Being resourceful

Can you match these calculations in Standard Index Form with their answers?

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

Can you see how this picture illustrates the formula for the sum of the first six cube numbers?

Can you work out the dimensions of the three cubes?

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

What is the largest number which, when divided into these five numbers in turn, leaves the same remainder each time?

Can you explain the surprising results Jo found when she calculated the difference between square numbers?

A circle of radius r touches two sides of a right angled triangle, sides x and y, and has its centre on the hypotenuse. Can you prove the formula linking x, y and r?

Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?