ATAR Notes: Forum
HSC Stuff => HSC Maths Stuff => HSC Subjects + Help => HSC Mathematics Advanced => Topic started by: jamonwindeyer on February 10, 2016, 07:26:06 pm
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Let’s face it, studying for math is much less enjoyable than many other things you’d prefer to be doing on a Wednesday night. And this is even more especially true when you realise, after 3 hours work slaving away under the dim lights of your desk, that absolutely nothing has sunk in. In fact, your pretty sure you just forgot how to subtract anything at all. Bloody fantastic.
Now I love my math, so I was never overly mortified when “STUDY TIME: MATH” popped up in my Reminder List. But I totally get it: Studying for math can suck. It can be discouraging and very boring. If you and maths study have a hate-hate relationship, then obviously, you want to study as little as possible. Maximum gain for minimum pain.
This guide contains my favourite 5 methods for efficient, effective and powerful study of any level of HC Mathematics. They are all very different, and aim to break the repetitiveness of doing questions from a textbook with no end goal. I used them all at one point or another, and I stand by each of them as super useful. Use them in conjunction with a regular dose of good old fashioned practice.
Method 1: The Teacher
Best For: Weekly Revision
As soon as possible after your lesson with a new concept, sit in front of your Webcam (or record your voice on your phone). Record yourself giving a 2-minute explanation of what you have just learned. You can use your notes, but the idea of this exercise is to capitalise on that first couple of hours after a lesson when your like, “Oh I totally understand that.” Capturing that moment has two benefits: 1 – You immediately re-enforce the concepts, and you remember 75% of what you teach! 2- You now have a handy, quick resource to refer to as a refresher.
Method 2: The Race
Best For: Improving Speed
Find yourself a chapter in your textbook (erg, sorry, no more textbook stuff after this I promise) with a lot of very quick, very easy questions. Put 5 minutes on the clock, and race through as many as you can. These should be questions which take 3 lines max and focus on one specific skill: factorisations, surds questions, derivatives, indefinite integrals, simplifications, probabilities, etc. Keep a record of how many you got correct, then come back in a fortnight and try and beat it. This is an awesome way to polish up basic skills pivotal to the course: It’s like the grown up version of repeating your times tables.
Method 3: The Scholar
Best For: Pre-TRIAL/Pre-HSC Study
Find yourself a past Mathematics paper (preferably HSC/Trial papers). You are going to time yourself for 15 minutes, and in this 15 minutes, you have one job. Read the paper thoroughly, and try and roughly do the questions in your head. Not calculations, but the process. Just looking at a paper full of questions and provoking your brain to remember how to tackle them is an extremely beneficial exercise. However, it has an added benefit. Mark questions that you can’t do with a highlighter (be honest with yourself, otherwise this isn’t effective). These questions are your study for the evening. This is awesome because you know you are doing questions which will actually improve your HSC results, because you are specifically addressing your trouble areas.
Method 4: The River
Best For: Formula Memorization
Get it? The river? DE-RIVER? Never mind…
2 Unit students now receive a reference/formula sheet for their exams. I can have an argument about how this is bringing HSC Math even further below the level of University Math on another day, but at the moment my main gripe is this: I bet teachers are going to stop deriving formulas now!
Deriving formulas is, without a doubt, my favourite way to remember them. What better way to remember (and further, understand) Newton’s method than to recreate the logic of the man himself!
To remember tricky formulas, derive them. Seriously, it works a charm. Experiment with definitions and do some rearranging to arrive at the new result. Some are quite difficult, in this case, be sure to jump on the forums and ask for a hand! I’ve said it before, I love derivations.
Method 5: The Scientist
Best For: Problem Solving Practice
This method is primarily useful for topics with real world applications (probability and calculus, but also sequences/series, algebraic techniques, etc)
Take something you see in real life, and try and examine it mathematically. A few examples I actually did at my desk after getting home of an evening:
- What are the odds of getting a royal flush in a game of Texas Hold Em?
- How long would it take me to save for a new car with a certain interest rate/deposit amount?
- How much force would a skydiver hit the ground with after jumping out of a plane (a bit of Physics involved with that one, but you get the point)
You’d be surprised how much easier something sinks in when it has tangible applications to what is in front of you. Further, it gives you practice of essential problem solving skills, super handy for those 5 markers at the end of your paper.
So that’s my 5 effective (and different) methods of studying for Math? Do you have any more? Post your favourite methods below (strange names are optional). I've attached my tips in a fancy document below, print it and stick it to your desk!
To post your study method, make an ATAR Notes account here. Happy study!
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Hey Jamon
Do you think it important to focus on specfic weaknesses in maths and for every question you struggle with, try to understand the underlying theory behind the question (for questions you struggle with)?
