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Can you sketch graphs to show how the height of water changes in different containers as they are filled?

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

Is it possible to find the angles in this rather special isosceles triangle?

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

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

Get into the exponential distribution through an exploration of its pdf.

Can you find the solution to this algebraic inequality?

Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?

In a right-angled tetrahedron prove that the sum of the squares of the areas of the 3 faces in mutually perpendicular planes equals the square of the area of the sloping face. A generalisation of Pythagoras' Theorem.

It is impossible to trisect an angle using only ruler and compasses but it can be done using a carpenter's square.