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October 20, 2025, 11:34:03 pm

Author Topic: 3U Maths Question Thread  (Read 1516563 times)  Share 

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nimasha.w

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Re: 3U Maths Question Thread
« Reply #975 on: October 25, 2016, 06:17:09 pm »
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hey! I'm unsure on how to do this question

Rikahs

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Re: 3U Maths Question Thread
« Reply #976 on: October 25, 2016, 06:24:41 pm »
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Could someone help me with iv) and v). Thanks!!
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Cindy2k16

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Re: 3U Maths Question Thread
« Reply #977 on: October 25, 2016, 06:38:59 pm »
+1
hey! I'm unsure on how to do this question

Hi if you draw out the triangles for the tan and cos you'll realise they are two (different) angles of the same right angled triangle (the sides of the triangles will be the same). Therefore using the sum of a triangle, which is pi, the tan and cos (basically the angles of the triangle) will add up to Pi/2
Hope this helps
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RuiAce

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3U Maths Question Thread
« Reply #978 on: October 25, 2016, 06:40:31 pm »
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Hi if you draw out the triangles for the tan and cos you'll realise they are two (different) angles of the same right angled triangle (the sides of the triangles will be the same). Therefore using the sum of a triangle, which is pi, the tan and cos (basically the angles of the triangle) will add up to Pi/2
Hope this helps
Nice one, but remember that this one was just a coincidence. In general questions aren't this coincidental and I'd hope you know the method for other cases
Could someone help me with iv) and v). Thanks!!
This was addressed recently but I'm on my phone right now so I'm not really bothered to search for it. But literally use part a ii to do iv. It is obvious that A=2theta and B=alpha
« Last Edit: October 25, 2016, 06:47:30 pm by RuiAce »

Rikahs

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Re: 3U Maths Question Thread
« Reply #979 on: October 25, 2016, 06:44:49 pm »
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what is the method of other cases.....
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RuiAce

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3U Maths Question Thread
« Reply #980 on: October 25, 2016, 06:46:15 pm »
+1
what is the method of other cases.....
You have to draw a triangle no matter what. But the other cases is when the RHS is not equal to Pi/2. (The method, of course, overlaps such that you can do it for Pi/2 RHS as well)

You have to put cos in front of everything and expand out the compound angle. As said I'm currently on my phone so I'd rather not do a question just yet but if you find another one I can do it when I'm home

Edit: Basic idea is that in general they are NOT the same triangle; here they are.
« Last Edit: October 25, 2016, 07:10:23 pm by RuiAce »

MysteryMarker

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Re: 3U Maths Question Thread
« Reply #981 on: October 25, 2016, 07:09:00 pm »
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Hey could someone explain how to do this question please?

Cheers.

RuiAce

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Re: 3U Maths Question Thread
« Reply #982 on: October 25, 2016, 07:19:39 pm »
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Hey could someone explain how to do this question please?

Cheers.



(ii) is easy. Since g(x) is the inverse of f(x), g(3) = 0 if and only if f(0) = 3 which is easily checkable.

And in part (iii), you're just finding g'(3) which is easily done using the formula given in part (i)
« Last Edit: October 25, 2016, 07:40:32 pm by RuiAce »

MysteryMarker

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Re: 3U Maths Question Thread
« Reply #983 on: October 25, 2016, 07:32:56 pm »
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(ii) is easy. Since g(x) is the inverse of f(x), g(3) = 0 if and only if f(0) = 3 which is easily checkable.

And in part (iii), you're just finding g'(3) which is easily done using the formula given in part (i)

Oh thanks, at first i didn't really understand what the question was asking me to do haha. What i don't get is where you differentiated f'(g(x)), why does it get times by g(x) in the next line, where does that come from?

RuiAce

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Re: 3U Maths Question Thread
« Reply #984 on: October 25, 2016, 07:39:57 pm »
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Oh thanks, at first i didn't really understand what the question was asking me to do haha. What i don't get is where you differentiated f'(g(x)), why does it get times by g(x) in the next line, where does that come from?
Let me fix up my typo; a dash was missing there

nimasha.w

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Re: 3U Maths Question Thread
« Reply #985 on: October 25, 2016, 07:42:39 pm »
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hi with this question, the answer to it is 11P5 x 3! x 12 and i don't really understand where the 12 comes from

RuiAce

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Re: 3U Maths Question Thread
« Reply #986 on: October 25, 2016, 07:46:23 pm »
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hi with this question, the answer to it is 11P5 x 3! x 12 and i don't really understand where the 12 comes from
Technically it should be 12P5 x 3!. Which is equivalent to the formula you gave

Note that the family are just treated as one. The family AS A BUNDLE can be arranged anywhere among the other 11.
Provided the family members themselves sit together they can sit anywhere between the other people.

FallonXay

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Re: 3U Maths Question Thread
« Reply #987 on: October 25, 2016, 07:53:06 pm »
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Hello!

How would you do part iv and part v of Q6b?

Thanks!
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Rikahs

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Re: 3U Maths Question Thread
« Reply #988 on: October 25, 2016, 07:57:43 pm »
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Are there any articles on tips for SHM?
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RuiAce

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Re: 3U Maths Question Thread
« Reply #989 on: October 25, 2016, 07:58:23 pm »
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Hello!

How would you do part iv and part v of Q6b?

Thanks!
Scroll up. Part (iv) is already addressed.

Also I should note for part (v): Note that v^2 = 5d/F(theta). i.e. the F(theta) gets reciprocated.
Hence, if F(theta) is maximised, then v^2 is minimised.

I'll properly address part (v) later, but it'll be regurgitating what i said here in a more formalised manner.
Are there any articles on tips for SHM?
Jamon has a guide to everything. If you have some specific grey areas provide a question indicating where you find difficulty