We will start with the obvious things that you may have heard before. These tips may sound obvious, but they’re among the more important / commonly applicable ones, so be sure to remember them!
- Cross out incorrect answers with a single line
HSC Markers read everything that can be read, even if you’ve crossed out an answer. If you’ve written an answer but change your mind afterwards and write another answer, cross your old answer out with a single diagonal line using your pen. Do not use liquid paper. This ensures that even if your final answer is wrong, there’s more chance you’ll receive partial marks for the question (as long as the marker can see you did SOME things correctly).
- Show ALL working out
Some students prefer to write things out step by step – that’s generally the better / safer approach, as showing working out ensures you will get at least partial marks, even if your final answer is incorrect.
In the past, one of our top students (who later went on to achieve a state rank) preferred to do entire questions just by using his calculator’s memory, storing everything into the A, B, C … to M memory slots! We always had to remind him to remember to write out his ‘working out’ after he wrote his final answer – it was also a great way to check his answer.
- Look for clues from previous parts of a question
All HSC maths exams (from General maths, 2 unit to Extension 2) structure their questions in terms of part a, b, c, etc. Use the answer from the previous parts as a clue to your current part (even if it’s not a ‘hence’ or ‘hence or otherwise’ question).
- Use your calculator’s memory!
For questions / parts that require you to use a numerical result from a previous question / part, you’re better off using the stored number in your calculator rather than your rounded written answer. This applies especially true in subjects like HSC Physics and HSC Chemistry where you’ll be doing much more numerical calculations.
For Mathematics Extension 1 & 2 students
- Work a proof question from BOTH sides
For questions that require you to show LHS = RHS (e.g. typical induction questions like “Show that f(x) = g(x) is true for all x > 0″), realise that you don’t need to work strictly from LHS to RHS.
Instead, start with the LHS, see if you can simplify it / progress it as usual. Then when you’re stuck, check the RHS and try progressing with that. Usually you will find this approach makes equating LHS and RHS much easier.
Think of these types of questions as requiring you to make LHS and RHS meet, but there’s a valley in the middle. Instead of pushing LHS all the way through the valley (down the valley, then up the valley), push LHS all the way down, then push RHS all the way down, so they meet at the bottom.
- Don’t be afraid to use graphs as part of your answer
Sometimes, graphs are appropriate as part of a mathematical proof. For example, if you’re required to prove some inequality, you can use a graph (and some calculus of course) to show that a line is tangential to a curve, in order to support your inequality.
- REMEMBER the definition of the log integral:
int dx/x = ln |x| + C
Remember that when you integrate 1/x you get the log of the ABSOLUTE VALUE of x, not just x by itself. Although you won’t lose a mark for not including the absolute value signs, some questions with definite integrals (e.g. requiring you to find the area under a curve) will result in logs of negative numbers and hence impossible to evaluate unless you remember to include the absolute value signs. Don’t get tricked!
- Strategies for ‘hence or otherwise’ questions
In multipart questions, the last part is usually either a ‘hence’ or ‘hence or otherwise’ question. When you have ‘hence’, you have no choice but to use the previous result(s) to do the question. When you have ‘hence or otherwise’ you have an option either to use your previous result(s), or take a wholly new route to the answer.
Here’s the tip: if you can see that the question reduces to anything you recognise, its often actually FASTER to use your ‘otherwise’ option. For example, in tricky Extension 2 question 8 type questions, you are often required to show LHS = RHS, or LHS > RHS, or LHS < RHS. If you can re-formulate the equation into something you recognise, then it’s just a matter of writing out your proof for that thing you recognise, then reshuffling it back into the required form.
The reason why this is a better approach is because for harder questions, the amount of time you could sit there potentially thinking (on how to do it using your previous result(s)) is highly variable (could take a very long time), and risky (you may not even see the answer after spending plenty of exam time). If you can reduce it to a recognised form and write out a memorised proof for it, even if it’s not the most elegant / efficient proof, you will score full marks, and the time you take is only dependant on how much you need to write out.
thematics is much like training for sports. Your core skills ultimately comes down to how much practice you have had. There is a limited number of ways an exam can ask you questions. If you have gone through two or three complete (reputable) HSC maths textbooks, good chances are that you have seen most of the ways questions can be asked.