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7 Definitive Maths Tips For Acing Your HSC Exams

In this article, the tutors from the Maths Team share their best tips for acing your HSC trials!

Are you ready to ace your HSC exams? How confident are you in your skills? Do you know how to study effectively? Not sure? Well, it’s a good thing you came here! In this post, our Maths Team (who are HSC Experts!) share their 7 definitive Maths tips for acing your HSC exams.


1. Context-Based Learning

Have you ever thought of something that you needed to do, walk out of the room, and then forget what you needed to do? And then you walk back into the room and suddenly remember what you forgot!

Or, have you had a situation where you just couldn’t recall that formula during the exam, but the moment you step out of the exam room you suddenly remember how to do it!

Recent studies into context-dependent memory have shown that a person recalls particular thoughts based on the context in which they learnt it. In the example above, your brain learnt that you needed to do something, but once the context changed (you step into another room) the brain can’t recall that thought anymore.

But, how does this apply to study?

This means that you should simulate an exam environment when you’re studying so then your brain will associate those concepts with the exam environment and you will be able to recall it more effectively during the exam. A few ways you can do this:

  • Study at a desk (not on your couch, not in your bed, not on the train)
  • Study in a quiet place (don’t listen to music!)
  • Remove all distractions
  • Study in 2-3 hour blocks

2. Learning by Explaining

Do you ever feel like you know why a question is true but you’re not sure how to explain it? Many teachers say that being able to explain a concept is the ultimate level of understanding. This is because it forces you to think of the concepts in a clear and concise way. This engages the brain to reflect more deeply on the concepts and helps you notice any gaps in your knowledge.

So, how do you do this to study?

Simple, teach your friends or siblings or even your parents. What’s the best method for this? Let’s have a look:

  1. Before you start, make sure that you know what you’re talking about
  2. Pick out some questions of the concept you want to teach, or write your own
  3. Get some blank paper or a whiteboard
  4. Grab a friend or parent who doesn’t know the concept
  5. Teach them!
  6. Walk them through the process
  7. Test them to make sure they understand the concept and can answer questions
  8. Ace your Trial exam!


3. Locating and Improving Your Weaknesses

It’s very easy to get into a pattern of doing the first half of every paper, or doing the multiple choice section and then taking a break – you’ve earnt it!

But are you improving?

Too often students will study simply to absorb or get faster at the content – but to achieve great results, take some time to focus on your weaknesses so that you can directly address them in your study sessions!

Sift through past papers for the questions that you know you aren’t as confident with – maybe probability is your Achilles’ heel! Or maybe you are never quite able to get all of the marks in a maxima-minima problem – whatever it may be, focus more on these problems and spend less time on the problems that you are already good at!

Furthermore, if you structure your study sessions about specific targets – for example “I want to become a probability wizard!” – then you may find that studying for your exams is more enjoyable and less overwhelming.


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4. Experiment with Time Management

It can be quite useful to set yourself different time limits when completing past papers, depending on what specific goal or objective you are aiming for:

Slower Time Limit

Pick a few days where you are going to deliberately set yourself a longer time limit (maybe an extra hour) to complete a paper – this will encourage you to thoughtfully consider each question, and reduce stress. This is good to carefully consider every aspect of questions in a more relaxed manner but still be put under the stress of time.

Faster Time Limit

Not giving yourself as much time can help establish which questions actually take you the longest! Each second will feel slightly shorter, so you will know where time is being wasted! However, the faster time may be a bit more stressful and intense – don’t over-do it!

Unlimited Time Limit

Give yourself as much time as you need to finish a paper – thoughtfully consider every single question and give it your best attempt.

This method ensures that you have enough time to go through every aspect of the paper – and to not be deterred by the harder or more tedious questions that you may not have given as much attention to or skipped. As you have more time, you should set higher standards for how you set your working out and present your solution – this ensures that you understand the topics!

Of course, you should not present this much detail in an exam – only do this occasionally!


5. Write out a Cheat Sheet

Do you know that feeling you get when you ALWAYS have that one question you’ve seen time and time again, but you always forget how to do? Let’s get rid of that feeling!

Write out a list of all of the ‘tricks’ and formulas (or even just types of questions) that you may forget – here’s a few common ones to start you off!

