Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.
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?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
1 + 3 + 5 + ... + (2n - 1) = n²
Use the diagram to show that any odd number is the difference of two squares.
Note that 15 = 8² - 7² as well as 4² - 1².
Write the number 105 as the difference of two squares in as many different ways as you can?
The number 1155 can be written as the difference of two squares in eight different ways, can you find them?