More often than not, whenever you ask someone “How do I study for 4U Maths?” their response is generally: “Easy — do more Past Papers!”.
What they rarely tell you though is HOW you should be doing them.
Even though I might make a lot of references to 4U Maths in the article, the advice applies just as much to lower levels of Maths as well!
Maths study is like exercise — the later you start, the less fit you should expect to be at the end. Maths is very much a muscle/skill (unlike other subjects which might be more focused on recollection of theory), and as such, requires consistency, dedication, and training. The more you run, the better you become at running. And the more questions you solve, the better you become at problem solving. Simple.
But let’s focus on how to effectively use Past Papers — this is going to be the real key to your success at Maths.
- Use Past Papers to identify gaps in knowledge, and textbooks to plug them.
- Use Past Papers to develop skills, confidence, speed, and marks.
- Scroll to bottom for links to resources.
“A raw mark of 70/100 in the HSC exam will give an E4.*”
*scroll to the bottom to see that I didn’t just pull this number out of thin air.
Remembering that the HSC exam consists of 10 MCQs, and 6 x 15 mark Questions, in order to get 70 realistically, you only need to:
- nail all questions up to and including Question 14, and then
- try scrape as many marks as possible in the last two questions.
This is going to be the goal that this article is aiming to push you towards. To achieve this, you need to follow two simple steps. If you’re already hitting this mark consistently, jump to Step 2!
Step 1: Know Your Unknowns
You need to figure out all the gaps in your knowledge.
The mistake most students make is jumping straight into textbook questions. This is in many cases not the best thing to do, unless you have a plan.
- Textbook questions are often different to exam style questions.
- It’s very hard to impose exam style time restrictions when doing questions.
- Doing textbook questions won’t help you figure out what you don’t know.
The following strategy below is an extremely powerful method to identify, and then quickly fix up holes in your knowledge.
- Choose any random school trial paper (one with solutions)
- Spend TWENTY minutes attempting Question 11 only.
Your aim is to get 15/15 in those twenty minutes.
- Mark your paper and make a list of the topics you struggled with.
- Revise those topics using your favourite textbook(s).
Keep following this general exercise until you are comfortably hitting 14 or 15 for Question 11. Then do the same strategy for Q12, Q13, etc.
- Gradually understanding, and working on weaknesses.
One of the most daunting feelings when studying is realising that you need to revise every single thing in the whole syllabus. With this approach, your goal in each study session is clear, small and achievable. All you have to do is fix up issues with the content that appeared in Question 11, which will only ever be a few concepts.
- Exposure to the type of questions they ask in an exam.
You should be grateful that teachers have very limited creativity when it comes to writing exams. If you’re able to expose yourself to as many questions as possible, nothing will be able to stump you in the first few questions.
- Time taken is only twenty minutes!
It’s far less draining than doing a whole 3 hour paper. This tends to be the biggest motivator.
- It builds confidence!
Note: Older Past Papers (pre-2012) are more reflective of the old HSC style questions, which typically had only integration in Q1. Try to avoid doing too many of these papers because there is no point in doing integration over and over again. If you can’t find any Q11s that have other topics, feel free to just start at Q12. Q11/Q12 are roughly the same in difficulty.
Step 2: Improve Speed
Now that you’re hitting that 70/100 in your exam, the only thing holding you back now is how fast you can do the questions.
How To Improve Speed In Exams
Improving speed is easier said than done. When asked what slows them down in an exam, typical student responses are:
- “I spent too much time trying to figure out this question I was stuck on.”
- “I didn’t realise how much time I spent and forgot to move on.”
- “I was going too slow in the earlier questions and didn’t have enough time for the later questions.”
At the risk of sounding like a broken record, the best solution to these problems is more practice and more Past Papers.
A New Goal
- Reach Question 16 with an hour to spare.
To do this, you need to be completing each question in twenty minutes (slightly more than a minute a mark).
Now trying to achieve that for the whole 3 hour paper in one go is again, extremely draining, and the last thing we want to burn out. Instead, we again split our work into small bite sized chunks (although slightly bigger this time):
- Set aside SIXTY minutes of solid study time.
- Pick a Past Paper w/ solutions.
- Do the MCQ, Q11, and Q12 in no more than sixty minutes.
- Mark the paper.
What you need to be focusing on now is being able to finish the questions in the given timeframe, but also maintain a high level of accuracy. There is no point in speeding through an exam if you get half of it wrong!
Once you are doing this confidently, move on to completing Q13, Q14 and Q15 in one hour. This is going to be a big challenge, but is definitely achievable.
While you are still focusing on speed, if you encounter a concept that you are unsure about, you should still be revising it and doing extra questions on it! With enough practice, you should start to see your marks and confidence increase.
Once you get very close to your trials however, you need to be doing entire Past Papers. It’s incredibly important that you are able to practice a whole exam and get used to the time pressure.
If you’re following the two steps above consistently, and with dedication, I promise you you will start to see some big changes in your confidence, your skills, your attitude towards Maths, and most importantly your marks! 🙂
Coroneos’ 100 Integrals + Worked Solutions
One of the topics in 4U that you need to perfect is Integration. Not only does it have its own topic (which is already a large part of the course), but its application is essential in Volumes and Mechanics.
We’ve created a booklet with worked solutions, but there’s no point in learning the trick/manipulation/technique/answer to a particular question if you don’t understand how to use it in other questions. So alongside the worked solutions, we’ve also included how to approach the question, and questions similar to it.
It is not an exhaustive list of methods of course, but it should at least get the ball rolling if Integration isn’t your forte 🙂
Here is the PDF!
*Appendix — Why 70 ≈ Band E4.