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March 29, 2024, 04:16:53 pm

Author Topic: Mathematics Question Thread  (Read 1297044 times)  Share 

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RuiAce

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Re: Mathematics Question Thread
« Reply #780 on: October 21, 2016, 10:09:04 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!
Well if you need to describe the motion based off what you have.

Suppose you have the graph of the displacement.

Velocity is the first derivative of the displacement
Therefore if the graph is increasing, velocity is positive
If graph is decreasing, velocity is negative
If graph is at a stationary point, particle is at rest


Acceleration is the second derivative of the displacement
Therefore if the graph is concave up, acceleration is positive
If the graph is concave down, acceleration is positive
If we are at a point of inflexion, acceleration is constant (possibly 0 but we don't know).



And say we were given the graph of the velocity.
Velocity is the first derivative
Hence v > 0 means particle is travelling away from the origin (+'ve direction, to the right, however you memorised it)
v < 0 means particle is travelling in the other direction from the origin (-'ve direction, to the left etc.)



And those are just some examples. If you know what the derivatives actually MEAN then this is more intuitive than trying to rote learn a few dot points.

onepunchboy

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Re: Mathematics Question Thread
« Reply #781 on: October 21, 2016, 10:10:38 am »
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Hey anyone know how to find the asymptotes for tan graphs? For normal tanx graph asymptote is at pi/2 and 3pi/2 but what if it was tan(1/2 x) or tan (2x) how to find new asymptote.. thanks

RuiAce

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Re: Mathematics Question Thread
« Reply #782 on: October 21, 2016, 10:12:16 am »
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Hey anyone know how to find the asymptotes for tan graphs? For normal tanx graph asymptote is at pi/2 and 3pi/2 but what if it was tan(1/2 x) or tan (2x) how to find new asymptote.. thanks


nibblez16

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Re: Mathematics Question Thread
« Reply #783 on: October 21, 2016, 10:13:23 am »
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How do we know how to solve the last 2 questions

jakesilove

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Re: Mathematics Question Thread
« Reply #784 on: October 21, 2016, 10:16:51 am »
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How do we know how to solve the last 2 questions

Hey! For the second part, you need to think about the cases. Pat can win on the first turn (probability same as i) ), or Pat can win on the second turn. If he wins on the second turn, it will be (1-P(win on first turn))*P(win). Then, we add up these two cases!

You need to create some sort of 'series' which you can add up in a sum-to-infinity type equation for the last part. Can you see how?
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BPunjabi

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Re: Mathematics Question Thread
« Reply #785 on: October 21, 2016, 10:20:31 am »
+1
Guys have confidence, we will smash it!
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Blissfulmelodii

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Re: Mathematics Question Thread
« Reply #786 on: October 21, 2016, 10:21:41 am »
+1
Guys have confidence, we will smash it!

Really good attitude to have  :) :)
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Rikahs

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Re: Mathematics Question Thread
« Reply #787 on: October 21, 2016, 10:26:01 am »
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Hi,

I saw a post above that "monotonic increasing" is when f'(x) greater than or equal to zero.
Can someone please 100% confirm this, i always thought when it said "monotonic increasing" it meant f'(x) was just larger than 0 and not equal to it.

Thanks!!!
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jamonwindeyer

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Re: Mathematics Question Thread
« Reply #788 on: October 21, 2016, 10:27:12 am »
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Hi,

I saw a post above that "monotonic increasing" is when f'(x) greater than or equal to zero.
Can someone please 100% confirm this, i always thought when it said "monotonic increasing" it meant f'(x) was just larger than 0 and not equal to it.

Thanks!!!

Confirming, monotonic means \(f'(x)\ge0\) ;D

Rikahs

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Re: Mathematics Question Thread
« Reply #789 on: October 21, 2016, 10:27:27 am »
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Hi again,

What kind of question would want you to make the discriminant greater and equal to zero?
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RuiAce

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Re: Mathematics Question Thread
« Reply #790 on: October 21, 2016, 10:27:35 am »
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Hi,

I saw a post above that "monotonic increasing" is when f'(x) greater than or equal to zero.
Can someone please 100% confirm this, i always thought when it said "monotonic increasing" it meant f'(x) was just larger than 0 and not equal to it.

Thanks!!!
Ditto to Jamon.

Monotonic means it can equal.
STRICTLY means it can't equal.

RuiAce

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Re: Mathematics Question Thread
« Reply #791 on: October 21, 2016, 10:28:19 am »
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Hi again,

What kind of question would want you to make the discriminant greater and equal to zero?
The discriminant is positive OR zero when ALL you care about is real roots.

When it's strictly positive (greater than zero), i.e. >, it means your two real roots must be DISTINCT.

nibblez16

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Re: Mathematics Question Thread
« Reply #792 on: October 21, 2016, 10:28:37 am »
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Hey! For the second part, you need to think about the cases. Pat can win on the first turn (probability same as i) ), or Pat can win on the second turn. If he wins on the second turn, it will be (1-P(win on first turn))*P(win). Then, we add up these two cases!

You need to create some sort of 'series' which you can add up in a sum-to-infinity type equation for the last part. Can you see how?

Its still confusing...

g98

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Re: Mathematics Question Thread
« Reply #793 on: October 21, 2016, 10:33:53 am »
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Hi, I have a couple of questions:
1. If the question doesn't specify do we leave answer in exact form or decimal and would we get marked down for either?
2. If we answer a question and you could take out a common factor - should you do that or not - some past paper answers do it and some don't and would we get marked down either way?
3. What are acceptable abbreviations for proving geometrical questions?
4. do we leave our answer in improper fraction or mixed numeral - if not specified in question?
5. If not specified in question how many decimals should you round to?

Thank You!

Belindka

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Re: Mathematics Question Thread
« Reply #794 on: October 21, 2016, 10:35:22 am »
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Hey!
Just wondering, would changing our calculators to radians by default change our calculations for other answers that don't need radians? I always have mine in degrees and change it to radians whenever i need it   ???

Thanks!