Should I choose a course similar on what I did in high school?

It always helps to choose a course that’s similar to what you’re already familiar with, but it isn’t necessary. Generally, if you choose a uni course that’s in the same field as many of the subjects you completed in your HSC, you will find first year rather breezy. However, it isn’t necessary at all because the vast majority of uni courses do not assume any knowledge on your part – everything is taught from scratch at the beginning of first year, albeit at a much faster pace than what you’re probably used to.

For example, if you did English Advanced, Maths Extension 1, Maths Extension 2, Physics, Chemistry, it’s perfectly fine for you to choose Combined Law if that’s what you want to do. Many typical HSC subject combinations that result in sufficiently high ATARs that allow you to get into courses like Combined Law have nothing to do with law (sadly Legal Studies doesn’t scale particularly well, so we have a peculiar situation where many first year law students have done well in Maths Extension 2).

Short answer: do what you want to do, there’s no need to limit your options based on what you did for your HSC.

I scored a high ATAR, should I only look at high ATAR courses?

This is related to, but rather the opposite situation of the first point. Many students who get a relatively high ATAR, say 95+, suddenly have an urge to ‘not waste ATAR’ and thereby limit their choices only to the uni courses with similarly high ATAR entry requirements. This is a dangerous thing to do because the choice you make here could define the career of your long term future!

We see a disproportionately large fraction of students with very high ATARs (99+) that end up doing Combined Law or Medicine. I’m sure many of them are genuinely passionate and interested in these courses, and will make great lawyers and medical practitioners, but surely just as many are there because they haven’t got much of a clue as to what they want in life, but were blessed with the ability to achieve such a high ATAR. For some of these students, things will work out – they will adapt and find that they enjoy and/or are good at what they do. But for the others, they may live to regret their choice years later, when they realise they have no aptitude or passion for the path they’re on. This can lead to long term resentment against their career choice, or the student having to cut their losses and transfer to an unrelated uni course a few years later, having wasted time and HECS (uni isn’t free, remember that!).

It’s never a good idea to base your uni course choice solely on what you can ‘buy’ with your ATAR. The ATAR entry requirements for uni courses reflect only the relative supply and demand for each course, but people should realise that most people in a crowd are just following the crowd – they have no idea what they want individually. It’s perfectly fine to choose the highest ATAR requirement course within the field you want to get into – for example, if you’re into Maths / Physics and are keen on doing Engineering, then by all means choose the highest ATAR cut-off Engineering course (usually ‘Aeronautical Space’ at USyd). But don’t choose Combined Law just because you can!

On this point, I should also mention that there’s no correlation between the ATAR cut off of a uni course, and the inherent difficulty of the course. ATAR cut off only reflects how popular a course is. Some courses with humble ATAR cut offs (e.g. Engineering, Science) are notoriously difficult, both in terms of the amount of contact hours required per week (this means how many total hours of lectures and tutorials you need to
attend) as well as the failure rate each semester. Generally speaking, an Engineering or Science student can expect to attend Uni 4-5 days per week, and a Commerce student can get away with 3 days per week (some semesters you can get a timetable that only requires 2 days per week!).

Short answer: if you have the luxury of a high ATAR, choose something you’ll enjoy and be good at. There’s no point doing a course like Medicine if you have no interest or passion for it.

Combined degree vs single degree

Another question I get quite often is whether to do a combined or single degree. In my opinion, both are fine choices – it depends on what sort of career you’re after. The advantage of a single degree is that it’s over faster, and you’re on your way to the next stage of life (working somewhere as a graduate for most) quicker, younger and with less of a HECS debt. The advantage of a double degree is you’re more well-rounded as an individual. It’s preferable to combine degrees that span a wider breadth of fields, rather than combine two very similar degrees. E.g. Engineering / Commerce would be a good choice. The goal here is to open as many doors as possible.

When you’re entering your penultimate and final years of uni, you’ll begin the arduous and often frustrating process of submitting applications for graduate roles at various companies. Doing courses that are practical in a wider range of fields opens more doors up. At the same time, it could be argued that being more specialised helps with being considered more favourably by employers, but from personal experience, employers care more about your work experience, your uni marks and how you conduct yourself in the interview.

Even if you change your mind later, it’s not too much hassle to switch from one to the other. Of course, dropping a course is easier than taking one up (you can always drop from Combined to Single degree). Note that as long as your marks are decent, (Credit Average should be sufficient for most streams, Distinction Average is definitely adequate) you’ll find that a transfer to a different degree structure will be possible.

Short answer: it doesn’t matter, both are fine choices, and switching from one to the other in the middle of uni wastes little or no time, and is pretty easy with decent marks.

What course should I choose?

I’ve left the most important till last. While I’m not going to tell anyone what degree to do, I can give some guidelines that will help you reach the right choice.

