5 Methods for Studying Mathematics

[jamonwindeyer]

Hey Jamon,
I have been doing quite a few past papers throughout the year and I've realised my biggest weakness in extension 1 is circle geometry questions. I've memorised all the properties of the circle and generally when I look at the worked solutions they make sense however I never seem to be able to see a way of solving these questions when I look at them. Do you have any advice or any tips on how to approach geometry questions specifically circle ones??

Thanks in advance 

Hey hey! Jake's post covers everything I'd say, but as an additional piece of advice, do Geometry questions last if you struggle with them! I certainly did too, and I always left them until last this way you get the easier marks out of the way, it's all about mark maximisation

[Blissfulmelodii]

Hey! Clearly not Jamon, hopefully you won't get too offended aha.

My general tips for circle geometry is to just write out any information that you can based on the formulas/relationships you know. Write it out in full, using proofs/brackets etc. but also plot the information you find on the diagram you've drawn into your writing booklet. Over time, you should be able to see where you're going; ie. what pieces of information link to other bits of the diagram, and how an answer can pop out of that. Even if you don't get the answer, you'll get the bulk of the marks, because you've done the bulk of the work!

The other way to answer a question is to work backwards. Assume that what you're being asked to prove is true, and then see what happens if it is. Will another angle be equal? With sides be the same length? Once you've figured that out, you know exactly what you need to prove! Then, do the first suggestion above to GET to this proof.

Let us know if we can help with specific questions! Everyone struggles hard with this section, so don't feel alone

Jake

Not at all! thank you so much for replying
I know my teacher has told me in the past to prove what you know and go from there (i.e. if your asked to find an angle, find all the other angles that you know until the one you require is obvious) is that kind of what you are saying?

The working backwards part actually makes a lot of sense, thanks

[jakesilove]

Not at all! thank you so much for replying
I know my teacher has told me in the past to prove what you know and go from there (i.e. if your asked to find an angle, find all the other angles that you know until the one you require is obvious) is that kind of what you are saying?

The working backwards part actually makes a lot of sense, thanks

Yep, that's pretty much what I'm saying! However, by working backwards even a tiny bit, even some of the time, you can kind of 'zoom in' on the sort of information you decide to find; if you know you need to find an angle, perhaps you can focus on getting out the two other angles in that triangle etc. Like Jamon said, these questions are often really difficult, and most students leave them until last. That being said, don't not answer the question just because you don't think you'll get it; at the very least, write down as much as you can to gain a couple marks here or there

Glad we can help! Let us know if you have any other questions.

Jake

[SSSS]

Hey. I have been really stressed because I'm doing the hsc in 2017 Anyways, apparently prelim is SO IMPORTANT FOR HSC in maths but I regret that I didn't spend a lot of time on maths. Is this true? If so, what should I do? I have an assessment in 9 weeks

[RuiAce]

Hey. I have been really stressed because I'm doing the hsc in 2017 Anyways, apparently prelim is SO IMPORTANT FOR HSC in maths but I regret that I didn't spend a lot of time on maths. Is this true? If so, what should I do? I have an assessment in 9 weeks

When people say "so", they are probably exaggerating. But mathematics is a subject where the preliminary course is not to be neglected. This is because up to 20% of what is examined on the final exam may be preliminary content.

Mathematics is the only subject where preliminary content can be examined in the HSC. This does not apply to any other course.

If you have an assessment task in 9 weeks and the whole of the preliminary course is on it then that is ridiculous. This assessment task should only consist of topics you've had thus far. On the other hand, you can very well be examined on some preliminary stuff in the half-yearly exam.

Many students who play their preliminary year out poorly still perform well in their HSC year anyway, regardless of the subject. This is because Year 11 does not count, and Year 12 gives you all the opportunity you need. That being said, it does mean that throughout the year you need to direct your studying techniques to cater for all the preliminary content that hasn't sunk in. There is absolutely no reason to stress at all, because there is time. However it's something that you can not neglect.

[rinagee12]

I like the idea of speeding through basic questions - definitely going to try it  Somehow I managed to scrape into the high 80s/low 90s with my school assessment mark even though Maths has always been a weak point for me, and I know feel like the truth of it is going to show in the exam next week. I still struggle with grasping some of the fundamental concepts and keep losing marks over silly errors in my calculations. I find that watching YouTube videos on maths has helped significantly. In jogging my memory, pointing out the common pitfalls when solving problems and maybe increasing my chance of getting a few marks

[MagmaMeerkat]

Hey! Any tips to go about the actual exam in terms of question order/timing??

I prefer to go straight to the last question during reading time instead of attempting multiple choice, and then working through Q16 and 15 before going back to mulitple choice to start the paper from the beginning. A little confusing, but just wanted to see what other people think or have planned to do?

Good luck with studying everyone!

[RuiAce]

Hey! Any tips to go about the actual exam in terms of question order/timing??