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Hey Jamon
Do you think it important to focus on specfic weaknesses in maths and for every question you struggle with, try to understand the underlying theory behind the question (for questions you struggle with)?
Hey Conic... From an economics perspective, this is exactly what you should be doing. This is surrounding the concept of 'declining marginal utility' - if you're bad at something, putting in some work can give you good improvements. If you're great at something, the same amount of work won't give you that much improvement... because you're already great at it.
Think of it this way: if you give $50 to someone who is a millionaire, they don't care that much.
If you give $50 to a homeless person who is starving and begging for change in Woolworths, then you will make big changes to his happiness.
In this scenario, the questsion you're bad at = the person in need. $50 = your study. The millionaire = questions you're good at.
It's only natural that giving effort to what you're bad at will have the biggest impact on your final grade.
And, of course, it's almost important to understand the underlying theory behind maths questions if you're struggling with them. - that's what makes it easier :)
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Hey Conic... From an economics perspective, this is exactly what you should be doing. This is surrounding the concept of 'declining marginal utility' - if you're bad at something, putting in some work can give you good improvements. If you're great at something, the same amount of work won't give you that much improvement... because you're already great at it.
Think of it this way: if you give $50 to someone who is a millionaire, they don't care that much.
If you give $50 to a homeless person who is starving and begging for change in Woolworths, then you will make big changes to his happiness.
In this scenario, the questsion you're bad at = the person in need. $50 = your study. The millionaire = questions you're good at.
It's only natural that giving effort to what you're bad at will have the biggest impact on your final grade.
And, of course, it's almost important to understand the underlying theory behind maths questions if you're struggling with them. - that's what makes it easier :)
This is such a great explanation. Thanks so much Brendan. You are awesome ;D
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This is such a great explanation. Thanks so much Brendan. You are awesome ;D
No worries!
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I think I read it somewhere, maybe here from ATAR notes lol, is to create acronyms
SURD-
S for signs
U for units
R for rationalise
D for does it make sense?
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I think I read it somewhere, maybe here from ATAR notes lol, is to create acronyms
SURD-
S for signs
U for units
R for rationalise
D for does it make sense?
That's my acronym (or at least I'd never seen it written online before I wrote it on here), so I think that's us!! ;)
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For me, and lots of other people i have talked to, the best way to study for mathematic exams is to do LOTS of practice papers!! Other subjects you can do notes, etc, but for maths especially PRACTICE PAPERS ARE THE ANSWER...
Hope this helps 8)
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For me, and lots of other people i have talked to, the best way to study for mathematic exams is to do LOTS of practice papers!! Other subjects you can do notes, etc, but for maths especially PRACTICE PAPERS ARE THE ANSWER...
Hope this helps 8)
I'm pretty sure 100% of the people on this forum will agree there
Scanning this post I reckon most of what Jamon said relates back to before trials and HSC, i.e. throughout the year
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Personally I think the best way to studying in maths are past papers (obviously). Also learn from your mistakes and understand the underlying theory behind the questions which you struggled with
Try to focus more on the harder/question and topics (if you're strong with the basics)
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>Method 1: The Teacher
This is great actually
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>Method 1: The Teacher
This is great actually
Glad you like it! My favourite of the list ;D I've fallen out of using it at uni though, I really should try and get back into routine :P
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I have a big problem with stupid mistakes - often losing 10 or 15 marks to them... Any tips on minimising these mistakes? Apart from do lots of practice :p
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I have a big problem with stupid mistakes - often losing 10 or 15 marks to them... Any tips on minimising these mistakes? Apart from do lots of practice :p
You nail it when you say that practice is your best bet. Method 2 in the list above might be beneficial for you, doing lots of more "basic calculations" like simple derivatives, factorisations, integrals (etc) to really get the hang of the simple things. Besides this, how is your time management in exams? Do you find yourself rushing? That definitely won't help the prevalence of silly errors :)
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You nail it when you say that practice is your best bet. Method 2 in the list above might be beneficial for you, doing lots of more "basic calculations" like simple derivatives, factorisations, integrals (etc) to really get the hang of the simple things. Besides this, how is your time management in exams? Do you find yourself rushing? That definitely won't help the prevalence of silly errors :)
Yeah, my time management isn't too bad... I think a big thing is maintaining focus for three hours (while kind of rushing because you need to keep on top of time)
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Yeah, my time management isn't too bad... I think a big thing is maintaining focus for three hours (while kind of rushing because you need to keep on top of time)
That's good! Maintaining focus is easier when you know you're doing the real thing ;) try and do as many past papers as you can to get into the routine of it, that's the best way to go!!
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That's good! Maintaining focus is easier when you know you're doing the real thing ;) try and do as many past papers as you can to get into the routine of it, that's the best way to go!!
Ok, thanks!
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When doing past papers, should we start from the last question (The hardest question) and then move our way to the beginning of the exam?