• Always do something you are personally passionate about and have an interest in. You won’t be good at something unless you enjoy it.
• Don’t worry about the money. In ANY field, if you’re good at it, money takes care of itself. One thing about the world is it’s full of average people. In whatever field, whatever career path, most people you encounter are average, and those that rise to the very top are invariably people with a genuine passion for their field. If you don’t do something you enjoy, you won’t be good at it, and in a free market society like ours, your earnings will always reflect the value you contribute to others. If you’re average like everyone else, you will make average earnings and be stuck in a career you resent. Do what you’d be good at, and money will take care of itself. “Find a job you love and you’ll never work a day in your life”
• Don’t assume this will be your career path set in stone. Life is serendipitous and full of unexpected twists and turns. Many highly successful gained their success from following their true passion rather than strictly applying their tertiary education (and I’m not talking about the Bill Gates and the Steve Jobs in the world, these are normal people like you!).
• Find out as much as possible about the degrees you’re considering, what sort of career possibilities they open up, and whether you’d enjoy the sort of work that entails. Research is key! Don’t just assume lawyers do the things you see on TV, or bankers all wear suits looking at the markets all day.

Short answer: do what you will enjoy. If you don’t enjoy your field, you won’t be good at it, and you’ll lead a very average and unexciting career path.

Since 2009 the Board of Studies has been in consultation with teachers around NSW to set changes to the way HSC mathematics courses are assessed and examined. The proposed changes have been announced and are ready for full implementation from 2012 onwards. This means class of 2012 (new year 12 students of this year’s term 4) will be the first year to be affected by these new exam structures.

The main changes are set out as below:

Mathematics (2 unit)

1. There will be 10 “objective response” questions worth one mark each. Sample question:

   

   Source: Board of Studies

Objective response questions are questions with a correct answer – usually in the form of multiple choice, but also can involve asking you to write a specific number in boxes.

2. There will now be six questions, each worth 15 marks. The paper will now be out of a total of 100 marks, to be done over 3 hours.
3. Each question will also contain short-answer parts.

Mathematics Extension 1

1. There will be 10 “objective response” questions each worth 1 mark, just like Mathematics 2 unit.
2. There will now only be four questions, each worth 15 marks. The paper is now a total of 70 marks.
3. Each question will also contain short-answer parts.

Mathematics Extension 2

1. There will be 10 “objective response” questions each worth 1 mark, just like Mathematics 2 unit.
2. There will now only be six questions, each worth 15 marks. The paper is now a total of 100 marks.
3. Each question will also contain short-answer parts

What could this mean for students?

The following is inferences I’ve made as to the practical implications of these changes, they are my opinions and not based on studies or facts. I invite you to consider my arguments and form your own opinions.

Intuition will be rewarded

The introduction of 10 marks worth of objective-response (mostly multiple choice) questions can be of benefit to some students. Many maths questions give a clue as to the correct form of the answer – students with a good intuition can often ‘sense’ what the correct answer looks like, and introducing multiple choice questions will benefit such students.

Silly mistakes are less severely punished

Students who are less careful with their work and often make ‘silly mistakes’ will also benefit from multiple choice questions. Errors that are carried forward are less likely to lose you marks if you’re dealing with multiple choice. However these benefits are limited to the first 10 marks of section 1.

More time for less marks

According to background information published by the Board of Studies, they seem to be aiming to do away with the current ‘speed test’ style of the calculus-based exams, hence why they are reducing the total number of marks while allowing the same amount of time for all three exams (Mathematics 2 unit from 120 marks to 100 marks, Extension 1 from 84 marks to 70 marks, and Extension 2 from 120 marks to 100 marks).

This is unfortunate because relaxing the time limit on these exams will make it harder to differentiate the top students from the rest. A student who is familiar with all the topics and has studied hard before their exam will have no problem with the old time requirements, so relaxing the time limit makes the exams unnecessarily easier.

Reasons behind the change

There are a couple of reasons behind these changes, namely:

1. A varied format makes things fairer: the Board has been trying to change the format of maths exams to appeal more fairly to a wider variety of students. By having a more varied format, it can be argued that the exam is now fairer to a wider variety of students.
2. Cost reduction: before 2012, the marking centre needed 8 teams of markers to mark a maths exam, now they only need 6 teams (1 for each question) and multiple choice can be marked by computers.
3. Exams marked out of 100: the Board argues that since other subjects (Biology, Chemistry, Physics) can be marked out of 100, there should be no reason why maths exams cannot. Making the exams marked out of 100 adds minor conveniences to the marking process.

About the author

Matthew Lim is a mathematics tutor at Dux College. Apart from taking several classes at our Parramatta location, he is also involved in course materials design.

Here are some tips for how to make the most of the last couple of days studying before your big exams.

In what order do I study for my subjects?

Look at your exam timetable and work out which exams come first and so on. The 2011 HSC timetable is available here. Generally, it’s advised that you study for your last exam first, and your first exam last, that way you are studying for your first exam till the very last day before the first exam.

For example, for most people, English paper 1 and paper 2 will be their first exams. This means you should leave studying English till last, so that the content will be freshest in your mind just before 18th October when you sit paper 1, and the following day when you sit paper 2. For most people, there will be several days in between your next exam after English, so you can use these days to revisit the subject to be examined next. Don’t rest too much after each exam! The clock is ticking fast to your next one.

