Many of you don’t know what exactly you want to study yet, what marks you need or even what marks you would expect to get in the HSC. Hence it is very easy to fall into the trap of “I’ll start applying myself in Year 12, the marks don’t count this year anyway”. This is especially dangerous in Maths. Everything in the Year 12 syllabus relies on a very strong foundational understanding of the preliminary material. What that means is you need to start studying now while the marks don’t count. That way any barriers you hit along the way, and there will be many, can be overcome before it matters. Studying for your HSC is a different beast to getting good marks in junior years. There are more tasks more often, requiring a much deeper understanding of the content than you previously needed, and it is harder to brush off a poor result. This shouldn’t discourage you however, as there are many more resources available to you and your academic ability has increased dramatically in the last few years (perhaps more than you realise).
The Most Useful Approach
Ideally, by the end of Year 11 Mathematics you should have an internalised and rigorous understanding of the preliminary material. Year 12 only builds on this content and has little time for revision. A shaky foundation can leave you misunderstanding entire topics.
Read the syllabus. Download the syllabus from the NESA website and look at the section “Year 11 Course Content”. Every topic that can possibly be asked in the HSC exam is here. It almost feels like cheating to know exactly what questions you will get in an exam. This is especially relevant this year as teachers may miss some of the changes to the syllabus and the number of practice papers is limited.
Understand the content. It is very important to realise the difference between having an understanding and being able to get a question right on a particular topic. Many students rote learn methods for solving questions without knowing why those methods work. This is detrimental. It stops you from being able to generalise that knowledge and apply it into new domains, which is the very essence of Mathematical thinking, and the basis of almost every question in the HSC (particularly those towards the end of the paper). For every theorem in the syllabus, you should have an idea of the proof and an appreciation of its importance in regards to other areas of the syllabus. If you can’t figure out or understand a proof, get a teacher to explain it to you.
Practice, Practice, Practice. You improve in Maths through reading the textbook about as much as you improve in tennis by watching Wimbledon. Start getting into the habit of doing questions from the textbook, particularly the ‘challenges’ section of each chapter as these test a higher level of thinking. This has a strong emphasis in the new syllabus and many students will not realise the importance these questions have in developing your Mathematical ability. This is particularly important for Extension students.
In summary, use Year 11 to get ahead of the pack and solidify the techniques you’ll take into Year 12. In Mathematics, you can’t leave any topic unattended and your understanding needs to be watertight.