How you study for maths is ultimately up to you. There’s no ‘right’ or ‘wrong’ way. There’s only your way.
However, it helps to have some sort of a starting point! Some of you may already know how you like to study for mathematics. But if you don’t, no worries – scan this list! Just make sure you gradually discover what’s best for you! (i.e. likely not the entire list.)
Notes are a toughie. Many students do use notes, but not all.
The reason why some people don’t advocate for notes is because they stray somewhat from the nature of maths. Mathematics subjects are inherently very skills-based. Notes do help understanding of the concepts, which is certainly still important. But simply reading over the concepts doesn’t jog your brain’s ability to solve problems enough. This is why some people might advise against them – they stop using notes after they’ve written them!
But you can make them more useful! If you choose to use notes, the key is to think about what would you refer back to when solving problems. For me, I’d say keep it down with the formulas – I can just print my formula sheet and annotate it! Rather, I’d be thinking examples. I’d ask myself “what kind of sample responses would be useful, or easily adaptable, if I’m struggling at a problem?” Depending on the context, they could be just a simple graph, two-line responses, or page-long responses.
I’d also be thinking about tips. For example, in maths methods, when might I choose to use a logarithm law. Or for further, exactly how do I identify if a sequence is arithmetic or geometric.
And also traps I came across whilst learning! For example in further, which Earth geometry formula to use for latitude/longitude. For specialist, perhaps not subbing back in for x in integration by substitution.
Overall, I’m in the middle about notes!
I tried posters as a gamble for one of my subjects back when I accelerated my learning. It’s hard to say if they’ll help you the way they helped me. But this is just my experience.
I made posters work that year by pulling out thick, permanent markers and writing in size 72 font. (Okay, I don’t know what size, but the point is it was big.) The drawback was that I obviously needed a LOT of posters. But I did it because I couldn’t see enough point in filling a poster with 500 equations. I could’ve done A4-paged notes for that instead.
On the posters, I basically put in the bare minimum. I just told myself how I’d approach the common problems in the exam. I only chucked in a full example if I felt it was short enough.
The benefit of this was that it made a selection of questions in the exam obvious. There was no way this strategy was going to help me solve every single problem. But I knew there was going to be questions in the exam that tested me on common concepts. (For you, these would include, but not be limited to the 60% ‘simple familiar’ problems.)
I stuck these posters up on my wall and took a glance at them every night. I’d usually mix up which I looked at every night. Then I’d brainstorm in my head how to put each of these techniques into practice. That was a nice way of jogging my memory every night. Come exam day, those common questions literally became free marks in my maths exam.
Well, that’s up to you. You don’t have to use posters the same way I did.
I’d probably argue that posters are a variation on conventional notes. They have the same intent; it’s just that the execution differs. If you choose to use posters, you should consider how you would make effective use of them.
Your textbook is meant to help you learn and revise concept-by-concept. (Likely followed up with a topic review.) Usually, you aren’t supposed to get through all textbook problems. They typically put in more just to give you additional practice and exposure.
Throughout the year, it’s likely that your teacher will assign you homework questions. If time permits, you may choose to go over the minimum expectations they set. But you should always aim to complete the bare minimum.
But come study time, textbooks remain advantageous when you’re having difficulty on specific concepts. They provide examples on said specific areas. They also provide practice problems for them. You might feel like you’re doing the same questions again, but it’s unlikely your brain remembers the details from then. So it’s practically jumping into problems fresh anyway! Furthermore, you can also consider doing problems you haven’t done previously. This is perhaps the most opportune time to chase them back up!
You can circle or highlight questions you’ve struggled on first time round. You can also cross out questions that were easy first time round, or after you redo them. Alternatively, if you want to resell your textbooks after the QCE, start compiling a list of these somewhere! Either way, you’ll hopefully have a better picture of questions you should revisit!
At some point, it’s likely you’ll say “I have no idea what’s going on.” When you hit a roadblock, start by taking things slowly. Go back to what you already know, and try to gradually work your way to what you’re at now.
Of course, it’s still highly likely that sometimes things don’t work out. Just make sure you’ve genuinely tried your best. When you’ve done that, but to no avail, you should start asking around. (After all, how else are you going to finally learn it?)
There’s quite a few sources you can go to for help.
The only thing to remember is to keep within reasonable boundaries. Once you start bombarding someone else, they’ll feel like your slave and start to feel tired. Show to them that you’ve genuinely tried yourself first.
The main benefit here is that they can tailor their responses for you more. Tell them exactly what you know and what you’ve tried. That way, they’ll help address exactly where your troubles may be.
Nearly all VCE and HSC students will tell you that past papers are the best tool for studying maths. Let us first see why.
Practice is important in mathematics, because it trains your brain’s way of responding to problems. Practising with past exams gives you the best indication of what to expect in yours. Some key things to watch out for:
I get you. The only exam you really have is the precious QCAA sample. You may want to consider saving that one for when you know you’re mildly confident at that maths subject.
But be resourceful.
There’s a lot of content overlap between your syllabus and the VCE’s/HSC’s. (In fact, I’m almost led to believe they looked at the VCE syllabus, and made appropriate tweaks with the HSC’s.) With that in mind, you’d at least hope that the VCE/HSC past exam questions and question styles will mimic those of your exam too! Pinch off the questions relevant to your syllabus from both VCE and HSC past exams. After doing those problems, you should understand what exam-style problems are like more!
(Disclaimer: Obviously, I cannot say for sure that the exam styles will match up perfectly. But I strongly believe that no other source would be able to do it any better. But even if they don’t, you still have a much larger supply of questions available! There can never be enough questions to help you practise your maths.)
So you may hear past students talk about mimicking exam conditions. This involves no notes and no distractions. Just the paper, your writing tools, the clock, and 90-ish minutes of silence doing it.
This is a strategy I can’t confidently recommend to you yet, simply because there wouldn’t be enough suitable papers available. By suitable, I mean that they’d only cover content in your syllabus. (The VCE and HSC syllabuses don’t correspond perfectly to yours.)
I also don’t advise doing your one sample paper in exam conditions. You may get a huge last minute anxiety burst if you don’t achieve as well as you hoped.
It’s only something I’d recommend in two years from now for a newer cohort. You really need enough relevant past papers to execute this strategy.