Session 1: The problem-solving mindset - what are STEP and...

UCL Online STEP and AEA Preparation Sessions
Session 1: The problem-solving mindset - what are STEP and AEA?
STEP and AEA examinations test advanced mathematical thinking and problem
solving. By working through questions from STEP and AEA you learn to formulate
and solve complex problems, often by putting together ideas from different parts of
your mathematical knowledge. Being able to do this and present a well-written
solution to a problem are the kind of skills required to study university mathematics
This is the first in a series of online sessions that will help you to develop a mindset
for approaching STEP and AEA. The ideas you’ll meet in these sessions will not only
be relevant to STEP and AEA examinations but also more generally to your future
studies and for any general problem-solving you ever need to do!
To find an effective way to approach a problem often requires a willingness to
experiment and play around with the information you have been given. Looking at a
special case of the problem might be helpful. Keeping a track of your ideas and
organising your thoughts is important as is making good use of symbols, notation
and diagrams. In this session some of these ideas will be illustrated using past paper
questions. We’ll also look at how to write solutions, discuss how problems can have
many different solutions and the notion of an elegant solution.
To get you warmed up, here are some questions which are based on a recent STEP
question. These will be discussed in the first lecture.
What is the value of 1012 – 12?
What is the value of 1012 – 992?
What is the value of 5012 – 4992?
Find integers a and b such that a2 – b2 = 2000
Find integers c and d such that c2 – d2 = 1 000 000
For which positive integers n is it possible to find integers s
and t such that s2 – t2 = n ?