English – a tip for everyone

In paper 1, you have three sections. The first is short answers, the second is a creative writing task, and the third is almost always an essay (sometimes a speech, but usually an essay). You should do the essay first, then the short answers, and finally the creative writing task.

The reason is simple: in case you find yourself running out of time by the time you completed 2 sections, the creative writing tasks is the most forgiving section in that scenario than any other section. You can potentially grab most of the available marks in creative writing as long as your story contains all the necessary elements of a well-written story, and captures belonging in a meaningful way. But the same can’t be said for the essay – if you spend only 30 minutes on it, you would probably only be able to put in 75% of the points required.

Mathematics

The best advice for all levels of maths is to do as many past papers as possible. If you’re aiming for a band 6, focus on the question 7 and 8 (if you’re doing Maths Extension 1 or Maths Extension 2) or question 10 (for 2 unit students). These are the questions with the most creativity, and are the most difficult – getting good at doing these questions will differentiate you from the rest.

For the many maths (2 unit) students, remember not to neglect some commonly forgotten bits of info that will cost you easy marks:

• Simpson’s rule
• Trapezoidal rule
• Trigonometry exact values
• Sine and cosine rule (you learnt this in year 10 but it will be needed sometimes!)

For higher levels of Maths (Ext. 1 and 2), know your integration substitutions. It’s easy to forget which situations demand which technique.

All questions are of the same value, but are in increasing difficulty. Try to go through the exam as quickly as possible the first time around, and skip the questions where you can’t immediately see the path to the answer. Then use the time left over to focus on the skipped questions and also check your work. Don’t get too comfortable with a slow pace at the early questions!

For extension 2, some less obvious things that will help you are: know your speed of curves (helps with graphing undefined / undefined situations), know how to apply LIATE (google it if you’ve never heard of it!) for integration by parts – to work out which bit to set as u and which to set as v.

Don’t lose focus

Think about this: each HSC exam you do now is worth the total of everything you’ve done for that subject at school for the entire year 12. All the preparation you put in for your half yearlies, trials and assessment tasks throughout year 12 – each exam now is worth the total of all of that for one subject. That’s why, now is the worst time to lose focus. You’re at the home stretch now, but your focus and dedication is needed most here.

On the other hand, it’s important also to not get too stressed out. Stress is good – it leads to productivity, and this short term stress before these big exams is normal, but don’t let it negatively affect you. Do your best, and you will be fine.

The life ahead

Don’t lose perspective – there’s a bright future waiting for you regardless of how things go now. Do try your best, but don’t think it’s the end of the world if you don’t get the ATAR you need. There are alternative ways of getting into the Uni course you desire.

Which subjects should I choose?

If your goal for the next two years is to maximise your ATAR, our advice to you is: choose the subjects you think you'll be good at among the subjects that offer decent scaling. Now as with most things in life, there are exceptions to this statement which we'll cover later. But before we continue, let's have a quick look at how HSC scaling works.

A crash course on HSC scaling

The way scaling works is raw exam marks at the end of year 12 are converted into scaled marks. This is to allow a direct comparison between graduates doing different subjects – sort of like swapping all of the world's currencies to a single currency so values can be compared.

Scaled marks are different to your HSC marks (actually they have nothing to do with each other, other than both being derived from your raw marks). In a nutshell, scaled marks are what determines your ATAR, so if your sole goal is to maximise your ATAR and get into the university course you want, maximising your scaled marks should be your goal for the HSC. At the end of year 12, a graduate does not see what scaled marks he or she scored, only HSC marks are shown. However their ATAR is calculated based on their scaled marks, that's why scaled marks are what's important.

How well a subject scales determines whether your raw exam marks will be pushed up or down, and by how much, when being converted into scaled marks. Doing subjects with low scaling will mean you'll need to score higher marks and higher percentiles to obtain the same scaled marks as doing subjects with higher scaling. To find out how well different subjects scale, we need to look at Table A3.

Table A3

The latest Table A3 (as at time of writing this article) is here

Table A3, entitled "Descriptive statistics and selected percentiles for HSC marks and scaled marks by course" is a set of statistics published by the UAC each year, after their Report on Scaling is published. The latest Table A3 (as at time of writing this article) is here – just Google ‘table A3' for the latest one.

Table A3 shows the HSC and scaled marks for each subject at various percentile levels, as well as the means (averages). The figure to pay attention to is the scaled mean for each subject. The scaled mean is the average scaled marks achieved per unit among the candidature of that subject for that year. For example, HSC Biology had a scaled mean of 26.9 in 2010, this means the average Biology student graduated with 26.9/50 scaled marks per unit, or 53.8/100 for the subject. The scaled mean is also an indicator of how high the subject scales, and whether it ‘scales up’ or ‘scales down’ in common schoolyard parlance.

