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March 29, 2024, 11:00:49 am

Author Topic: 3U Maths Question Thread  (Read 1230455 times)  Share 

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RuiAce

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Re: 3U Maths Question Thread
« Reply #1995 on: May 13, 2017, 08:31:17 pm »
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heey whats the proper way to graph P(x) = (x-2)(x+2)^2 (3-2x)

like its positive so we start on the bottom right but now what? thank you
Careful. That's a degree FOUR polynomial, i.e a quartic. Not a cubic - note the presence of the -squared on (x+2)

Start by writing down any x-intercepts (which should be staring right at you because the polynomial was already factorised. Then, look out for any multiple roots before deducing which corner it starts and finishes

itssona

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Re: 3U Maths Question Thread
« Reply #1996 on: May 14, 2017, 11:29:18 am »
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Careful. That's a degree FOUR polynomial, i.e a quartic. Not a cubic - note the presence of the -squared on (x+2)

Start by writing down any x-intercepts (which should be staring right at you because the polynomial was already factorised. Then, look out for any multiple roots before deducing which corner it starts and finishes
ohh okay thank youuu
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itssona

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Re: 3U Maths Question Thread
« Reply #1997 on: May 16, 2017, 01:12:48 pm »
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heey, how do you find amplitude in simple harmonic stuff?

like I found the period with 2pi/n where I had acceleration= -6x^2

and 6 is n
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RuiAce

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Re: 3U Maths Question Thread
« Reply #1998 on: May 16, 2017, 01:15:11 pm »
+1

heey, how do you find amplitude in simple harmonic stuff?

like I found the period with 2pi/n where I had acceleration= -6x^2

and 6 is n
That's not enough information to find the amplitude

jakesilove

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Re: 3U Maths Question Thread
« Reply #1999 on: May 16, 2017, 03:14:47 pm »
+1
heey, how do you find amplitude in simple harmonic stuff?

like I found the period with 2pi/n where I had acceleration= -6x^2

and 6 is n

The question will likely give you a maximum value, which is likely to be the amplitude.
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itssona

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Re: 3U Maths Question Thread
« Reply #2000 on: May 16, 2017, 08:15:14 pm »
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The question will likely give you a maximum value, which is likely to be the amplitude.
so if it says "initially it was at rest at x=2" then that means its amplitude is 2?

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RuiAce

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Re: 3U Maths Question Thread
« Reply #2001 on: May 16, 2017, 09:42:33 pm »
+1

so if it says "initially it was at rest at x=2" then that means its amplitude is 2?
Yes. This is observed by deduction.

In the equation you gave it was implied that the centre of motion is \(x_0=0\). This gives our reference point.

Then we know that for SHM, the particle is at rest specifically at the end points of motion. Hence \(x=2\) is an endpoint.

The amplitude is the distance from an endpoint to the centre of motion. Clearly the answer is 2 here.

itssona

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Re: 3U Maths Question Thread
« Reply #2002 on: May 17, 2017, 12:37:03 pm »
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Yes. This is observed by deduction.

In the equation you gave it was implied that the centre of motion is \(x_0=0\). This gives our reference point.

Then we know that for SHM, the particle is at rest specifically at the end points of motion. Hence \(x=2\) is an endpoint.

The amplitude is the distance from an endpoint to the centre of motion. Clearly the answer is 2 here.
omg that cleared it up thank you so so much Rui :)
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itssona

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Re: 3U Maths Question Thread
« Reply #2003 on: May 17, 2017, 06:13:26 pm »
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Heey how would you do these:
 in how many ways can 6 boys and 2 girls be arranged in a row if the two boys:
a)are not together?
b)there are at least 3 girls between the boys
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jakesilove

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Re: 3U Maths Question Thread
« Reply #2004 on: May 17, 2017, 08:25:49 pm »
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Heey how would you do these:
 in how many ways can 6 boys and 2 girls be arranged in a row if the two boys:
a)are not together?
b)there are at least 3 girls between the boys


Sorry, the question doesn't make sense. I assume you mixed up the boys/girls? So, rewriting,

In how many ways can 6 girls and 2 boys be arranged if:

a) The boys are not together
b) There are at least 3 girls between the boys


Let's start with a)

Without worrying about the boys being together part, there are

ways of arranging the people could be arranged. Then, we need to subtract the number of times that the boys are together.

