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In this article, Anthony Morris provides some
tips and strategies to mastering HSC
mathematics. Anthony Morris is a gifted
mathematician who came 1st in the State in Math
Extension 1, 4th in Math Extension 2 (HSC 2007)
and won a bronze medal in the International
Mathematics Olympiad. Anthony currently studies
Advanced Mathematics at UNSW on scholarship.
In
this article, I will examine the main issues
facing HSC students studying mathematics. Like
English, almost all students study some level of
mathematics. The most common questions
confronting students are:
·
What level of Math should I study and how do
each of the different subjects scale?
·
How can I improve my marks and eliminate
careless mistakes?
·
How difficult is Extension 2 Mathematics and
what strategies can I use to tackle the course?
We
address these questions below.
What level of Mathematics should I take?
One of the first decisions confronting HSC
students is “How many units of Math should I
study?”. In deciding, you need to consider both
your own ability in mathematics and the relative
scaling of each subject.
The Mathematics Extension courses are the
highest scaling subjects in the HSC, and this
has significant implications for your ATAR. For
instance, as Richard’s article makes clear, if
you wanted to score an ATAR of 99, you would
only need to be about average in Math Ext 2 and
in the top quarter of Math Ext 1. In contrast,
you would need to be in the top 3% in 2U Maths
to achieve an equivalent mark. What is even more
staggering is if you wanted to score over 97,
you would only need to be in the top 80% of the
Math Ext 2 course, and 50% of the Maths Ext 1
Course, i.e. you could be average-below average
and still be on track for a top ATAR.
It is hence clear that Math Ext 1 and 2 are a
must if you are good math.
Even if you are average in the Preliminary
Mathematics Extension course, Extension 2 may
definitely be worthwhile simply because it is
scales very highly.
How can I improve my marks and eliminate
careless mistakes?
While there is undoubtedly a certain amount of
natural acumen involved in mathematics, with the
correct technique you can dramatically increase
your marks. Here are three of the things that
have worked for me:
1. Understanding your formulae
One of the most important (but also most
tedious) parts of preparation for a mathematics
exam is knowing all the formulae in the course.
‘Knowing’ is more than just memorising. You need
to understand your formulae, know when and where
to apply it, and to use the formulae without
making mistakes. You should build familiarity
with your formulae through repeated practice,
that is by constantly using them to do questions
and exercises on each topic.
Practice gives meaning to your formulae and will
make it clear when and how to apply the formulae
to a given circumstance.
Very soon, doing questions will become second
nature. However, memorisation without context
and practice will not help you because you won’t
even know what formulae to use and when to use
it.
For this reason, at Talent 100, every time we
teach a formulae we always test it with a series
of typical HSC questions so students know
exactly what formula to use and how to apply it.
It is also often useful to remember how a
formulae is derived. When you can see the logic
behind the formulae, it will be much easier to
understand and to remember. Take for example,
differentiation from first principles. Even if
you forget the formula, you can quickly derive
it once your realise it is the gradient between
any point, and another point that is very small
distance “h” away from that point. This formula
describes the tangent, when these two points
become progressively smaller or when h0.
This same principle to remembering formulae can,
and should be applied to almost all formula in
the HSC. You will notice that you get a much
better understanding of the underlying maths and
are able to memorise your formula quickly and
effectively.
2. Set out your work properly
One of the most important ways to improve your
marks in mathematics is to set out your work
properly. Just as an Economics or English essay
requires you to structure your paragraphs in
clear and logical fashion, it is likewise
important that you set out and structure your
mathematical explanations clearly.
Clear setting out helps you:
·
avoid making careless mistakes in the first
place;
·
gives your examiners a clear picture of the
logic and flow of your argument; and
·
provides a strong platform for “cracking” the
harder questions.
If you are making a lot of careless errors, you
should avoid skipping steps. Spend the time to
write a few extra lines and avoid giving away
cheap marks.
Also, it is important to understand that
Extension exams (especially the Extension 2
exam) require more than just a correct numerical
answer for most questions – they require an
explanation as to how you arrived at your
answer. My most important piece of advice when
taking the Extension 2 exam is to include all
your working out and set it out so that it is
easy to understand.
Some simple tips to make your proofs clearer
include:
·
Write a series of equations down the page rather
than in a single line, ensuring that you will
have enough space for each equation.
·
Explain what the variables you introduce mean by
either indicating clearly on a diagram or by
writing at the top of your proof “Let x be the
...”
·
Generally, explain the steps in your proof, i.e.
talk to your examiners rather than letting them
guess your logic. For example, in a harder
permutations and combinations problem, don’t
just state the answer but explain where the
solution comes from, or in an induction proof,
explain where you used your assumption for n = k
when proving true for n = k + 1. ‘Talk’ to your
marker in your proofs and explain why it is
true, don’t make them guess your logic.
·
Draw BIG diagrams. In geometry questions a
larger diagram lets you to mark in more angles
and allows you to see things more clearly. In
curve sketching questions, you are able to
indicate the important features accurately.
By doing these things, not only will you make it
easier for the marker to understand what you are
doing and award you part marks if you made a
calculation error along the way, but you also
reduce the chance that you will make a careless
mistake, and you make it easier to check where
you went wrong if you did.
At Talent 100, we know the best way to improve
your exam technique is to repeatedly put it into
practice. This is why every week our homework is
set in examination style, structure and
difficulty to give you weekly feedback as to the
type of mistakes you make under exam conditions.
3.Perfect practice makes perfect
Once you have revised all your theory, the most
effective way to study in the final few weeks
before the HSC exam is to do as many exam papers
as possible under exam conditions. Here it is
important that you aim to completely eliminate
ALL your careless mistakes. I personally used
to lose a few marks in the first few sections of
an exam because I would forget the constant of
integration or not change the limits when making
a substitution. However, after doing full exams
for practice I was able to completely eradicate
these mistakes in the first 4 or 5 questions of
the exam.
When you sum up all your careless mistakes, you
may find they can add up to 5-10 marks - the
difference between a good mark and a great mark;
a Band 5 and a Band 6. You must learn to avoid
giving away any unnecessary marks
At Talent 100, we aim to develop perfect exam
practice through exam-style homework and
rigorous mock-exams. Students are asked to
re-write homework corrections to ensure they do
never repeat those mistakes in the future. In
addition, our HSC Students sit 10 weeks of
mock-exam papers to discover any shortcomings
before they sit their trials and HSC Exams
(which collectively account for 70% of their
entire marks). If you’re looking to score top
marks in Mathematics, Talent 100 can help you.
About Talent 100
Talent 100 is Sydney's most effective HSC
Tuition and UMAT Preparation College, specialising
in Physics
Tutoring, Chemistry
Tutoring, Maths
Tutoring and English
Tutoring for Year 9 to 12. Find
out why students at our tutoring college
consistently outperform their peers 4 to 1.
Talent
100 also provides UMAT
Preparation Courses under the
name MedStart UMAT
Preparation and Training courses Try
our Free
UMAT Sample Questions and Practice Papers.
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