Or search by topic
Sketch the graph of the function $\text{h}$, where:
$$ \text{h}(x) = \frac {\ln x} x, \quad (x>0) $$
Hence, or otherwise, find all pairs of distinct positive integers $m$ and $n$ which satisfy the equation:$$n^m=m^n $$
STEP Mathematics I, 1988, Q1. Question reproduced by kind permission of Cambridge Assessment Group Archives. The question remains Copyright University of Cambridge Local Examinations Syndicate ("UCLES"), All rights reserved.
Can you find a three digit number which is equal to the sum of the hundreds digit, the square of the tens digit and the cube of the units digit?
How many numbers are there less than $n$ which have no common factors with $n$?
Frosty the Snowman is melting. Can you use your knowledge of differential equations to find out how his volume changes as he shrinks?