How to beat your maths and stats exams
Part 2. During the exam
This guide follows on from Part 1, “Before the exam”. You’ve done your revision, and you know your
subject. How do you make it easy for the examiners to give you the credit you deserve?
Good (and bad) exam technique
Let’s start with some good advice.
Start by looking over the paper and deciding which questions will be the easiest. Then tackle these
first and get some marks in the bank. You might not have time later...
If you get stuck then move on to the next question, leaving a bit of space in your answer book, and
return to it later — don’t spend 45 minutes puzzling over one piece of algebra.
Prioritise your effort. It’s better to answer five questions well than six questions badly — there are
no bonus marks for completing everything.
Look at the marks (if they’re given) and assess the likely length of answers accordingly. Four marks
are unlikely to require four pages of working if you’re doing it efficiently.
Read each question carefully; don’t just skim it for key words. Look out for the following phrases.
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If a question states “Hence show that” then the previous result or piece of bookwork must
be used. Note that this is often the “unseen” element of the question and may require a
clever argument.
If a question states “Hence, or otherwise, show that” then you may use some other
method, but using the previous part of the question is often the most efficient way to
proceed.
“Use method X”. The examiner is testing your knowledge of method X, so there’s no point in
using method Y. If the question tells you to find the vertex of a parabola by completing the
square, there’s no point finding it using calculus.
“Show that X=Y.” Method is key here, so every step of your working should be clearly
stated. Never fudge your working so the correct expression magically appears. This will just
annoy the marker, whereas admitting you’re stuck shows you know what was meant to
happen.
Explain what you’re doing: argument is important (especially in later years), not just calculations.
Use words as well as symbols, e.g. “Let   xt b . It follows that...”
Check your intermediate steps and simplify if possible — this helps you avoid wasting time up blind
alleys. At degree level, unlike school, it’s often impossible to “carry through” an error — errors often
make the questions either trivial or impossible.
Make sure you’ve answered exactly the question that was asked. For example, if asked for the
particular solution of a differential equation with given BCs, don’t just stop at the general solution.
In multiple-choice questions especially, small errors can lose a lot of marks; the “distractors” (wrong
answers) in MCQs are often obtained by making common mistakes in the working. With such a high
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premium on accuracy, it’s especially important to check and double-check, even at the expense of
missing out a question or two.
Now, a couple of really bad ideas, which are worth avoiding if you can.
Leaving early. You never know when inspiration might strike! Also, you can almost always use the
spare time to check or clarify your answers, earning a few more crucial marks.
Rushing to tackle all the questions in sequence — see the comments above and below.
What examiners are looking for
Typically, examiners are looking for the following.
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Evidence that the students know what they’re doing — not just half-recalled templates.
Accurately stated “bookwork” (definitions, theorems, proofs etc.)
Logical links between statements and indications of strategy — not disconnected lines of
algebra. (Lecture examples should be a decent model here.)
We also typically expect competence in algebra, calculus etc. — lack of fluency can derail solutions
completely, so make sure you stay in practice with this basic stuff.
Let’s also explode a few myths...
The final answer isn’t where the marks are won. We want to see you explain why this is the answer;
your working is the main part of your solution, and it has to make sense to us as well as to you. The
“number at the end” is often the least interesting part of the process, with the fewest marks
attached.
Scatter-gun approaches don’t work. If you write down ten statements at random, of which only
three are relevant and correct, you’re unlikely to get credit for these three, because the evidence of
understanding isn’t there.
Marks are not a universal currency — one mark can and will correspond to different amounts of
work in different questions and different papers. (However, they should be comparable orders of
magnitude; see above.)
Exams are designed so that a student who has revised properly and understands the material should
be able to pass, i.e. to achieve over 40%. (This doesn’t mean you should aim to scrape a pass,
though! If you’re smart enough to aim accurately for 40%, you’re smart enough to do a lot better
than this.) On the other hand, to complete every question perfectly within the time you really have
to know exactly what you’re doing: 100% is a very rare mark. So you may well be better pacing
yourself to complete five questions out of six in the time available — see the advice above.
Examiners aren’t trying to catch you out. We want to give you a fair chance to show what you can
do; this does involve avoiding errors, but if you help us out we’ll give you all the credit we can!
Finally: luck does matter a little in exams, but you can make your own luck. If you revise sensibly,
understand the subject and keep your head during the exam, your chances should be pretty good...
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