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.