The average scaled mean is 25 (due to the standardisation method used to convert raw marks into scaled marks). Therefore, it can be said that subjects with a scaled mean of > 25 have ‘above-average scaling’. So back to our example, Biology with a scaled mean of 26.9 scales slightly better than the average subject. Generally anything with a scaled mean beyond 30 is a good and safe choice. Some of the more common subjects that meet this criterion are:

• English Advanced (32.5)
• English Extension 1 (36.4)
• English Extension 2 (36.3)
• Mathematics (30.7)
• Mathematics Extension 1 (39.8)
• Mathematics Extension 2 (43.8)
• Physics (30.5)
• Chemistry (31.7)
• Economics (31.0)

Now having said all that, remember we said you should choose the subjects you would be good at amongst the subjects the subjects that scale well. You'll be worse off if you chose a subject purely for its scaling, although you're terrible at it

Relative difficulty in achieving the same scaled marks

Table A3 also tells us something interesting. If you look at the scaled marks achieved for each percentile, and compare these across 2 or more subjects, you can get a picture of the relative difficulty in achieving the same result.

For example, say you're considering 2 subjects, and must choose one or the other but not both. Say the subjects are Chemistry and Senior Science.

If you achieved the 90^th percentile in Senior Science (meaning out of 100 randomly selected students, you beat 90), you would obtain 32.8/50 scaled marks. You would have obtained more scaled marks if you achieved the 25^th percentile in Chemistry instead (34/50). So ask yourself, is it easier to beat 90 out of 100 students in Senior Science, or 25 out of 100 students in Chemistry? Of course, the difference in scaling between these two subjects highlights that Chemistry has a higher quality candidature than Senior Science, but the difference between 90^th and 25^th percentile is big enough to more than compensate for the fact that you're up against a higher quality candidature in Chemistry than in Senior Science.

Lets look at another example. Say you're considering between Agriculture and Mathematics (2 unit) Here are the Table A3 stats for both:

From the table, if you achieved the 90^th percentile for Agriculture, this wouldn't even give you as much scaled marks as if you achieved the 75^th percentile in Mathematics. Now the difference here isn't as remarkable as the previous example, but it still highlights the point – do you feel 90^th percentile in Agriculture is easier or 75^th percentile in Mathematics is easier?

Not to mention Agriculture's scaling stats are probably skewed positively by selective schools like James Ruse, Hurlstone etc that like to accelerate their year 11s to finish their HSC Agriculture each year – if you take the achievements of these schools away, the true scaled mean is probably much lower.

Let's look at one more example, this time say you're wondering whether you should choose Maths Extension 1 (with intention to do Extension 2 in year 12) or stick with Mathematics (2 unit).

The first thing that might jump at you is the super-high scaled mean for Maths Extension 2 – indeed Maths Extension 2 is the highest scaled HSC subject (out of all the commonly available ones, excluding certain language subjects). If you did Maths Extension 2, even achieving in the 25^th percentile would mean you score more scaled marks than someone achieving the 90th percentile for Mathematics (2 unit). Think about that for a second! It's more beneficial to your ATAR to achieve only the 25th percentile in Extension 2 than it is to achieve the 90^th percentile in Mathematics (2 unit)!

One more thing – if you do Extension 2, your Maths Extension 1 counts for 2 units instead of 1 – so the marginal positive effect of taking Extension 2 to your ATAR is even greater because Extension 1's scaling is so high as well (excluding certain language subjects, Extension 1 is the second highest scaling subject). That's why most 99+ ATAR scorers have done Maths Extension 2 – it's simply the ‘easiest’ way to score a 99+ ATAR. This, combined with Extension 2's extremely high scaled mean, is why we advise all our students to take it up if they are capable at maths.

Common misconception: lots of students seem to think if they do a hard subject like Maths Extension 2, if they do poorly they may actually be ‘scaled down’; instead of up.

This is incorrect as you can see from the table above. Scaling only occurs in one direction regardless of what percentile you achieve. For Maths Extension 2, you'll get pushed up even if you only achieve the 25^th percentile, which results in a 42.3/50. A 42.3 is easily a mid-high band 6 in most other subjects, but maybe a band E2 for Maths Extension 2. My point is even if you do relatively poorly in a hard subject, you still get the benefit of its high scaling.

When should I ignore scaling in choosing a subject?

The only time you should not pay attention to the scaling statistics of your subjects is if you know you can do so well in a subject that, despite its low scaling, the scaled marks you achieve will be greater than what you could have achieved in an alternative subject. Or in summary, only ignore scaling if you're extremely good at a particular subject. It's difficult to tell whether you'll be really good at something before actually starting year 11, so our advice is to ask teachers and past students to get an idea of what sort of skills are needed to succeed in a particular subject.

For example, suppose you're considering between Food Tech and Physics:

Physics is the safe choice, but suppose you're really passionate about Food Tech. You need to be confident that you can achieve, say, the 90^th percentile in Food Tech as opposed to around 65^th percentile in Physics (to achieve the same scaled marks). There's quite a gap in percentile for the same amount of scaled marks, but if you're confident you'll be really good at Food Tech, then go for it.

Even if you’re not aiming for such a high ATAR, doing well in any level of mathematics will get you closer to your goal in no small amount.

With every subject, there’s the content, then there’s technique. This fact is especially significant in maths extension 2 – things like knowing shortcuts / quick methods to verify the correctness of answers, how well you know your way around your Board-approved calculator, how well you understand the marking process and how to get partial marks, etc.

