Reasoning, convincing and proving
problem
The london eye
Age
14 to 16
Challenge level
The 80 spokes of The London Eye are made from 4 miles of cable. What is the approximate circumference of the wheel?
problem
Would you like a jelly baby?
Age
11 to 14
Challenge level
What is the smallest number of jelly babies Tom must take, to be certain that he gets at least one of each flavour?
problem
Magical products
Age
11 to 14
Challenge level
Can you place the nine cards onto a 3x3 grid such that every row, column and diagonal has a product of 1?
problem
To run or not to run?
Age
11 to 14
Challenge level
If an athlete takes 10 minutes longer to walk, run and cycle three miles than he does to cycle all three miles, how long does it take him?
problem
Interpolating polynomials
Age
16 to 18
Challenge level
Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.
problem
Particularly general
Age
16 to 18
Challenge level
By proving these particular identities, prove the existence of general cases.
problem
Polynomial interpolation
Age
16 to 18
Challenge level
Can you fit polynomials through these points?
problem
Advent calendar 2011 - secondary
Age
11 to 18
Challenge level
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
problem
Calculating with cosines
Age
14 to 18
Challenge level
If I tell you two sides of a right-angled triangle, you can easily work out the third. But what if the angle between the two sides is not a right angle?