Ahh, the external exam. The new monster. In this article, I talk through what I believe you should know at the very least in preparation for it.
The basic structure
For your external assessment, you will sit two papers.
Paper 1 is a technology-free paper. This means you will NOT use your graphics calculator or anything similar in the exam.
Paper 2 is a technology-active paper. It assumes that your calculator will be right there next to you.
The papers are both 90 minutes long, with an additional 5 minutes for reading only. They each contribute to 25% of your final mark. But considering that you have to sit them back-to-back, that’s quite intense! (Your internal assessments are spread out through the year at least!)
The most important factor here is perhaps the difficulty!
The difficulty of the questions will be spread out across both exams at the very least. It’s possible that each of the two exams will follow the same difficulty spectrum.
60% of questions fall into the ‘simple familiar’ category. It’s intended that the techniques required to solve these problems are reasonably obvious. For example, some questions will be similar to those you’ve seen in your textbook.
20% of questions fall into the ‘complex familiar’ category. If you haven’t studied enough, you may find some trouble. However, in general students that have prepared will be able to break the question down into components. Each component can then be approached using concepts that fall into the above category.
You might struggle with these initially, but with practice you begin to see patterns. You’ll see the sequence of techniques repeated from question to question. The questions should only become ‘common sense’ material in the long term.20% of questions fall into the ‘complex unfamiliar’ category. These are the ones that weed out the strongest candidates. Common things you’ll find here include:
Use of techniques from a wide variety of topics.
Information in the question not explicitly being presented to you. By that, I mean you need to figure some of it out yourself! An example could be the need to find extra angles before using the sine rule.
The techniques required are no longer obvious. You should think about what techniques make sense before jumping into them! (In saying that, your first guess may not always work. Sometimes, you just need to try again!)
For the last two categories, you may be asked to evaluate the reasonableness of your answer. This requires you to give your own judgement based on precursory numeric/algebraic computations.
Building your way up
How should you prepare for mathematics exam? Well, there is no one unique correct answer. ‘Studying’ is an odd thing in that everyone has different optimal strategies. In fact, even your best friend may find strategies that are highly effective on you, having no impact on them!
So I can’t simply pull out what’s going to work for you out of a hat. But I can provide some recommendations!
My four basic recommendations
Before rushing into practice, ensure that you genuinely understand the concepts. That’s what the examiners will assume when you sit your QCE final exams. You should be able to flip through your textbook, and be able to say “I understand this equation/formula/theorem/…”. And consequently, be ready to apply it.
What happens if you can’t? No stress – just spend some time figuring it out! Common obstacles include mind blanks, gaps in prior knowledge, or external factors like too much studying.
I heavily doubt you’d need to know them all the way to the core! If you’re a passionate student, you may wish to investigate proofs of various formulas/theorems. But I understand that many students would not have the time for this; heck, I don’t know if I would!
Know your techniques! The examiners assume that you can reproduce certain methods such as:
Curve sketching with the second derivative.
Optimisation problems.
Finding tangents to curves and areas under curves.
Interpret probabilistic statements like P(X≤4).
Apply approximate normality in problems on the binomial distribution.
Construct diagrams involving use of bearings and potentially more.
Rearrange an equation to make a new variable the subject.
Never abandon your textbook. Or at least, not until you’ve practiced enough and deserve your confidence.
Use resources from the other states! Who says you should be limited to only what you’ve got?
“Practice makes perfect?”
Cliche, right? Still applied to mathematics a lot. It’s not entirely true, but we tag it with mathematics often.
The skills-based nature of mathematics is the culprit here. The distinguishing aspect of mathematics from other subject areas is the problem solving required. On one hand, the exam isn’t going to test your memorisation; it is not a mind dump. On the other hand, whenever you do memorise something, it’s likely a technique or a pattern. But that question your teacher showed you on this technique is unlikely to be the same one in the exam!
So how can you ‘get good’? This is why people associate practice with mathematics. (It happens in both Vic and NSW.) Think of the brain as a muscle. You exercise to keep your muscles strong and fit. You need to be consistent with your practice to make you brain comfortable at the sight of mathematics.
