Can you work out the equations of the trig graphs I used to make my pattern?