Can you make sense of these three proofs of Pythagoras' Theorem?
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.
In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?
Which of these games would you play to give yourself the best possible chance of winning a prize?
This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?
Here are two games you can play. Which offers the better chance of winning?
A dot starts at the point (1,0) and turns anticlockwise. Can you estimate the height of the dot after it has turned through 45 degrees? Can you calculate its height?
Why does this fold create an angle of sixty degrees?
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
