Working systematically

This problem explores the biology behind Rudolph's glowing red nose, and introduces the real life phenomena of bacterial quorum sensing.

Exponential functions grow pretty quickly...

Given the mean and standard deviation of a set of marks, what is the greatest number of candidates who could have scored 100%?

Build series for the sine and cosine functions by adding one term at a time, alternately making the approximation too big then too small but getting ever closer.

Can you crack these very difficult challenge ciphers? How might you systematise the cracking of unknown ciphers?

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.