Mathematics Question Thread

[phebsh]

When you say that you're "constantly failing them", in your scenario what does that encompass? Some things to think about:
- Not understanding the question
- Not associating the question with relevant topics
- Simple getting lost in the wording
- Silly mistakes such as misreading numbers and valuse
- Not choosing correct formulae/methods
- Unable to make a choice on formulae/methods
- Sample solutions make no sense
  - Inspiration to use said formula/method confusing
  - Flow of logic confusing
- Spending too long on a question and not moving on
- Grasping probably one half of the content but not understanding the other half
- Difficulty in retaining all the methods

Think about all of these, then clarify your issue further (preferably also with your own areas of concern, not just the list above)

Not knowing how to answer questions and the answers were so far from what I would have guessed. And by failing I literally mean when I count up my marks, I fail the test.

[RuiAce]

Not knowing how to answer questions and the answers were so far from what I would have guessed. And by failing I literally mean when I count up my marks, I fail the test.

Then may the thought process continue.

When you attempt to answer a question, what do you do? Why is it potentially unlike anything you guessed?
- Have you thought about what topic the question might come from?
- Have you spent enough time thinking about a method/formula (with OR without your reference sheet)?
- If what you guessed is far off, explain a thought process with examples of a question, and how you unintentionally derailed from the intended approach
- How do you break down a question?
- Are you able to take the time out to compare a question you've done/seen, to another you're now encountering?
- Are you proficient with the standard methods for each topic, before adapting to weirder questions like those on past papers?
- Extra: Have you considered the possibility of multiple approaches arriving at the correct answer?

There's no point in just telling you what to do without sufficient context. Everyone has their own struggle, and it's about being able to clearly identify where your own are, before you can get some properly beneficial advice.

[phebsh]

Then may the thought process continue.

When you attempt to answer a question, what do you do? Why is it potentially unlike anything you guessed?
- Have you thought about what topic the question might come from?
- Have you spent enough time thinking about a method/formula (with OR without your reference sheet)?
- If what you guessed is far off, explain a thought process with examples of a question, and how you unintentionally derailed from the intended approach
- How do you break down a question?
- Are you able to take the time out to compare a question you've done/seen, to another you're now encountering?
- Are you proficient with the standard methods for each topic, before adapting to weirder questions like those on past papers?
- Extra: Have you considered the possibility of multiple approaches arriving at the correct answer?

There's no point in just telling you what to do without sufficient context. Everyone has their own struggle, and it's about being able to clearly identify where your own are, before you can get some properly beneficial advice.

So when I see a question I think about the method associated with the topic and any relevant formulas. If the question is out of the ordinary or of a higher difficulty level, this sounds silly but it scares me and I can't think of how to approach it.

[pikachu975]

So when I see a question I think about the method associated with the topic and any relevant formulas. If the question is out of the ordinary or of a higher difficulty level, this sounds silly but it scares me and I can't think of how to approach it.

Sounds like a problem that you don't know the content and instead are rote learning textbook/past paper questions. Instead, try to go and understand the content FULLY, like where formulas come from and what they mean, then try and see if you can apply it to questions.

[RuiAce]

So when I see a question I think about the method associated with the topic and any relevant formulas. If the question is out of the ordinary or of a higher difficulty level, this sounds silly but it scares me and I can't think of how to approach it.

For the most part, what pikachu said.

On top of that, honestly being scared isn't abnormal. I study a maths degree and even then I still get intimidated by some 4U questions every now and then.

But if you let yourself stay scared, that's going to cause problems. It's just like anything in life; you have to control that fear. Instead of worrying about how weird the question is, take the time to start breaking it down into a sequence of steps, and slowly piece every bit of the puzzle together. Not only do you need to know what you know, but you need to anticipate the possibility of adapting it to a foreign scenario, and trying out ideas in the hope it'll actually get there.

[gilliesb18]

Another one on derivatives sorry
And this is a yr 11 question btw...
(x^3)/(x^2+ 1)

Thanks!!

[EEEEEEP]

Another one on derivatives sorry
And this is a yr 11 question btw...
(x^3)/(x^2+ 1)

Thanks!!