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When doing past papers, should we start from the last question (The hardest question) and then move our way to the beginning of the exam?
I think doing it from the start to the end is better as it builds up in difficulty
The thing is, if you start off with the last question and you are stuck on it, how are you going to answer it? (unless you skip it and do the other questions first)
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Considering we're the first year to get a formula sheet, how much harder do you think this exam will be compared to 2015, 2014 etc.
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Considering we're the first year to get a formula sheet, how much harder do you think this exam will be compared to 2015, 2014 etc.
Not too hard, because there's no point in being brutal to you guys with it. But I reckon it'll be noticeable enough so that you aren't given too many free marks for using a formula anymore (since they're all right in front of you).
Wouldn't be surprised if the difficulty becomes similar to the 2013 paper. (2014 was easy tbh)
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Not too hard, because there's no point in being brutal to you guys with it. But I reckon it'll be noticeable enough so that you aren't given too many free marks for using a formula anymore (since they're all right in front of you).
Wouldn't be surprised if the difficulty becomes similar to the 2013 paper. (2014 was easy tbh)
ok, that doesnt sound too bad :)
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Not too hard, because there's no point in being brutal to you guys with it. But I reckon it'll be noticeable enough so that you aren't given too many free marks for using a formula anymore (since they're all right in front of you).
Wouldn't be surprised if the difficulty becomes similar to the 2013 paper. (2014 was easy tbh)
2014's paper was quite easy, besides a fairly nasty geometric proof that was more reminiscent of the early 2000's ;D
I'm personally thinking (and the CSSA being quite difficult this year is part of my reasoning) a little harder than that, we may be heading back to the difficulty that we saw from papers in, say, the early 2000's/late 1990's. Harder than anything recent, for sure. But I agree with Rui, I think mainly that will just manifest in less free 'formula marks.'
This is all speculation though, best to just prepare as best you can and be super confident!! ;D
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instead of completing past HSC maths papers in 3 hours I am giving myself 2hours and 15 mins instead to finish the paper. is this a good idea?
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instead of completing past HSC maths papers in 3 hours I am giving myself 2hours and 15 mins instead to finish the paper. is this a good idea?
This is your choice of studying technique and you need to decide if it is a good idea. These strategies pay off for some people whereas they falter for others.
You need to figure out whether or not this will benefit you. If it does then go for it; it's not like nobody does this sort of thing, but not everyone does.
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instead of completing past HSC maths papers in 3 hours I am giving myself 2hours and 15 mins instead to finish the paper. is this a good idea?
I massively agree with Rui, but I will add that I was setting myself 2 hours to do Mathematics Exam by the end of my study period, and I found it worked really well for me!! Perhaps this is because I did so many practice papers that I needed to add some extra pressure by the end, but yeah I did this and it worked well for me! :)
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Thank You! This was useful!
How would you tackle the last question for the exam?
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Thank You! This was useful!
How would you tackle the last question for the exam?
Definitely leave it for last; they're usually not worth enough marks for you to spend a lot of time on it. There are generally multiple parts, and the first one or two are pretty achievable for most students. However, if you recognise that the last part is seriously difficult, but only worth 2 marks, I would just write some maths down that seems relevant and move on with your life. It just isn't worth wasting a lot of time on something that will get you a max of 2 marks, particularly if you can bullshit one of those marks. If you have plenty of time; definitely give it a proper crack! But you can easily get a band 6 without getting 100% on the last question :)
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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 :) :)
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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! 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
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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 ;)
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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
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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
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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 :o
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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 :o
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.
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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 :P
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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! :)
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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
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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?
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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.
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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! :)
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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 :(
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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.
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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!
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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.)
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Thanks so mcuh for the response! I'd put examples but everythin you said is applicable to what I need to do! I am just stressing because I haven't been spending a lot of time on math.
By the way my first assessment is 10%. If I get in my 60s or 70s, do I still have a chance of getting a band 6?
Mod edit: Merged posts. For things like these, please resort to modifying your post if you have more to add :)
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Thanks so mcuh for the response! I'd put examples but everythin you said is applicable to what I need to do! I am just stressing because I haven't been spending a lot of time on math.
By the way my first assessment is 10%. If I get in my 60s or 70s, do I still have a chance of getting a band 6?
Short answer to that question is yes. Band 6's don't vanish that easily. (I could give a long version but it's too early into the HSC for that)
Well given you're aware of the time factor then you will want to get a start there. It just means you need to practice more and practice more.
Although, don't wear yourself out either. Don't exhaust you to the point that studying/preparation becomes ineffective. Also, make sure to focus on relieving the stress first. You can't get as much done whilst stressing than when you don't. That doesn't necessarily mean to just stop stressing; it just means to put aside a sufficient amount of stress and get started (once you start studying you may feel the stress disappears).