I prefer to go straight to the last question during reading time instead of attempting multiple choice, and then working through Q16 and 15 before going back to mulitple choice to start the paper from the beginning. A little confusing, but just wanted to see what other people think or have planned to do?

Good luck with studying everyone!

Is there any reason you prefer this approach? Because fact is (whilst multiple choice is entirely up to personal preference), the mathematics exam is designed to go in increasing order of difficulty. Not decreasing.

This implies that the questions at the start of the paper can be completed much more easily than those at the back. Not only do they take less time, but they are less hard. This then implies that you can guarantee the marks you can get earlier in, rather than spend too much time on Q16 not knowing what to do and then lose all your time for everything else.

Timing wise, as a rule of thumb you have 3 hours (180 minutes) and 100 marks, so don't spend more than 1.8 marks on a question. But of course, that rule of thumb is always broken and ultimately you just need to glance at the clock often enough

[MagmaMeerkat]

Thanks for the reply RuiAce!

I'm a 3U student so it's usually Q15 and 16 that are the questions that I kind of 'focus on', since the beginning of the paper is - as you said - obviously easier.
Attempting those questions first in my trial helped to see the extent of how difficult the exam became, but in the end Q12 and 13 had a tricky part or two so I probably had spent too much time on the last questions - so I'm just re-evaluating my strategy.
Would you recommend just going in order of the paper?

[RuiAce]

Note that of course, ultimately it is entirely up to you what you choose to do. Some things may happen to work for just you.

That being said, being a 3U student doesn't exactly mean you'll fare better at the Q15/16 level problems though. It just means that, as opposed to the rest of 2U, you have an advantage in a more wider exposure to problems and hence some more unique ways of thought. That simply makes Q15/16 in 2U (potentially) simplified relatively speaking.

On the absolute scale though, Q11-14 are always going to be easier than Q15-16. The marks in the earlier questions are easier to grab, and in general you should always start from easiest and go up if you want mark maximisation.

[MagmaMeerkat]

I definitely want to focus on mark maximation, so for my practice papers I'll have a go starting from the beginning and leading up to the last questions. Thanks so much for your advice!

[mbdtHSC]

Any advice for performing to a level in an actual exam that reflects how well I do for past paper practice? I have this really worrying trend where I can go through past papers and definitely see significant improvement with each paper, but during the real exam I feel sort of "spaced out" and can't do difficult questions that I would be able to do normally.

This sucks even more because my school's past papers are notorious for being quite difficult and I'd really like to start improving my maths marks because its the only subject dragging me down

[RuiAce]

Any advice for performing to a level in an actual exam that reflects how well I do for past paper practice? I have this really worrying trend where I can go through past papers and definitely see significant improvement with each paper, but during the real exam I feel sort of "spaced out" and can't do difficult questions that I would be able to do normally.

This sucks even more because my school's past papers are notorious for being quite difficult and I'd really like to start improving my maths marks because its the only subject dragging me down

Well firstly you need to figure out why you 'space out'. Is it nerves, genuinely not knowing what to do or etc.

Because you need to figure out where the problem is to take relevant action. And then, you need to do some papers in exam conditions to ensure you're trained for it. Consider also doing hard papers, such as those from Sydney Grammar, if your school's papers tend to be above the standard difficulty.

[SSSS]

Hey Guys! I have an assessment exactly in a week! So daunting. the problem is that we did a past paper and I got 60%.  The problem is I want to smash this first assessment. I have to practise locus, I am getting mixed up when I differntiate or integrate [sometimes I do both in a question like if it wants me to do the chain rule I will divide it by the power], I can't do hard volume questions in integration. I don't know what I should do. Practise or do questions in the textbook? Any advice will be appreicated much!

[RuiAce]

Hey Guys! I have an assessment exactly in a week! So daunting. the problem is that we did a past paper and I got 60%.  The problem is I want to smash this first assessment. I have to practise locus, I am getting mixed up when I differntiate or integrate [sometimes I do both in a question like if it wants me to do the chain rule I will divide it by the power], I can't do hard volume questions in integration. I don't know what I should do. Practise or do questions in the textbook? Any advice will be appreicated much!

Provide some examples. At this point I have a bit of an idea of where the struggles are but not a clear idea.

Locus - Seriously, the main thing is to make sure you know your parabolas. Know how to rearrange to the (x-h)² = 4a(y-k) forms and etc. Make sure you know to find the vertex BEFORE you find the focus or directrix.

You're going to have to provide some more examples on the calculus stuff. Both the mix-up and the volumes. Thing with volumes is that there are always a few that can get you just because they're dodgy, whereas mixing up differentiating and integrating sounds more like a lack of understanding or too much confusion.

Until you provide more examples, all I'm gonna suggest is do more past papers. Past papers all the way. (Picking questions out of trial papers may occasionally be better than just doing textbook stuff.)