Hacks for Extension 2 Mathematics

The Syllabus

Make sure you know the syllabus inside out since every single assessment must be based on those dot points. I would suggest organising all your notes under the syllabus dot points to make sure you haven’t left anything out. Highlight all the key terms and formulas so that they stand out during your revision and annotate each topic with any tips or frequent errors you find yourself making.


Ask Ask Ask

Maths is a skill which is best developed over time rather than crammed in the night before. It relies on active and sustained learning throughout your HSC year. So don’t be afraid to ask for help – whether it be from your school teacher, your tutor or your peers. No one is going judge you or remember that you didn’t understand how to graph an inverse function, but you will certainly pay for it down the track if you can’t do it in an exam.


With a seemingly infinite number of maths questions out there, memorising the solution to one question is unlikely to help you ace the exam. I would instead recommend trying to understand the problem solving methods that are commonly used in different topics and question types. For example in Extension 2 Integration, I would familiarise myself with common situations where Integration by Parts or Partial Fractions are used. I would also focus on integrals where the substitution is not given (since unlike Extension 1, Extension 2 does not provide the substitution). That way when you use your existing knowledge to tackle any new question with confidence, accuracy and speed.



Practice Papers

Honestly, this is the holy grail when it comes to doing well in maths. Unlike subjects like English, the marking rubric is pretty fixed and unbiased. The results from a self-marked exam give a pretty accurate indication of how you are performing and your weakness areas. Marking yourself also helps you become familiarised with the marking rubric, so you know how much working out you need to guarantee your marks.


Make sure you’re completing the past papers under exam conditions too. I’ve personally seen many people who do well in the classroom but badly in exams. This is because exams come with higher stakes, more pressure and limited time. The only real way to overcome and get used to the stress is practice. So, stop making excuses. Find a quiet space, remove any distractions, set up a timer and do the practice exam.


There is clear difference between a textbook and a practice paper. Textbook questions are there for you to learn and understand. They are generally easier since you know what topics they are on. Practice paper questions are designed to simulate the actual exam. They are harder because they omit most of the leadup and don’t specify the topics being tested.


Remember, past papers at least two weeks before the exam.



Don’t neglect Advanced Maths

One of the biggest mistakes Extension 2 students tend to make is not studying the Advanced content properly. Sure, you are only doing the Extension 1 and Extension 2 exams. This gives many a false sense of security, but past HSC exams have tested Year 11 and Advanced content in the Extension 1 paper.


For example, both the Pigeon Hole Principle and Combinatorics were tested in the 2020 Extension 1 exam despite being Year 11 topics.  Of course, the content may theoretically be less difficult, but you will be more prone to losing easy knowledge marks or making silly mistakes due to lack of practice.


This point is especially important with the new syllabus. Back in the day things were simpler – Extension 2 was harder Extension 1 and Extension 1 was harder Advanced. But now topics like Continuous Random Variables are purely Advanced content. If you overlooked Advanced, you would undoubtedly struggle if any of those topics came up in the exam.


The takeaway? Remember that both Extension 1 and Extension 2 are out of 100. You don’t want to be losing marks in either exam. Extension 2 generally focuses on Extension 2, Extension 1 comprises mostly Extension 1 with some Year 11 and Advanced. So, look at where the content overlaps. You probably don’t need to revise Year 11 Inequalities given you are studying Extension 2 Proof. But topics like Probability, Combinatorics or Financial Maths? I would definitely brush up on them in the weeks leading up to the exam. After all, it’s better safe than sorry!



Exams are all about mindset. If you believe you’re going to fail, chances are you probably won’t perform well. If you believe you have a chance, then you will at least be motivated to keep learning and improving. Make sure you build your understanding early on so you can spend the days leading up to the exam on revision. Leave the easiest practice papers to the end. That way even if you run out of exam prep time, you’ve done a sufficient amount of challenging questions. The day before an exam, I would recommend looking through your notes again and doing mostly easy questions. This approach does wonders for your confidence and can help you destress before the exam. It is highly unlikely the same question will appear in the exam, so you should prioritise mindset over cramming on that last day.


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