problem
Triathlon and fitness
Age
11 to 14
Challenge level
The triathlon is a physically gruelling challenge. Can you work out which athlete burnt the most calories?
problem
Vector walk
Age
14 to 18
Challenge level
Starting with two basic vector steps, which destinations can you reach on a vector walk?
problem
Summing geometric progressions
Age
14 to 18
Challenge level
Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?
problem
Always perfect
Age
14 to 18
Challenge level
Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.
problem
Perfectly square
Age
14 to 16
Challenge level
The sums of the squares of three related numbers is also a perfect square - can you explain why?
problem
Back fitter
Age
14 to 18
Challenge level
10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?
problem
What's that graph?
Age
14 to 18
Challenge level
Can you work out which processes are represented by the graphs?
problem
Sitting pretty
Age
14 to 16
Challenge level
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?
problem
Iff
Age
14 to 18
Challenge level
Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?
problem
Partly circles
Age
14 to 16
Challenge level
What is the same and what is different about these circle questions? What connections can you make?
problem
Bendy quad
Age
14 to 16
Challenge level
Four rods are hinged at their ends to form a convex quadrilateral.
Investigate the different shapes that the quadrilateral can take.
Be patient this problem may be slow to load.