Prove that 3 times the sum of 3 squares is the sum of 4 squares.
Rather easier, can you prove that twice the sum of two squares
always gives the sum of two squares?
Crack this code which depends on taking pairs of letters and using
two simultaneous relations and modulus arithmetic to encode the
Given the mean and standard deviation of a set of marks, what is
the greatest number of candidates who could have scored 100%?
Scientific processes involving two variables can often be represented using equations and line graphs.
In this problem, $9$ processes, their equations and graphs have been mixed up and shown below. In each case, the two variables are represented by the letters $x$ and $y$ and the labels from the axes of the graphs have been removed.
Which can you match up? What is the interpretation of the variables $x$ and $y$ in each case?
Can you identify the physical interpretation of three key points on each of the graphs?
The numbers have been carefully chosen to represent certain time/length/unit scales for particular physical phenomena. Can you deduce the reason for the choice of any of the numbers?