Tag: HSC Exams

General tips for maths exams

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.

Minimising human error during HSC exams

By virtue of its definition, human error is something we all do. In the more quantitative HSC subjects such as Mathematics, Physics and Chemistry, human error can be a big cause of losing marks in exams. For example, how often have you walked out of an exam room, and realise only moments later that you’ve lost a few marks in a question or two due to ‘silly mistakes’? Or when, coming out of an exam room, you chat with your friends about how they did question X Y Z etc and realising you missed a tiny detail that cost you marks? This happens all too often for many students, and the truth is, human error happens to all students, even the top ones.
Common places to make ‘silly mistakes’

In HSC exams (as well as assessable school exams, since they are all similar to HSC exams), students mainly make their silly mistakes in a few ways:

  • Long, complex algebraic proofs (e.g. long proofs in Maths Extension 2, causing you to copy the previous line’s expressions incorrectly)
  • Long calculation-based questions requiring long working-out and calculator work (e.g. molar calculations in Chemistry)
  • Multiple choice section in science exams

It is quite impossible to make a ‘silly mistake’ in humanities-type subjects like English, or in the long-answer sections of science exams in the same ways as those described above.

Check your work after you finish

Since there’s only a few situations where silly mistakes can be made, students should be mindful of which areas of their exams they need to check over when they have spare time near the end of their exams.

In most cases, you would only have a little bit of time left after you finish your exam. Therefore, it is wise to know how to best prioritise your time in checking for mistakes before the exam time is up. This is assuming you’ve already done all the questions – if you’ve left some questions blank, obviously finish them before you begin checking your work.

Physics and Chemistry exams

For science exams like Physics and Chemistry, after you finish your exam, you should first check your entire multiple choice section (the first 15 questions). A good way to do this is to hide your answer sheet, so you do not see your original answers, reducing their influence. Seeing your original answers is not a good idea, as they may influence you into making the same mistake as you first did. Hiding your original answer forces you to mentally do the question again from scratch, and increases your chances of picking up an error that you’ve missed in your first attempt at the questions.

As you do the multiple choice section for the first time, it is a good idea to circle the questions that you are unsure of (on the question sheet), so that when you finish your exam, you should look at the circled questions first.

After you completely check over your multiple choice section, look over your calculation questions. In Physics, these could be questions involving projectile motion, Special Relativity (time dilation, length contraction etc), motor torque, forces on charged plates / conductors / charged particles etc. For Chemistry, these questions could be molar calculations, pH calculations, volume calculations, galvanic cell potentials etc.

Some topics in Physics could be assisted with methods covered in Mathematics subjects. For example, in the Space module, we learn how to do projectile motion calculations – these questions are much easier when analysed within the Extension 1 framework of projectile motion. Of course, it would be faster if you use the formulae in the formula sheet, but for checking purposes, you can use the Extension 1 method to verify your answers.

Science calculation questions often require the use of calculators, so not only do you have to check your algebra and working-out, you also need to check your final answer, making sure you didn’t key in something wrong on your calculator. A good tip here is to become very familiar with your calculator – learn how to use its memory slots so you can do an entire question very fast without needing to waste time writing things down (for checking purposes).

One last scenario that is unique to science HSC exams is that in some extended questions worth 5-8 marks (e.g. discuss, analyse, evaluate, assess), you may be required to identify a list of factors / issues. You should briefly re-read your long answer responses, making sure you’ve covered all the factors / issues that are required, and also check that you’ve concluded the question with an assessment or evaluation, if required. The final conclusion in assess / evaluate questions are worth a mark, and while this appears obvious to some students, many still make the mistake of leaving their questions unconcluded.

Maths exams

There are two approaches to doing maths exams, and which approach you choose depends on your style. Some students prefer to move through their exam as quickly as possible, leaving much time at the end to go over the entire exam again (where possible). Other students prefer to go through their exam as carefully as possible, leaving much less time at the end, for selective checking. There’s no right or wrong approach, and we have 99+ students who adopt either approach.

