You may have heard people call the HSC a game, or liken it to a game. Well there is an element of truth to this view, depending on how you look at it.

In order for the HSC to be fair in ranking students for the purposes of University entry, a comprehensive system of HSC scaling is used, hence why we have the UAC and the notion of ‘scaling’ and ‘scaled marks’. The scaling process itself is firmly justified mathematically, and is technically fair (to those who understand the mathematics of it – first-year statistics anyone?). This is also PART of the reason why English is a compulsory subject (because the HSC scaling process relies on having a common subject taken by all HSC students as a sort of ‘parametric variable’ to enable comparison).

Now, without going into how scaling works (read our HSC scaling explanation for more info), it’s a given that this scaling system has a HUGE effect on your final result – your ATAR. Obviously choosing subjects that have scaled well in the past would have a big positive impact on your ATAR, simply because of the effect of scaling. Of course, these subjects scale high because they are comparatively ‘harder’ to get higher marks in, according to the scaling system. But the problems with advising people to choose higher scaling subjects are:

1. If you don’t enjoy the subject, you may get a low mark anyway. No amount of scaling can save a disinterested and unmotivated student from getting a low mark in a particular subject.
2. Choosing subjects for their scaling will not prepare you for the University course you may end up with.

But perhaps the biggest problem of all is the fact that the all-important subject selection decisions are made at the end of year 10. Effectively, the effect of HSC scaling would already be set in stone before you even started year 11! So why advise year 11s and 12s about HSC subject scaling at all when they aren’t able to change their subjects by then anyway? (with the exception of taking up Extension 2 maths). So in this respect, yes the HSC is like a game, because if you understand the rules of scaling, you can use it to your advantage in choosing your subjects wisely at the end of year 10.

Therefore, YES it is an EXCELLENT idea, if you are in years 7-10, to familiarise yourself (at least on a basic level) of how HSC scaling works, and how this should affect your subject selection decisions (if at all). However, if you’re already in year 11 and 12, this is not an option for you.

Nevertheless, year 11s and 12s that have already chosen their subjects for the Preliminary and HSC course should note that there’s actually one more important benefit of knowledge about HSC scaling.

The efficient allocation of study time

The main benefit of knowing how HSC scaling works, is to use it to plan your study schedule effectively. The reason is since some subjects are more highly scaled than others, some subjects have different rates of diminishing returns than others. Put in another way, some subjects are worth your time more than others.

General rules

Generally, the best way to allocate effort and time to your subjects is:

1. If your skill is about the same in all subjects, spend more time on the higher-scaled subjects
2. If your skills are much more advanced in high-scaled subjects than in lower scaled subjects, focus slightly more in your lower-scaled subjects
3. If your skills are much more advanced in lower-scaled subjects than in higher scaled subjects, focus MUCH more on your higher-scaled subjects

The above may appear to be ‘common sense’ to some students – and rightly so, it is not a magical formula or a breakthrough strategy in HSC study. The key to a 99+ has always been to do well in as many subjects as you can!

But to illustrate the above, consider the following simple example:

Say you’re doing as well at Chemistry, and as you are doing at Maths Extension 2, then instead of splitting your study time equally between the two (just because they are both worth 2 units each), you should spend more time on Extension 2, simply because it scales higher. The higher scaling means that your return on effort is higher in Maths than in Chemistry (basically the benefit from studying is higher in Maths than in Chemistry, in this case).

In a similar example, say you are very, very good at Maths Extension 2, and terrible at English Advance. In this case, simple logic states you should spend more time studying for English and less time on Maths (despite the fact that Maths would have a much higher scaling effect than English). The reason is because if you’re already very good at a highly scaled subject, chances are you’re going to get close to a 50/50 scaled mark per unit for your Maths subjects, whereas if you spend more effort and time into English, you may raise your English scaled mark from 40/50 to 45/50 – all in the noble cause of maximising one’s ATAR.

Diminishing returns on scaling
Looking at Table A3 statistics gives an indication as to how scaled marks taper off at higher percentiles for different subjects. Generally, higher-scaled subjects have a greater diminishing return at higher percentile achievements than lower-scaled subjects.

To illustrate what this means, compare the 2008 scaled marks for Mathematics Extension 2, and Chemistry (both are highly scaled subjects, but the former is extremely highly scaled). At the 99th, 90th and 75th percentile, the scaled mark for Mathematics Extension 2 is 49, 47.5 and 46 respectively, whereas the same for Chemistry would be 48, 45.5, and 42 respectively. This shows that, assuming raising your percentile rank from 75th to 99th percentile is of similar effort across subjects, it is far more worth your time spending it on Chemistry than it is on Mathematics Extension 2. If you raised your percentile from 75th to 99th in Chemistry, you would have gained 6 scaled marks per unit, instead of 3 scaled marks per unit for Maths Extension 2.

