3U Maths Past Paper Strategies

Breaking down the secrets of NSW's highest performers.

Laura Hardy

Laura Hardy

State Ranker & 99.85 ATAR

My number one piece of advice for 3U students would be: don’t be afraid to struggle in maths.

Maths is very different from other subjects students take for their HSC. In many courses, the content is comparatively simple to grasp, but communicating understanding of the content, for example by writing a well-crafted essay, is the source of difficulty. In sharp contrast, trying to understand maths content has been known to bring many a student to embarrassing tears in a secluded corner of their local library, myself included. Surprisingly (perhaps), this is not a bad thing.

To succeed in 3U (or any other level of maths, really), you need to be willing to embrace the struggle. That feeling when you look at a question, and have no clue how to solve it. You need to build the courage to try something, anything, even if it ends up being completely wrong. Often when I’m tutoring, I’ll ask a student, “What have you tried so far for this question?” and their answer will be “I didn’t know how to start.” Their answer should be “I didn’t know how to start, but what I did try was…”  You can’t be right until you’ve been wrong, many, many times.

Your goal in preparing for the HSC can therefore be broken into two components:

  1. Make sure you know how to start as many questions as possible.

  2. Build the confidence to maximise your marks on the inevitable questions you don’t know how to do.

What holds most students back from achieving those top marks in their 3U exam is undoubtedly Question 14. Although much of the 3U paper consists of relatively straightforward content application questions, Question 14 is much more insidious and contains the style of question which your panicky exam brain is likely to draw a blank on. This is not to say that preparing for Questions 11-13 is easy or won’t take consistent work, but rather to highlight that your attempt at Question 14 will differentiate you from your peers. So let’s talk about some concrete strategies for smashing our two goals.

Goal 1: Know how to start as many questions as possible.

This is going to come down to your consistent practice throughout the year. You should be doing maths multiple times per week, outside of class. The summer break between year 11 and year 12 is a great time to forget everything you’ve learned, so don’t let that happen. You’ve got access to a myriad of resources, from past HSC questions, homework questions from your textbook, to trial papers from other schools [potential project library/snowflake plug here??]. If by the time you hit the HSC you’ve sat 10 full past papers, marked them yourself and understood the solutions, then you will ace Questions 11-13.

It’s absolutely quality over quantity though. Consistent, smaller amounts of focused work will benefit you more academically and drain you less mentally. Some of my favourite ways to study outside of regular homework were:

  • Watching YouTube videos e.g. from Eddie Woo or channels like 3Blue1Brown to help me consolidate difficult concepts.

  • Writing concise study notes for each topic, including worked examples of common exam questions on that topic.

  • Going through marked school assessment tasks or past papers I’d sat with a comb and making a list categorising all my mistakes into conceptual, silly mistake, or application struggle. This really helped me with exam technique as I learned to check carefully question types I often made errors on, as well as highlighting to me my weak topics which needed more revision.

  • Creating a mental “toolbox” of problem-solving tricks that used time and time again doing past papers. This included things like difference of two squares, the discriminant, trig identities and more.

Diligent study will ensure that you’ll have seen the vast majority of exam questions before and will be completely equipped to solve them. However, so will many of your more driven peers. So how do you elevate yourself into a band E4?

Goal 2: Maximise your marks on the questions you don’t know how to do.

This is where the struggle comes in. Don’t skip out on the hard questions in your weekly course of study. You don’t need to know how to do all of them, you don’t need to know how to do any of them. You just need to spend five, ten, thirty minutes trying them, before you go back to consolidation and goal 1. Your maths brain is essentially like a muscle, and if you spend the time, nourish it correctly, you’ll be able to lift heavier and heavier as the year goes on.

Concretely, the approach to these questions might go something like:

  1. Write down all the information given in the question

  2. Do all the calculations you can think of with the given information. Rack your brain. Check the formula sheet. Use that toolbox I mentioned earlier.

  3. Compare where you are now to the desired final answer. Work backwards if possible.

  4. If still stuck, come back to the question in a couple of days (or half an hour if it’s an exam situation). You’ll often be surprised at what your brain can come up with.

  5. If you still can’t do it, that’s okay! Read the solution to the problem, or ask your Project teacher/tutor and rest assured that your efforts have gone a long way toward strengthening that muscle.

Closer to exams, you shouldn’t just mindlessly be doing past papers. Instead, use that catalogue of conceptual mistakes you built up earlier to identify when you should be going back to the textbook/youtube for practice and explanation to consolidate your weak topics. Then, once you’re feeling solid, it’s time for the big guns. Choose a trial paper from another school, skip straight to Question 13 and 14 and give it your best shot. Mark, rinse and repeat. If it helps, you can work with friends – sometimes a fresh perspective is all you need to help you get the right approach to a problem.

This is all building up to give you the confidence to have a really good crack on the big day. Writing absolutely anything on your paper is better than nothing, and I’ll let you in on a hot tip: often you can get a couple of marks in the last part of the question by simply assuming the earlier parts (even if you left them blank) and working from there. I’m willing to bet you’ll be feeling anxious before the exam, and might freak out a little upon seeing the much-anticipated Question 14, but what you should remember is that nerves are just your body hyping you up to perform your best – a little adrenaline never hurt anybody who’s about to successfully lift the weights they’ve been training for.

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