2 out of 3
Can you make sense of these three proofs of Pythagoras' Theorem?
3 out of 3
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
1 out of 3
Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.
1 out of 3
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?
1 out of 3
Which of these games would you play to give yourself the best possible chance of winning a prize?
1 out of 3
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?
1 out of 3
Here are two games you can play. Which offers the better chance of winning?
1 out of 3
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?
1 out of 3
Why does this fold create an angle of sixty degrees?
1 out of 3
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