The best way to understand exactly how to optimise your study time allocation, it’s best to have a close look at the most recent Table A3 statistics for your subjects. Look at how many scaled marks you’ll gain as a result of equal leaps in percentile ranks, and decide how to best allocate your study time from that analysis.

Conclusion
So to answer the original premise – yes the HSC is like a game. It has a set of rigid rules, and those that understand the rules can use it to their advantage. However, as we discussed, the advantage to year 11s and 12s is only in allowing you to better allocate your time and effort across your subjects. No amount of scaling will save you if you simply do badly in your assessments and exams.
To get a 99+, there’s still no substitute for hard work.

Whether you do 2 unit maths, maths extension 1, or maths extension 2, doing well in HSC mathematics requires a similar strategy. In this article, we will briefly look at what makes a successful HSC maths student, as well as some exam preparation techniques which would be relevant to students today, as most have their all-important HSC trials and HSC exams coming up in the next few weeks.

Seeing connections between HSC topics
The most common characteristic shared by successful HSC maths students is their ability to see connections and patterns between the various topics of maths. This is important, as many questions are not worded in an immediately straightforward manner.
For example, a 4 unit (Extension 2) question may initially appear to be an integration question, but in part b or c, knowledge of polynomial roots or complex numbers needs to be used. Similarly, such questions involving a mesh of different topics are also common in 2 unit math and 3 unit (Extension 1).

Practice makes perfect

Training for mathematics is much like training for sports. Your core skills ultimately comes down to how much practice you have had. There is a limited number of ways an exam can ask you questions. If you have gone through two or three complete (reputable) HSC maths textbooks, good chances are that you have seen most of the ways questions can be asked.

Therefore, doing well in HSC maths, regardless of what level of maths you do, comes down to simple practice. This piece of advice is the most simple to describe and understand, but the most difficult to implement and follow through. The key is to set yourself an ongoing goal – decide how much exercises or hours you can do every day or week, then persevere.

Build up a habit for the long run and stick to it. Focus on sustainability, rather than studying for the short term. For example, if you can get into a simple habit of studying just an hour, purely dedicated to mathematics, on each school night, this would be so much more useful than being highly motivated for a period of a few weeks prior to exams, but being unmotivated throughout the year.

Convert real facts into a mathematical problem

Longer, more difficult maths questions tend to be phrased as a problem question. There is no rule of thumb as to which topics can be phrased in a long-worded question – any topic can be presented this way. However, some topics tend to have a greater abundance of such worded problems. For example, in maths Extension 1, there’s Applications of Calculus, which includes things like projectile motion and Newton’s Law of Cooling. In maths Extension 2, there’s even more! (Mechanics, volumes, conics, complex numbers and most of Harder 3 unit – to name a few).

Some students find it difficult to convert a worded scenario or problem into a mathematical / numerical problem. The issue is that students are mostly taught to think in terms of numbers and algebraic expressions, but only occasionally (or for some, rarely) get to practice on real-world worded problem questions. A good maths student would have had plenty of practice at synthesising complex worded facts into a numerical problem, especially by the time they need to prepare for their HSC trials and HSC exams.
In terms of good preparation, it is good to pay close attention to questions which are long, have multiple parts and represent mathematics in some real-world application. Doing these questions (and asking your tutor / teacher questions if necessary) will give you adequate preparation.

Avoid over-relying on your calculator

This point is not talked about much, probably because it is not raised often. But I’d like to shed some light on the issue. Pulling out your calculator for every arithmetic operation (e.g. you need to add single digit coefficients together) wastes your exam time, and increases the risk of pressing something wrong. In the end, for the more simple operations (e.g. adding / multiplying single or even double digits) is simply done faster in your head, than with a calculator.

I remember, not long ago while supervising an exam at university, I saw a first-year student take out his calculator and press 2 + 2 =. Maybe I have a strange sense of humour but I found the incident funny and memorable. However this does highlight a current issue for some HSC students. For some students, it has come down to total reliance on their calculator for all arithmetic calculations, even simple ones that ought to have been done mentally without a doubt.

I always tell my students, you can do an entire Extension 2 exam without touching your calculator. Most of the more advanced students know this. To minimise the incidence of human error, again, this comes down to practice. In everyday life, whenever you come across a situation where you need to add / multiply / subtract or even divide, (e.g. when shopping, or on the train, or at school etc) you should do the math in your head. Break the instinct of moving to grab your calculator. Think of the brain as like a muscle – the more mental exercises you give it, the better it will become.