Being curious

Which has the greatest area, a circle or a square, inscribed in an isosceles right angle triangle?

A napkin is folded so that a corner coincides with the midpoint of an opposite edge. Investigate the three triangles formed.

A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

If a sum invested gains 10% each year how long before it has doubled its value?

Explore the relationships between different paper sizes.

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.

Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?

Can you work out which spinners were used to generate the frequency charts?

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

Infographics are a powerful way of communicating statistical information. Can you come up with your own?