Mathematics is the highest scaling subject in the HSC. Being just average in Maths extension courses can boost your AtAR significantly.
Learn the tips and tricks to help you master mathematics, courtesy of Anthony Morris.
Anthony is a gifted mathematician who came 1st in the State in Maths extension 1, 4th in Maths extension 2 (HSC 2007) and won a bronze medal in the international Mathematics Olympiad. Anthony currently studies Advanced Mathematics at uNSW on scholarship.
this article examines 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 maths 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?
What level of Mathematics should i take?
One of the first decisions confronting HSC students is “How many units of Maths 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 Maths ext 2 and in the top quarter of Maths 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 Maths 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 Maths ext 1 and 2 are a must if you are good maths.
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 tips shared by some of the state’s top mathematicians:
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 you 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 h 0.
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 easy 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. One of the most important pieces 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. Alex shares with us that he used to lose a few marks in the first few sections of an exam because he would forget the constant of integration or not change the limits when making a substitution. However, after doing full exams for practice he 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).
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