As a general recommendation, higher achievers should aim to do their exams as quickly as possible, with the aim of having enough time at the end to comprehensively go through their entire exam a second time. However, not all students are able to do this. The important thing is to be comfortable with your chosen approach.

As always, it is a good idea to circle the questions (on your question sheet) that you have difficulty with on your first attempt of the exam. This way, you can selectively check over those questions first as you begin checking your exam.

One important thing to note is that in maths, there are many little mathematical tricks that allow you to check your answer very quickly. For example, in Maths Extension 2, it is advised for students to memorise the general equations for tangents for ellipses and hyperbolae, as this gives them much convenience when verifying answers in algebraic form. If you’re familiar with the many properties of the parabola, this would help in guiding you through the difficult proofs involving parametric equations. In Probability questions involving Permutations and Combinations, sometimes it is easier to arrange a set of possible actions, rather than the objects themselves. These little tips and tricks cannot be explained properly in words, as they need proper examples to demonstrate, but students should pick these up throughout their study.

In Maths Extension 2, students who are serious about achieving a high mark (e.g. a raw mark above 100/120) should realise that they should not allocate their time linearly to the questions from 1 to 8. Basically, questions 1-4 should take 10 minutes each, tops, and questions 5, 6 should take 20 minutes each, leaving plenty of time for questions 7 and 8. It is your performance in these last questions that set you apart from other high achievers, since most Extension 2 students are perfectly capable of doing questions 1-6 relatively well.

Practice makes perfect

As with every skill in life, reducing the occurrence of silly mistakes can be improved through practice. Do more questions, and mark them! Follow up and investigate on the ones you did incorrectly, and redo them. Always challenge yourself with difficult questions. Never become ‘complacent’ just because you’re doing well compared to your peers at school. Always remember, you are up against the entire state.

Practicing for Physics and Chemistry

For science subjects, you’ll need to split your time doing essay-type questions (discuss, assess, evaluate), short answer questions (describe, explain, justify, outline) and the calculation type questions.

For calculation questions, make sure you understand the physical principles behind why the answer is correct. Become familiar with your calculator’s functionality, especially in using its memory slots, as this is extremely helpful when doing those annoyingly long molar calculations. Lastly, make sure you are exposed to all types of calculation questions for your subject. Doing questions from good books (like Jacaranda Physics, Macquarie Physics, Chemistry Contexts, Conquering Chemistry etc) are a great start, but they are not enough. Do as many past papers / practice questions you can get from your school teachers / HSC tuition services, and have them marked.

Practicing for Maths

For all levels of maths, the approach is the same – do as many questions as you can. Some books are better than others – it is important to do the exercises in good textbooks, like Fitzpatrick (2 unit and 3 unit) and Cambridge (2 unit, 3 unit, 4 unit). However, you should note that some of the hardest and most unique questions can only be found inside HSC exams. That is because HSC exams are often written by University professors, and the questions found in them can sometimes be something unfamiliar to you if you only study using textbooks. For example, Maths Extension 2 question 8s have always involved University-level maths and often require very unique and colourful approaches to solve – such uniqueness is often lacking or in short supply in even the best of textbooks. Our tip is to learn ahead of your school, and begin practicing by doing past HSC exams / past trial papers from reputable schools as early in your HSC as possible. The key here is to see as many types of questions as possible, broadening your experience as much as possible before each assessable exam.

One of our tutors who came 2nd in the state for Extension 2 claimed to have completed over 100 Extension 2 papers as practice, back when he did his HSC (he started before his half-yearlies). Another of our tutors who came 3rd in the state for Extension 2 (in a different year) claimed to have completed over 60 Extension 2 papers as practice. Obviously such dedication is not required for most students, even for a 99+, but for an ATAR close to 99.95 or a state-rank, dedication to gaining nothing short of a comprehensive and complete understanding of your subjects is necessary.

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