Write 100 as the sum of two positive integers, one divisible by 7 and the other divisible by 11.
Then find formulas giving all the solutions to
7x + 11y = 100
where x and y are integers.
Rotate a copy of the trapezium about the centre of the longest side
of the blue triangle to make a square. Find the area of the square
and then derive a formula for the area of the trapezium.
Prove that if the integer n is divisible by 4 then it can be written as the difference of two squares.
The heptathlon is an athletics competition consisting of 7 events:
The values for a, b, and c in each event are given below:
In the table below are the best times and distances of an Olympic hopeful in training, as well as the World Records for each heptathlon event (as of April 2011).