We all know the commonly told tips that your teachers at school have no doubt told you many times by now (e.g. writing partial answers for partial marks). Here’s a few lesser known tips our maths tuition classes give our students as part of our Extension 2 maths course:

1. Volumes – easy way to check answer for volumes

Here’s a useful tip for the Volumes topic in Maths Extension 2 – Pappus’ Centroid Theorem. This theorem states that the volume of a solid of revolution generated by rotating a plane figure about an external axis is equal to the product of the cross-sectional area and the distance travelled by the cross section’s centroid.

Using this theorem, we can calculate all questions involving rotating a shape around an axis (e.g. circle around an axis to produce a torus) simply by finding the area of the cross section, then multiplying this with the distance travelled by the centroid of the cross section. It’s much quicker and reliable (because it’s simpler – less can go wrong) than using any of the prescribed methods, e.g. cylindrical shells or adding slices.

For example, what’s the volume of a circle, centre origin, radius 4, rotated about the line x=6? The answer is simply: the area of the circle – 16π multiplied by the distance travelled by the centre of the circle, which is 12π. The volume is therefore 192π^2 or 1894.96 cubic units. You can verify this with the cylindrical shells method.

Of course, in answering an exam question, you need to use the cylindrical shells method. The Pappus’ Centroid Theorem is just a useful tool to quickly check the correctness of your final answer. If there’s disagreement, you know you need to check your answer, and this would have easily saved you some lost marks!

1. Volumes, integration and other applications – the area of an ellipse and the volume of an ellipsoid

Here’s another tip to make you quicker at checking your integration results. It’s also helpful for other topics (e.g. volumes).

It’s a good idea to memorise the area of an ellipse:

And the volume of an ellipsoid:

These are not too hard to remember because in the special case of the circle and sphere, r=a=b and r=a=b=c respectively, which causes both equations to reduce to the equations of the area and volume of a sphere respectively.

There are occasionally situations where you have a definite integral you need to evaluate, where the expression to be integrated is in the form of an ellipse. For volume questions, solids of rotation would often form ellipsoids and knowing the simple formula could give you a quick tool to check the correctness of your answer.

1. Don’t be afraid to include explanations as part of your solution

Here’s a tip our extension 2 maths tutors love to give our students. In many situations in mathematics, especially in maths extension 2, some explanation saves you a lot of calculation.

For example, if you’re doing an integration and the form is that of a circle, instead of going through the x=sinα substitution, it’s easier to just write “This represents the area of a semi circle with radius r” – that’s all you need, then you can write the answer. Or if you need to evaluate a definite integral of an odd function with symmetrical limits, then the answer is always 0.

Sometimes you need to take cases – explain why some cases are impossible and this will save you time because you don’t need to cover them. Sometimes a graphical solution will show why one graph will never intersect another graph (hence no real roots to a related equation). The point I’m making is explanation goes a long way. The entire Mathematical Induction topic in 3 unit is based on explaining rather than using purely numbers, symbols and algebra.

Another situation would be proof questions (and we get many of these in Extension 2) that require you to prove LHS = RHS. Instead of starting somewhere random, you can start with what you’re trying to prove and write “If the above is true (what we’re required to prove), then:” and you can proceed to manipulate what you’re trying to prove. Just write ‘Then’ at the beginning of each line to signify you haven’t proven it yet, but if the original LHS = RHS, THEN so far these lines of working must all be true. Eventually, when you reach a situation that is in fact true (e.g. 1=1) then you’re finished, just write “And since the final line is true, the original LHS = RHS).

1. Integration by parts – LIATE

We all should know how to do integration by parts by now – but sometimes choosing which one should be u and which should be v can get tricky. A reminder, here is the definition of integration by parts:

OR

Choosing which one should be u (or f(x) if you prefer the first line) is an important decision – choose the wrong one and you’ll waste precious exam time going down a path that may lead to an impossible integral.

The general rule of thumb is to remember LIATE. LIATE stands for:

• Logarithm
• Inverse trigonometric functions
• Algebra (general polynomials)
• Trigonometric functions
• Exponential

You should give preference to the left-most function to be set as u. The reason for this is as you move from the left to the right in LIATE, functions become easier to integrate, so you should prefer to integrate the easy ones (e.g. trigonometric functions and exponentials are easy to integrate) and differentiate the hard ones (e.g. logarithms can’t easily be integrated).

1. L’Hopital’s rule

In the Graphs topic, there are many compound graphs that give rise to situations where you have infinite multiplied by 0. When this limit occurs, 3 possibilities arise:

• Graph turns to 0
• Graph turns to infinite
• Graph turns to a constant

To find out how, we suggest to students to learn how to use L’Hopital’s rule to discover the relative speed of curves. This rule only applies when the limit below turns to infinite or negative infinite, or 0.