Let's pretend that the boys ARE together. Then, we can essentially think of them as 'one entity': ie. there are 6 girls, and 1 'boy' entity. So, there are 7! ways of arranging this, multiplied by the two ways the boys could be arranged.

So, the answer will be the total number of ways, minus the number of ways that the boys ARE together. Thus,



Now, let's look at part b)

There are three possible cases; three girls are between the boys, four girls are between the boys, five girls are between the boys and six girls are between the boys. This is a bit unmanageable; it is easier to look at how many ways there could be two girls between the boys, one girl between the boys, and no girls between the boys! Then, we can subtract this from the total 8! ways we could arrange the people.

I have to run, but try thinking about these subcases, and how you would go about calculating them
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itssona

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Re: 3U Maths Question Thread
« Reply #2005 on: May 17, 2017, 08:42:03 pm »
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Sorry, the question doesn't make sense. I assume you mixed up the boys/girls? So, rewriting,

In how many ways can 6 girls and 2 boys be arranged if:

a) The boys are not together
b) There are at least 3 girls between the boys


Let's start with a)

Without worrying about the boys being together part, there are

ways of arranging the people could be arranged. Then, we need to subtract the number of times that the boys are together.

Let's pretend that the boys ARE together. Then, we can essentially think of them as 'one entity': ie. there are 6 girls, and 1 'boy' entity. So, there are 7! ways of arranging this, multiplied by the two ways the boys could be arranged.

So, the answer will be the total number of ways, minus the number of ways that the boys ARE together. Thus,



Now, let's look at part b)

There are three possible cases; three girls are between the boys, four girls are between the boys, five girls are between the boys and six girls are between the boys. This is a bit unmanageable; it is easier to look at how many ways there could be two girls between the boys, one girl between the boys, and no girls between the boys! Then, we can subtract this from the total 8! ways we could arrange the people.

I have to run, but try thinking about these subcases, and how you would go about calculating them

Omg thank u Jake! I think I got it now :D
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Re: 3U Maths Question Thread
« Reply #2006 on: May 17, 2017, 10:53:06 pm »
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Hi! Very rusty with locus and param, need someone to help with these

1) Find the gradients of the common tangents of the parabola y= x(x-4) and the circle (x-2)^2 + y^2 = 4 (Im not quite sure, do i diff both then simultaneous or?)

2) Find the locus of P(x,y) and state any restrictions on a, given:
a) PA + PB= 1, where A(a,0) and B (-a,0)
b) ABS PA - PB=2, where A(a,0) and B (-a,0)

Can someone please verify method for 1 or provide legit method and do 1 of the question 2s as wtf is that.

Tyvm :))
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Re: 3U Maths Question Thread
« Reply #2007 on: May 18, 2017, 09:00:35 am »
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what are the topic tests in the ext 1 maths topic test book? and how many are there? also are they in stock i had trouble with the physics book taking like 2 extra weeks coz everyone bought them and no stock ahhaha. but i got it before exams so yassssssss

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Re: 3U Maths Question Thread
« Reply #2008 on: May 18, 2017, 10:54:46 am »
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Hello,

I was wondering if someone could please help me with finding the second derivative of y=ln(tan^-1(x))?

Thankyou so much :)

RuiAce

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Re: 3U Maths Question Thread
« Reply #2009 on: May 18, 2017, 12:20:02 pm »
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Hello,

I was wondering if someone could please help me with finding the second derivative of y=ln(tan^-1(x))?

Thankyou so much :)