  1. The classic “Oh, this is when I add and subtract 1”
  2. Those last few formulas in Simple Harmonic Motion that I always forget to use!
  3. I ALWAYS forget to add my solutions for time onto the initial time in the SMH Tides Questions
  4. For the 2 UNIT solutions: “This is the one when I need to use a trig identity first!”
  5. Derivative of COS is negative SINE, so the integral of cos is POSITIVE sine

And while the Maths Team doesn’t generally recommend studying in the shower – you should laminate your list and stick it to the shower wall so that you can remind yourself of these tricks and tips every day!

But remember, writing out a cheat list isn’t proper study – you still need to make sure that most of your study sessions are spent knuckling down with some maths!


6. Be Realistic With Your Time Management and Ensure You are Taking Appropriate Rest!

It’s easy to give advice on time management – but it’s harder to put into action. There will be some days where you don’t meet your goals and expectations – and that is okay! Please don’t give yourself any additional stress because you couldn’t follow all of the tips in this blog, we all study in different ways.  This is called being realistic!

Going on Facebook and Netflix is NOT resting – turn off that blue, glowing screen and breathe in some fresh air and look at some trees!

Reward your mind and body with some proper rest.

The 2018 HSC Facebook Discussion Group might be a good source of laughs and banter – but your time might be better spent if you unfollow this group and take the last few months to focus on what’s important.


7. Checking Your Own Working

How often do you think to yourself, “If only I hadn’t missed out on a minus sign” when you are checking your answer with the solutions? Obviously, there is no way to compare your working with the solution in an exam, so techniques need to be developed to minimise these errors as much as possible:

Does the number at the end make sense?

Do you expect a positive or negative number from the question? What about its magnitude? Is the number big or small? In many questions, especially those on topics of motion (e.g. simple harmonic motion, projectile motion, mechanics) a rough idea on the sorts of numbers that your answer might contain can be obtained usually from looking at the numbers that are given in the question.

Also, a good thing to do if you have time is to substitute your numbers back into the equation given in the question. This is especially important for questions that rely on the previous parts as you can lose marks for carrying on errors if you don’t get the first part right.

Does my expression/equation make sense?

If you’re asked to find an expression/equation of something, how do you know if you’re in the right ballpark? If you can, a really easy way is to substitute numbers that you already know.

For questions involving initial conditions, substitute those initial conditions into your equation and see if your equation holds up. If it doesn’t, go back and see where you went wrong.

Also, if applicable, check what happens at the extremities. Doing a resisted motion question? It’s usually a good idea to check!  Integrating a function? Find its derivative and make sure that it matches the original function. As a bonus, you get to practice your differentiation skills!

Make it easy for yourself to find your own mistakes

Yes, you don’t have much time in the exam. But if you practice setting out your working and writing legibly, even though it sounds silly, that little bit of extra time you spend will repay itself multiple times over when you’re trying to figure out what went wrong in your solution.

Also, make sure you draw a nice, big, clear diagrams or graphs. This does not only help you make sure that right things are at the right place, but examiners would appreciate this so much more than you do!

Some things that you should not forget to include in your graphs are the following:

  • Labelling x- and y-axis
  • Labelling all asymptotes. Sometimes cluttering everything on x- and y-axis isn’t the best idea – so label asymptotes at the top/bottom (For vertical asymptotes) or at the right-most end of horizontal asymptotes!
  • Label the graph which is your solution, and trace it with a black pen! Sometimes, it’s also wise to trace and put an arrow saying ‘Solution graph’ – because undeniably, you may have done a few steps of those transformations. But you want to let the markers know that here is my ‘SOLUTION’!
  • Small things add up! Getting into the habit of checking your own working, before you compare your answer with the solutions will help you minimise errors during the exam and will help you understand what kinds of errors you need to be on the lookout for.

Written by Oak Ukrit

Oak is the Head of Mathematics at Matrix Education and has been teaching for over 12 years and has been helping students at Matrix since 2016. He has 1st class honours in Aeronautical Engineering from UNSW where he taught for over 4 years while he was undertaking a PhD. When not plane spotting he enjoys landscape photography.


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