For example, lets see what happens to the graph at y=xlnx close to x=0. We set f(x) = lnx and g(x) = 1/x so that f(x)/g(x) = xlnx. When we evaluate the limit for f’(x)/g’(x) we find it equals (1/x)/(-1/x^2) which equals –x. This would turn to 0 as x approaches 0 so this shows the graph y=xlnx turns to 0 instead of negative infinite at x near 0. Incidentally, this is also one of our HR manager’s favourite questions to ask potential candidates for maths tutors, even if they tutor lower levels of maths (you’d be surprised how many people apply to be a mathematics tutor but can’t even graph y=xlnx).

1. Use your calculator memory effectively

Become proficient in the use of your Board-approved calculator that you can take with you to the exam room. If you’re swift with using your calculator’s memory slots, this makes rechecking over your answers so much faster and accurate (if you happen to finish your exam with 20 minutes to spare, you can literally go through the entire exam once or even twice! If you’re good with your calculator, that is). And this helps even more in subjects like HSC Physics and HSC Chemistry where there’s lots of calculator work that requires a final definite numerical answer.

Another reason is exact values. Your calculator’s memory actually stores something to the order of 100 digits (much more than what’s only shown on screen when you press ‘=’). Sometimes when you’re supposed to get an exact value, if you put in your written down answer (that’s only rounded to 3-4 digits at most) you will get some answer like 1.99837734 but if you subbed in your memory-stored calculator, you will get an exact value of 2. In complex questions, even simple clues like knowing something is an exact value could be the difference between doing the question and skipping it altogether.

1. Multipart questions (attempt part 2)

We should all know to be able to attempt the next subpart of an exam question by now. E.g. if you can’t do part a, which required you to prove a result to be used for part b, you should use the result to do part b so that you can still score partial marks for the question.

Sometimes even within a single part worth multiple marks, there are two parts to the question (e.g. “Show that LHS = RHS and hence derive an expression for acceleration of the particle.”) In these examples, if you can’t do the question as they intended, just use the result you’re given and finish the second part of the question for partial marks. If the question was worth 3 marks, you should at least get a mark for your efforts.

1. Maths tutoring helps

Sometimes if you’re stuck with a teacher at school that’s not very knowledgeable, it would be wise to seek outside help. This situation is particularly common in disadvantaged schools – not all schools even offer extension 2, and for schools that do, not all their teachers assigned to the course are actually capable of teaching all parts of the course effectively. Getting outside help also gives you an important advantage over your peers when it comes to internal assessments (where you’re up against your peers for the top assessment ranks).

Learn to use the HSC Standards Packages

For almost all HSC subjects, the Board of Studies has standards packages publicly available for students to read http://arc.boardofstudies.nsw.edu.au/go/hsc/std-packs/. We recommend students look at the standards packages for their subjects – they will give you an idea of the quality required for a band 6 response. Standards packages are particularly useful for humanities subjects like HSC English where your expression and writing style also come into play. Get a feeling of what’s acceptable expression, and details like general paragraph length, the way literary techniques are referenced, how often a text is quoted and the length of quotes etc. Even if technically your knowledge is as good as anyone’s, a poorly structured essay (where you use poor expression, or reference the text in superficial ways or spend too much time on insignificant points etc) will mean the difference between a band 4/5 and a band 6.

Familiarity with the standards packages will also help with subjects like HSC Chemistry, Physics, Biology and the social sciences (Economics, Business Studies etc). In the case of the HSC Sciences, they give you fresh ideas of novel, acceptable ways of structuring your answer. Some questions can be fully answered in terms of a table or as a dot-point list (e.g. identify / outline questions). Also note the details featured in diagrams / graphs – full marks are given to students that remember details such as labelling the axes, or drawing a line / curve of best fit properly (ignoring outliers in appropriate situations) and being able to justify the choices made.

HSC sciences – always refer to the syllabus

HSC sciences like Chemistry, Physics and Biology, are prescriptive by nature. This means the syllabus tells you exactly what you need to know, content wise, and does a great job at that. While studying for these subjects, it’s always a good idea to have the syllabus in front of you, printed or on your computer screen. The dot-points give you a clear picture of what you need to know, and the scope to which you need to know each aspect of the course. For example, if a dot-point requires you to merely identify the qualitative aspects, this means you only need to be able to name the aspects it’s referring to, and qualitative means you won’t be required to do calculations on them.

Another reason is some syllabus dot-points are worded as if they are paraphrased exam questions. This is particularly true for dot-points requiring you to ‘Discuss the impacts on society of…” or “Assess the environmental impact of…”. You very well might get an exam question, worth around 7 marks, that basically asks you to demonstrate your entire understanding of one of those dot-points if they ask you in a general way.

Be careful for internal assessments however, as school teachers are known to set exam questions that are dubious in terms of whether they fit within the scope of the syllabus, so you must also cross reference your own materials with the notes given by your school teacher to make sure all gaps are covered.

HSC Maths – only do exam questions

When it comes to maths, exam questions and textbook questions aren’t the same. The former type are often are structured as a compound question with several subparts. Exam question are often designed with deeper consideration, and incorporates more unique aspects of mathematics (e.g. in Maths Extension 2 question 7 and 8). In contrast, textbook questions can get repetitive and give you a false sense of security. Because textbook questions lack variation in style, once you master the several types of questions it contains and are able to do its exercises, this does not mean you’ve experienced all types of questions an exam can throw at you, particularly if you go to a school that has a talented maths department.