Quotient Rule   
f/g
(f’ g − g’ f )/g2

[RuiAce]

Another one on derivatives sorry
And this is a yr 11 question btw...
(x^3)/(x^2+ 1)

Thanks!!

Since you're in Year 11, just smacking the quotient rule in is the best approach, as opposed to being clever with algebra Edit: This is the only recommended way for this question

[Leah_Mer]

Hey there! Just some HSC internal/external mark confusion here... I have read the really great article on this site about the way the HSC mark is calculated, but I'd love to get someones opinion on my personal situation! In 2U, I'm currently ranked about 4th in large cohort, but the average marks for our cohort are pretty low, and will probably be this way in the HSC as well! My question is, if I'm sitting on a band 4 after the trial exam for my internal mark (due to lack of study, so room for improvement in the hsc exam), how much potential is there for me to increase my final mark? Hypothetically, say I score over 90% the HSC, will my poor internal rank/mark and poor performance of my cohort in the exam mean that this significantly better score doesn't make a different to my final band? Hope this makes sense!

[Opengangs]

Hey there! Just some HSC internal/external mark confusion here... I have read the really great article on this site about the way the HSC mark is calculated, but I'd love to get someones opinion on my personal situation! In 2U, I'm currently ranked about 4th in large cohort, but the average marks for our cohort are pretty low, and will probably be this way in the HSC as well! My question is, if I'm sitting on a band 4 after the trial exam for my internal mark (due to lack of study, so room for improvement in the hsc exam), how much potential is there for me to increase my final mark? Hypothetically, say I score over 90% the HSC, will my poor internal rank/mark and poor performance of my cohort in the exam mean that this significantly better score doesn't make a different to my final band? Hope this makes sense!

Hey, Leah_Mer!

Your internal mark doesn't matter per se, rather your ranking and mark difference is. So, as you probably do know, the person who places first in the course will take the highest external mark to be their internal mark, and everyone will get scaled according to the gap between these respective ranks.

So, if you and the top 3 marks are relatively close, you'll receive a relative 'close' internal mark (maybe 2 - 4 mark difference). So, even if you didn't perform well internally, you can still make up for it with your external mark. Even if you have a weak cohort, placing fourth should still put you in a good position for a band 6 HSC mark.

[jamonwindeyer]

Hey there! Just some HSC internal/external mark confusion here... I have read the really great article on this site about the way the HSC mark is calculated, but I'd love to get someones opinion on my personal situation! In 2U, I'm currently ranked about 4th in large cohort, but the average marks for our cohort are pretty low, and will probably be this way in the HSC as well! My question is, if I'm sitting on a band 4 after the trial exam for my internal mark (due to lack of study, so room for improvement in the hsc exam), how much potential is there for me to increase my final mark? Hypothetically, say I score over 90% the HSC, will my poor internal rank/mark and poor performance of my cohort in the exam mean that this significantly better score doesn't make a different to my final band? Hope this makes sense!

100% what Opengangs said - So like, if you and a handful of other students can perform really well (most courses have "those students" that do quite well!) then the effect is likely to be quite low! 4th isn't a bad rank at all, so provided your cohort performs decently and you smash it out of the park, no reason you can't get a Band 6

[asd987]

hi can i get some help for part 2 of this question. Its confusing thanks

[RuiAce]

hi can i get some help for part 2 of this question. Its confusing thanks

This was a past HSC question and was already addressed in the compilation.

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When doing those practical GAD questions, how do I prove that a stationary point is a maximum/minimum when some other variable, say r, is involved?

Example from HSC 2003 Q10 b (looking at iii):



I can find the required result but I struggle to test both sides (<x and >x) when some other variable is involved as is the case here. What's the best way to do this?

Thanks

[RuiAce]

When doing those practical GAD questions, how do I prove that a stationary point is a maximum/minimum when some other variable, say r, is involved?

Example from HSC 2003 Q10 b (looking at iii):

(Image removed from quote.)

I can find the required result (Image removed from quote.) but I struggle to test both sides (<x and >x) when some other variable is involved as is the case here. What's the best way to do this?

Thanks

That second derivative is FAR too ridiculous. So we will consider testing both sides instead.
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Note that in general, there may not always be a nice approach. It varies from question to question how you could approach them. These ones are some of the worst types in 2U.

This will be added to the compilation thread.