The textbook as a resource
One reason to not (rush to) ditch your textbook is due to the supply of questions. It’s not limitless, but it’s still a bucket-load. It’s not going to mimic everything in the exam, but it gives your brain that extra training! The easier questions in the textbook will likely overlap well with the ‘simple familiar’ questions in the exam. Naturally, the harder questions also offer guidance with the ‘complex familiar’.
If by the end of it all you think the textbook’s too easy, well done! But you still had to make sure you understood all those concepts in it throughout the year!
Old exam papers
However, I wouldn’t want to say that the textbook is everything either. What textbooks don’t always offer are:
Questions not sorted by topics/concepts. That is, questions in a random assortment of topics.
Questions that require concepts from multiple topics. (But you may bump into some textbooks that do!)
That, and because your textbook questions are sorted by topic, they may look like ‘complex familiar’ questions at most! In Vic and NSW, the students/teachers believe past papers are one of, if not the most effect studying tool. After all, they were also written by examiners, just that they were in the past!
Of course, sadly you don’t have that. All you have that right now is the QCAA sample. But don’t fret too much, because the papers in the other states will still be similar! Throughout the year, I seriously encourage considering VCE past papers for Maths Methods. Your syllabus was designed heavily based off theirs, and hence the overlaps will be huge! You’ll also find some relevant content in HSC Mathematics (now renamed to Maths Advanced), just not as much as from Victorian papers.
Note 1: You may bump into different notation in the other states time and time again. It’s hard to pinpoint down exactly what they are, but just be alert of that issue.
Note 2: You won’t find questions on statistics in the old HSC Mathematics syllabus papers!
But don’t overwork your brain!
When I say practice in mathematics is about consistency, I actually mean that. Please try to avoid being that person that does the following two things!
Practically always studying mathematics. If you’re going to do this, you should be able to justify your reasons. Normally however, this just makes people sick of the subject even more. Sometimes this goes to the point that in the long run, they start intentionally trying to avoid it. (Of course, there are understandable exceptions such as during the lead-up to an assessment task. What I say here is for all other points in time throughout the year.)
Not having breaks! As counter-intuitive as it may appear, breaks can often be a great thing! Try challenging yourself to study for maths 5 hours non-stop one day. It’s very likely you’re gonna start struggling after the 3 hour mark.
There are other articles on breaks out there (I imagine); check them out! But as a loose rule of thumb, I recommend 10 minute breaks every hour, or 5 minute breaks every 30 minutes.
Dealing with stress
Before I close off this article, I want you to realise that stress is a real thing. I personally believe that stressing over exams is normal for us students. A lot of my friends have been there too.
But it’s likely a good thing, because it shows that you care! It shows your determination to do well. The main objective here is to figure out how to control it. What you don’t want is for that stress to start dominating you, to the point you stop behaving rationally as a human. (Which isn’t something you can always do, but at least reduce how often it happens!)
How do I know I’m stressed?
Through a lot of ways. But here are some common ones.
A sickening feeling swells up inside you.
You find it impossible to think about anything beside the exam.
Potential moodiness. (Happens to me a lot when I don’t understand what’s on the paper.)
Unusual eating and/or sleeping patterns.
Forgetfulness.
Note: Stress doesn’t have to be influenced by exams. It’s just that exams are one potentially huge source of it. You should always try to figure out what’s actually causing the stress, so that you can take better action.
Combating it
If you’re genuinely convinced that the exam is the cause of your stress, I’d try considering the following.
The classic ‘take-a-deep-breath’. Sometimes you may need to do this once; other times perhaps a lot. Give yourself an adequate time-out to regroup your thoughts. Very slowly start to think back in the positive direction.
Think about what specifically is causing the stress. You may find that you’re perfectly comfortable with everything else, but there’s just one barrier right now in the way.
Get help. Your peers are supposed to be a valuable asset – bounce questions around each other! (Or alternatively, hop onto our forums and ask us for help there!)
Breaks, as mentioned earlier.
Jump into something else less stressful! (This could be a break, but also something else productive like another subject!)
Remember, stressing is not a bad thing in itself; if anything it is perfectly normal. It’s all about how you manage it, and keep it reasonably well-contained.