There’s a limitation on the types of questions for each topic an exam can throw at you. If you do Maths Extension 1 and 2, it also takes great effort and skill to design a truly novel and unique maths question at that level. As an industry insider (yes I’m a teacher) I can tell you that many schools simply take exam questions from past papers of other schools. When I did my HSC Maths Extension 2, I actively sought out past trial papers from top private and selective schools for practice before my HSC trials. What I noticed was in one year, say 2002, there would be a question in school A’s paper, then in the next year, say 2003, there would be an identical question in school B’s paper. So it’s a good idea as a student to use past papers as practice – there’s definitely more exam papers worth doing than your time would permit, that’s why I recommend only do exam papers instead of textbook questions.

I spoke with a teacher who works at a top Sydney selective school about how their teachers set exam questions for their year 12 students – “We get exam questions from schools that are out of NSW – resources we know typical students don’t have access to”. So while exam questions are definitely recycled, they aren’t always from sources you’d expect. But it’s still worthwhile doing exam papers for practice, purely for the sake of familiarising yourself with the general style of exam questions which you can’t get from any old textbook.

For the HSC Physics syllabus dot-points:

• Perform a first-hand investigation to demonstrate the motor effect
• Perform an investigation to model the generation of an electric current by moving a magnet in a coil or a coil near a magnet
• Plan, choose equipment or resources for, and perform a first-hand investigation to predict and verify the effect on a generated electric current when: the distance between the coil and magnet is varied, the strength of the magnet is varied, the relative motion between the coil and the magnet is varied
• Plan, choose equipment or resources for, and perform a first-hand investigation to demonstrate the production of an alternating current

For the first dot-point, we wound wires five times, threading each loop through the region between two strong permanent (neodymium) magnets. We then applied a current of 3 amps through the wire (our power supply was auto current-limiting so no excessive heat was produced). With 5 loops threaded, each with 3 amps, the total effective current was 3×5 = 15amps, and a movement of the wires were observed. The direction of force on the wire was as predicted by the right-hand push rule (aka right-hand palm rule).

For the second dot-point, we tested each condition (distance, strength and speed of magnet) on a coil connected to an ammeter and we observed a direct correlation between strength of magnet and induced current, a direct correlation between speed of magnet and induced current, and an inverse correlation between distance of magnet and induced current.

For the final dot-point, we moved a magnet in and out of a coil connected to an ammeter. The ammeter needle’s direction of movement continually reversed, indicating that an alternating current was produced. We also used a hand-wound AC generator to power an incandescent light bulb.

Experiment two: Transformers and Induction motors

For the HSC Physics ( http://www.duxcollege.com.au/ ) syllabus dot-points:

• Perform an investigation to model the structure of a transformer to demonstrate how a secondary voltage is produced
• Perform an investigation to demonstrate the principle of an AC induction motor

For the first dot-point, we constructed a model transformer using a 300 turn coil as the primary and a 600 turn coil as the secondary. Primary voltage was 18V AC and the secondary voltage was measured (by an AC-capable voltmeter) to be approx 35V AC when using laminated iron cores. The secondary voltage was observed to fall significantly (around 22V) when laminated iron core was replaced with a solid bar of iron (more eddy currents were possible with unlaminated iron core, decreasing efficiency of the magnetic flux transfer). We then switched the primary and secondary coil so that the primary was now 600 turns and the secondary was 300 turns. The secondary voltage was measured to be 8.5V AC. The percentage inefficiency was calculated to be the same in the step up and step down versions.

For the secondary dot-point, we constructed a single phase squirrel cage induction motor. Single phase induction motors generate initial torque due to the presence of shading coils. These coils delay the flux transfer at carefully chosen parts of the surrounding stator so that the initial change in flux produces a torque on the rotor. The squirrel cage core is not connected to any electricity — it moves only due to Lenz Law — it chases the external rotating magnetic field. We observed that the speed of the induction motor was at its highest if using a laminated core. When we changed the orientation of the rotor so that flux has to pass through a section of air, we observed the motor slow down significantly. When we bridged this gap with a solid iron bar, the rotor sped up slightly, but was still slower than its original speed. This again illustrates that air and iron bars are not as effective in transferring magnetic flux as laminated iron.

HSC Biology first-hand investigations coming soon!

1. Exam question asking for correct procedure, safety issues, sources of error, or other related discussion
2. Practical exams

Practical exams are particularly important because all students will definitely have at least one in year 12, and they are often worth around 20% of total internal assessment. We recently filmed some of our in-class practical demonstrations of experiments that are most likely to come up in practical exams at school.

In addition to learning the theoretical content of the course, students should remember not to neglect preparing for first-hand investigations and other practical skills-based dot-points that are in the HSC Chemistry or Physics syllabus. These dot-points can be examined in one or several of the following ways:

Exam question asking for correct procedure, safety issues, sources of error, or other related discussion

Practical examsPractical exams are particularly important because all students will definitely have at least one in year 12, and they are often worth around 20% of total internal assessment. We recently filmed some of our in-class practical demonstrations of experiments that are most likely to come up in practical exams at school.

