# MAS114 Semester 1 exam advice

Here is some advice on the MAS114 exam: or, at least, on the first
half of it, which relates to Semester 1.

The exam consists of two hours to answer six questions, and you
should attempt them all. Broadly speaking, the first three are
relevant to Semester 1, and the second three are relevant to Semester
2.

80% of the course credit is from the exam; the other 20% from
online tests over the course of the year.

I have prepared some revision
notes for you to use. Note that they do not
contain *everything* you need to know, but you do need to know
everything that is on them.

Here is some assorted advice:

#### Write English sentences

Write *full English sentences* explaining what you're trying
to do occasionally. If you're trying to prove something by induction,
say so (and also say explicitly what it is that you're trying to
prove).

Even if your details are completely wrong, you can still get marks
for having a basically correct idea, but only if the examiner can tell
what your idea is!

#### Learn the ideas

While you don't need to know the tougher proofs to do the exam, it
may be helpful to read them when revising, all the same:

- One good way (not the only way) of understanding a definition is
to see it used, and proofs are good uses of definitions.
- Proofs often contain hints about how to do things in practice, and
the exam will ask you to put some of your knowledge into practice.

#### Learn the definitions both formally and informally

It will be vital in the exam to know (for example) what a
convergent sequence is, and what a Cauchy sequence is.

This means you need to memorise the formal definitions, but you
also need to keep in mind some informal picture of what they mean. You
also need to understand how the formal definition relates to the
informal picture you have in mind.

You will need to be able to do easy examples of proofs that various
series are convergent, or that they are Cauchy. For example, it would
be helpful to be able to prove directly that the sequences below are
all convergent, and that they are all Cauchy:

a_{n} = 7;
b_{n} = (n+1)/n;
c_{n} = 3/2^{n}.

#### Read the questions thoroughly

Not only that, read the *whole* question carefully before
starting. Take a few seconds to imagine how it might all work out,
before you start writing anything. This helps avoid some serious
blunders.

#### Read Sam Marsh's advice

Dr Marsh will soon be writing a complementary document of advice,
with other good suggestions in it.

#### Learn how to do the practical number theory stuff

You might find it helpful to use
my online revision
tool.

#### Do some past papers

I recommend doing them in timed conditions where possible. They're
available on Sam
Marsh's Semester 2
course page.