Inequalities

problem
Random inequalities

Age

16 to 18

Challenge level

Can you build a distribution with the maximum theoretical spread?
problem
Almost total inequality

Age

14 to 16

Challenge level
problem
'Tis whole

Age

14 to 18

Challenge level

Take a few whole numbers away from a triangle number. If you know the mean of the remaining numbers can you find the triangle number and which numbers were removed?
problem
Integral inequality

Age

16 to 18

Challenge level

An inequality involving integrals of squares of functions.
problem
Integral sandwich

Age

16 to 18

Challenge level

Generalise this inequality involving integrals.
problem
Squareness

Age

16 to 18

Challenge level

The family of graphs of x^n + y^n =1 (for even n) includes the circle. Why do the graphs look more and more square as n increases?
problem
Discrete trends

Age

16 to 18

Challenge level

Find the maximum value of n to the power 1/n and prove that it is a maximum.
problem
Fracmax

Age

14 to 16

Challenge level

Find the maximum value of 1/p + 1/q + 1/r where this sum is less than 1 and p, q, and r are positive integers.
problem
Thousand words

Age

16 to 18

Challenge level

Here the diagram says it all. Can you find the diagram?
problem
Climbing

Age

16 to 18

Challenge level

Sketch the graphs of y = sin x and y = tan x and some straight lines. Prove some inequalities.