HSC Chemistry

Perform a first-hand investigation and solve problems using titrations including the preparation of standard solutions, and use available evidence to quantitatively and qualitatively describe the reaction between selected acids and bases

This experiment is important because it is one of the most commonly chosen experiments for Prac Exams. Prac Exams could come any time throughout year 12 — but most of the time they occur as part of your trial HSC exams, and usually worth around 20% of total internal assessment. Therefore it is important to pay close attention to proper titration procedure and understand the underlying processes of neutralization reactions.

For this titration, our unknown was a solution of NaOH (the analyte) and our standard solution was oxalic acid (crystals in dihydrate form) — the titrant. Glassware was rinsed properly with either deionised water or with the solution it was to contain (conical flask, volumetric flask — water / pipette, burette — solution). A total of 1 ‘rough titre’ and 3 accurate titres were done. The average of the 3 accurate titres were recorded and used to finally calculate the concentration of the unknown NaOH. Our indicator was phenolphthalein due to its slightly basic endpoint (the titration was between a strong base and a weak acid, therefore the equivalence point would be slightly basic). Tip: If required to make your own standard solution, make sure you design your standard solution so that it was enough moles for you to do 3 titres.

How many times have you left an assessment task to the last minute because you didn’t pace yourself correctly, or you submitted low quality work / received low marks due to being overwhelmed by exams and assessments?  Have a read of the following insights and think about what you can do to improve your time management skills – this will surely be one extracurricular skill to have that will translate to higher marks!

Urgent vs. important

Firstly understand the difference between a task that’s urgent, and a task that’s important. One thing that separates successful people from the rest is that successful people spend most of their time doing important things, rather than urgent things. For example, on any given day you may have one or several friends on facebook to reply to, send birthday reminders, or reply to people saying ‘hi’ on msn – these are all urgent, non-important tasks. Stop doing these things!

Important tasks are things that count. For example, studying for your school assessments / exams – it’s a certainty that you’ll need to do that assessment or exam so why ignore it until the last minute? Starting that assessment task now rather than later – you’ll eventually need to do it so why not start sooner rather than later? Do you really need to stop everything and get distracted by ‘urgent, non-important’ things like if your friends are inviting you to join their multiplayer online game, or your dog needs a walk, etc? Obviously we’re not saying ‘lock yourself in your room and study for 18 hours a day’ – you need to strike a clear balance between study and recreation (see next point).

Set clear boundaries: work while it’s work time and rest while it’s rest time

It’s important to find a good balance between work and rest. Set a clear time of the day after which you’re ‘off the clock’. This time should be dedicated to leisure. Avoid things that remind you of work – e.g. you could have all school-related stuff in your study room, and keep your bedroom free of any school-related material, or keep your school-related material in your room and spend your leisure time in your lounge. Resting and working in the same room could be stressful as you can be interrupted by emails, msn messages from friends who stress you out, or simply glancing at unfinished assignments left on your desk. Just like work, rest is best done without distraction in order to fully regain energy for the next day.

Also never plan to do important tasks in your ‘spare time’ – there’s no such thing as spare time and if you have this habit, you’ll certainly leave many tasks undone and neglected. You’re either working or resting, both activities are important to maintaining a healthy and sustainable work ethic.

The 80:20 rule

Also known as the ‘Pareto Principle’ or the ‘law of the vital few’: when applied to the field of time management, this ‘rule’ states that 80% of your results come from 20% of your actions. While there’s no mathematical significance of the 80:20 split, this rule alludes to the non-linear return of time invested – i.e. if you only put in 50% of your effort, you will get close to 0% of the results. But if you put in 100% of effort, you will get 100% of the results. That’s why it’s important to invest as much effort as you can, maintain a sustainable healthy work ethic throughout the year, and not be distracted by non-important tasks.

Keep a todo list and follow through with your plans

All effective time-managers keep a todo list. Split your tasks into 3 categories and put a number / letter next to them to remind you of which they belong to:

1. To be done within the day
2. To be done within the week
3. To be done within the year

Your student diary can fulfil this task. In our modern age, you can also consider using your iphone to synchronise with google docs so that you have access to your todo list everywhere (while at school, or on the train etc).

Watch your sleep

The human body works most efficiently when you maintain a constant sleep schedule. Sleeping at around the same time every night (not too late) will ensure you’re energetic and motivated during the day. It’s impossible to follow through with any time management plan / todo list if you’re lethargic all day. As a general rule, aim to reserve 8 hours of sleep each night – and you can’t sleep bank (i.e. sleep 6 hours for 3 nights, then 10 hours over the weekend) – it doesn’t work and will leave you fatigued and unmotivated during the day.

About the Author

Terry Wu is a maths tutor at Dux College. Having achieved an almost perfect ATAR himself in 2009 and HSC state ranks, he is an expert at time management and study skills. He is a passionate advocate of the ability for students to do well in the HSC through ‘acquired skills’ such as effective time management, effective study skills and learning exam technique.