INTRODUCTION TO MATHS A LEVEL 2
For Statistics – a lot of you will recognise that word, a lot of you won’t even realise
that you actually know quite a great deal about this topic already.
Statistics focuses mainly on something called data handling.
Data handling involves all the little bits of Maths that you’ve done that don’t really
tie up into the core stuff that I’ve referred to already.
For example, calculating averages.
There’s a topic already in your S1 book that simply talks about working out the mean,
the mode and the median.
You should recognise those three words from your GCSE, as well as something new called
standard deviations.
Standard deviations refers to the spread of data, opposed to the averages, the middle
number and the third section that comes up a great deal in Statistics, especially in
your S1 module, is probability and I’d advise again, like I was referring to the summer
between your Year 12 and Year 13, revising what you know.
Probability and calculating averages are something I would spend that little bit extra time over
the summer holidays before your Year 12, learning through again.
It really does save you a lot of hassle when you’re getting through the subject for the
first time in Year 12.
In A level Mathematics like I mentioned before, you’ll only need to worry about two particular
modules in the Statistics.
The S1 and the S2.
Once again, if you are reading from earlier on, I told you that you had to do the first
four core modules and select two extra applied models after that.
Now a lot of people use to make that decision is what they’ll be doing when they get to
University and I generally advise students that if you’re going to follow something
that’s based on Sciences; so if you’re going into Bio Medial Sciences, Chemistry,
Biology.
If you’re going into Economics, Business Studies or Medicine even, S1 and S2 are going
to be extremely valuable to you.
When you get into University in particular, the content of S2 will provide you with so
much support, especially in your first year and to do S2 you’ve got to complete S1 as
well.
So for those of you considering anything going along those lines in your higher education,
I’d ask you to look at thinking about doing S1 and S2, even if they’re a little bit
more challenging for you they will support you in the long run.
Right, let’s go onto the two sections that a lot of you have no idea what they include.
There’s Mechanics and the other one is Decision Mathematics.
Now Mechanics and Decision both include once again two modules, M1 and M2 and respectively
D1 and D2.
M1 and M2 would be ideal for any student that’s considering doing Engineering, Physics or
something along both of those lines at higher education.
The modules focus on concepts such as Acceleration, Speed, Distance, Time Graphs and the subject
helps you to figure out equations that you can model different events across.
So for example, a projectile – when you throw a ball – how high is that ball as
it moves across a pitch?
We can actually calculate those distances using Mathematics and you are introduced to
those topics in M1 and M2.
Another thing is Centre of Mass, i.e. on a very obscure shape exactly where is the middle
of all of its mass acting upon?
Vectors – which some of you once again, depending on what GCSE modules you’ve done
will have met.
So Vectors involves discussion motion across a plane, across a two dimensional field.
You will not need to worry about Vectors in three dimensions in M1 or M2; however, Vectors
does come up in C4, one of the core modules I mentioned to you earlier on, in three dimensions.
And another two topics that do come up in Mechanics are something called Moments – that
some of you might have met in Physics as opposed to Mathematics GCSE – and Newton’s Laws
of Motion.
Once again, some of you might have covered this in Physics, opposed to Mathematics.
As you start doing Mathematics at a higher and higher level, a lot of you will realise
that what you study in Physics affects your Mathematics just as much as what you’ve
learnt solely in Mathematics.
It’s quite nice in a way because you start to appreciate how valuable Mathematics can
be when you’re learning lots of different subjects.
When I was doing Psychology at University, the Mathematics I’d learnt at Year 12 and
Year 13, my A level Mathematics, was one of the most valuable things I could have held
on to.
I was quite glad that I was actually so interested in it that it supported me.
So I would strongly recommend a lot of you look into your University subjects and decide
how much of your A level should be mirroring that to help you.
The final section is something that’s very new and has only really come into A level
Mathematics in the last decade.
It’s called Decision Mathematics.
If you were to speak to your parents, most of them probably wouldn’t have a clue what
on earth it is because it’s come along as Computer Science has become more and more
important.
As the Internet’s become more involved, as more things are handled by computers, Decision
Mathematics has become a more and more valuable source of information for us.
Decision Mathematics is one of my favourites, mainly because it’s completely different
to the other three modules.
It’s one of those that if you’ve got quite a logical mind, it’s wonderful.
If you follow rules very strictly, if you can appreciate how clear and precise you’ve
got to be when giving decisions and giving instructions, Decision Mathematics will be
something you’ll thoroughly enjoy.
Once again, it’s one of those modules that people take when they’re considering studying
Computer Science or something along those lines at University level.
Many of the problems involved in Decision Mathematics involves something called Optimisation,
i.e. finding the most efficient solution, the most efficient way of doing something.
Now this isn’t when you look at something yourself how do you do it most efficiently,
but what would you make a computer do to ensure that action if fulfilled in the most efficient
manner?
Hence methods are applicable to real world situations, and here again, like I’ve mentioned
before, there are two modules in Decision Mathematics.
So those are the four main sections.
What I would like to do if you can give me a few minutes, is actually go through two
examples for you.
One will be in C1 in the core first module that you’ll be learning when you first arrive
into Year 12, and then I’m going to show you something from Decision Mathematics which
is quite simple but it’ll allow you to appreciate how easy it is to learn Decision Mathematics
if you follow rules and if you can remember instructions very clearly.
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