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March 29, 2024, 07:20:28 am

Author Topic: Mathematics Question Thread  (Read 1296888 times)  Share 

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WLalex

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Re: Mathematics Question Thread
« Reply #765 on: October 21, 2016, 09:15:06 am »
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Its too late now just wing it  ;D.

But here:

1. if triangle is <0, roots are real, rational and equal
2. If triangle is =0 roots are unreal and unrational
3. If triangle is >0 roots are unreal, irrational and unequal

If the discriminate is less than 0 there is no real roots...
= 0 is 1 real root
> 0 is 2 real, unequal roots
> and equal to means real roots
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jamonwindeyer

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Re: Mathematics Question Thread
« Reply #766 on: October 21, 2016, 09:25:51 am »
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Its too late now, dont worry just wing it!

5 hours is heaps of time to get some things clarified mate :)

If the discriminate is less than 0 there is no real roots...
= 0 is 1 real root
> 0 is 2 real, unequal roots
> and equal to means real roots

This is the correct breakdown. Thanks WLalex! ;D and for your response above, awesome stuff ;D

RuiAce

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Re: Mathematics Question Thread
« Reply #767 on: October 21, 2016, 09:26:36 am »
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How do we know when to use a discriminant and which one to use (>, <, =)
Note that f'(x) ≥ 0 means monotonic increasing
f'(x) ≤ 0 means monotonic decreasing
f'(x) = 0 for stationary points

f'(x) > 0 means strictly increasing
f'(x) < 0 means strictly decreasing
When they don't say monotonic, assume strictly

WLalex

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Re: Mathematics Question Thread
« Reply #768 on: October 21, 2016, 09:28:04 am »
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Note that f'(x) ≥ 0 means monotonic increasing
f'(x) ≤ 0 means monotonic decreasing
f'(x) = 0 for stationary points

f'(x) > 0 means strictly increasing
f'(x) < 0 means strictly decreasing
When they don't say monotonic, assume strictly

so on top of this for clarity you will have to differentiate f(x) and make the discriminate less than 0 (as it will have no roots)
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RuiAce

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Re: Mathematics Question Thread
« Reply #769 on: October 21, 2016, 09:29:18 am »
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Hi, my answers say that d.) is correct but how did they get to this point?

WLalex

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Re: Mathematics Question Thread
« Reply #770 on: October 21, 2016, 09:30:56 am »
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Hi, my answers say that d.) is correct but how did they get to this point?

I would do the calculation the normal way (just add them all together) and then see which answer matches your answers via calculation
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RuiAce

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Re: Mathematics Question Thread
« Reply #771 on: October 21, 2016, 09:31:24 am »
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so on top of this for clarity you will have to differentiate f(x) and make the discriminate less than 0 (as it will have no roots)
In theory, if we were to fully complete the question

Not only do we want ∆ < 0, we want the leading coefficient to be positive. We basically want f'(x) to be positive definite.

Because if the leading coefficient were negative, and ∆ < 0, we would be strictly DECREASING.


However, it's easy to check that 1 > 0 and you are certainly right in using the discriminant here. Because f'(x) is indeed quadratic.
« Last Edit: October 21, 2016, 09:35:19 am by RuiAce »

RuiAce

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Re: Mathematics Question Thread
« Reply #772 on: October 21, 2016, 09:32:03 am »
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I would do the calculation the normal way (just add them all together) and then see which answer matches your answers via calculation
Takes far too long. That's what you do after you've finished the paper and it's time to check your answers, not during.

There are 13 terms to add up in the sum.

jamonwindeyer

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Re: Mathematics Question Thread
« Reply #773 on: October 21, 2016, 09:36:04 am »
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Takes far too long. That's what you do after you've finished the paper and it's time to check your answers, not during.

There are 13 terms to add up in the sum.

Eh, when in doubt go back to basics; the techniques are obviously more effective. But if you have a choice between spending 1 minute getting an answer you are 50% confident with, and 3 minutes getting an answer you KNOW is correct, then why not (assuming you know you've got the time). Plus, doing the calculator work for this with 13 terms isn't actually that bad :P

RuiAce

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Re: Mathematics Question Thread
« Reply #774 on: October 21, 2016, 09:39:26 am »
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Eh, when in doubt go back to basics; the techniques are obviously more effective. But if you have a choice between spending 1 minute getting an answer you are 50% confident with, and 3 minutes getting an answer you KNOW is correct, then why not (assuming you know you've got the time). Plus, doing the calculator work for this with 13 terms isn't actually that bad :P
Even at the fastest typing speed on the calculator that still takes me a full 45 seconds to get through all the options whereas I could've evaluated it in 15-25 :P

They say to check your answers for reasons - get an answer on the paper first, and then calm the paranoia down when you find time to.

Of course, if you have a stress attack though then yeah that's when you should just go back to basics or you'll be overly paranoid

WLalex

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Re: Mathematics Question Thread
« Reply #775 on: October 21, 2016, 09:49:58 am »
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Even at the fastest typing speed on the calculator that still takes me a full 45 seconds to get through all the options whereas I could've evaluated it in 15-25 :P

They say to check your answers for reasons - get an answer on the paper first, and then calm the paranoia down when you find time to.

Of course, if you have a stress attack though then yeah that's when you should just go back to basics or you'll be overly paranoid

Yep valid point Rui but since it was a simple calculation thats just where my mind went :)
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RuiAce

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Re: Mathematics Question Thread
« Reply #776 on: October 21, 2016, 09:51:24 am »
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Yep valid point Rui but since it was a simple calculation thats just where my mind went :)
At least it's 100% not penalisable

lha

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Re: Mathematics Question Thread
« Reply #777 on: October 21, 2016, 09:58:31 am »
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You know those velocity graphs or acceleration graphs and it says describe the motion of the particle at t=whatever? Can someone give me a run down on how to do that please!

kavinila

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Re: Mathematics Question Thread
« Reply #778 on: October 21, 2016, 09:59:58 am »
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hey guys! i was just wondering if someone could please quickly run through locus? i don't think i understand it and i just noticed it in the syllabus 😳 please and thankyouu!!

RuiAce

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Re: Mathematics Question Thread
« Reply #779 on: October 21, 2016, 10:05:05 am »
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hey guys! i was just wondering if someone could please quickly run through locus? i don't think i understand it and i just noticed it in the syllabus 😳 please and thankyouu!!
Find the section on locus