Inequalities

problem
Which is bigger?

Age

14 to 16

Challenge level

Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?
problem
Which is cheaper?

Age

14 to 16

Challenge level

When I park my car in Mathstown, there are two car parks to choose from. Can you help me to decide which one to use?
problem
Powerful order

Age

14 to 16

Challenge level

Powers of numbers might look large, but which of these is the largest...
problem
Near 10

Age

14 to 16

Challenge level

10 must remain within easy reach...
problem
Inner equality

Age

16 to 18

Challenge level

Can you solve this inequalities challenge?
problem
Unit interval

Age

16 to 18

Challenge level

Can you prove our inequality holds for all values of x and y between 0 and 1?
problem
Erratic quadratic

Age

16 to 18

Challenge level

Can you find a quadratic equation which passes close to these points?
problem
Farey neighbours

Age

16 to 18

Challenge level

Farey sequences are lists of fractions in ascending order of magnitude. Can you prove that in every Farey sequence there is a special relationship between Farey neighbours?
problem
Classical means

Age

16 to 18

Challenge level

Use the diagram to investigate the classical Pythagorean means.
problem
All-variables Sudoku

Age

11 to 18

Challenge level

The challenge is to find the values of the variables if you are to solve this Sudoku.