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March 29, 2024, 08:51:38 pm

Author Topic: 4U Maths Question Thread  (Read 659978 times)  Share 

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jakesilove

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #30 on: February 18, 2016, 10:41:00 am »
+2
For the poly ques how do u find the leading coefficient? I only know that there are 2 known roots
and for the trig ques  i dont know how to simplify it after implicitly differentiating

please help thank you

Katherine, these questions were insanely difficult. I wasn't even able to properly get the last one (I'm incredibly tired right now, so I'll blame it on that). Still, as I'll explain that second question should NOT be a multiple choice. If you find yourself spending too much time on a multiple choice, MOVE ON, because it isn't worth the marks. Still, my head hurts and I'm going to go sleep...





If someone else can come up with a better, proper answer please feel free to contribute!
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Spencerr

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #31 on: February 18, 2016, 12:15:11 pm »
+2
exsiny + eysinx = 0

After differentiating with respect to x and grouping the dy/dx onto one side we get

dy/dx = -(exsiny + eycosx) / (excosy + eysinx)

Going back to the main equation that they give us (this was the tricky part) Rearranging we get.
exsiny = - eysinx

Then subbing that in to:

dy/dx = -(exsiny + eycosx) / (excosy + eysinx)

We get
dy/dx = -(-eysinx + eycosx) / (excosy - exsiny)
         = (eysinx - eycosx) / (excosy - ex siny)

Factorise out the ey from the top and ex from the bottom and you get the answer

This was a pain to type up haha, what program or website do you use jake to post the solutions?
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brenden

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #32 on: February 18, 2016, 12:19:18 pm »
+1
exsiny + eysinx = 0

After differentiating with respect to x and grouping the dy/dx onto one side we get

dy/dx = -(exsiny + eycosx) / (excosy + eysinx)

Going back to the main equation that they give us (this was the tricky part) Rearranging we get.
exsiny = - eysinx

Then subbing that in to:

dy/dx = -(exsiny + eycosx) / (excosy + eysinx)

We get
dy/dx = -(-eysinx + eycosx) / (excosy - exsiny)
         = (eysinx - eycosx) / (excosy - ex siny)

Factorise out the ey from the top and ex from the bottom and you get the answer

This was a pain to type up haha, what program or website do you use jake to post the solutions?
Hey dii!

Try the tex code :)

Code: [Select]
[tex][/tex]
When you type things in between it it looks like this.



It's super easy to learn, here are a list of resources: List of LaTeX Resources

In particular, this one is great for learning: LaTeX typeset in Maths boards


✌️just do what makes you happy ✌️

jakesilove

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #33 on: February 18, 2016, 12:20:24 pm »
0
exsiny + eysinx = 0

After differentiating with respect to x and grouping the dy/dx onto one side we get

dy/dx = -(exsiny + eycosx) / (excosy + eysinx)

Going back to the main equation that they give us (this was the tricky part) Rearranging we get.
exsiny = - eysinx

Then subbing that in to:

dy/dx = -(exsiny + eycosx) / (excosy + eysinx)

We get
dy/dx = -(-eysinx + eycosx) / (excosy - exsiny)
         = (eysinx - eycosx) / (excosy - ex siny)

Factorise out the ey from the top and ex from the bottom and you get the answer

This was a pain to type up haha, what program or website do you use jake to post the solutions?

Wow, that's beautiful! I initially did the same thing Diiiiiii, but didn't think to substitute the original equation back in! Absolute genius.

I literally use Word, then screenshot my response and upload it to Imgur so I can upload it to the forum. On Word, there is an "equation" feature which is actually very intuitive. I would highly recommend it; it's super useful!

Or, use to Tex code! I'm not as proficient at that, but it is also quite intuitive.

Again, thanks for the brilliant answer.

Jake
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RuiAce

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #34 on: February 18, 2016, 01:22:55 pm »
+1




Also, to ALL MX2 students I suggest purchasing the calculator CASIO fx-100 AU PLUS for it's ability to do COMPLEX NUMBER OPERATIONS in the exam! This calculator is indeed, board approved!

For the multiple choice question, whilst the method provided by Jake is essentially what a short response requires, multiple choice can be hastened by simply SUBSTITUTING x=1-2i directly in! If what I typed into the calculator is right, A, B and C ALL don't equate to 0.

Multiple choice tricks.

FURTHER EDITING: In fact, there is one last trick. A and B are automatically wrong because the last root has to be a fraction! Not an integer! Non integral (adjective for integer in this case) roots are the only cause the leading to coefficient to deviate from 1.

In the long method, this means that the (ax+b) could be SAFELY written as (x+b)! Then, only constants have to be equated.
« Last Edit: February 18, 2016, 01:40:25 pm by RuiAce »

RuiAce

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #35 on: February 18, 2016, 01:52:16 pm »
+1


« Last Edit: February 18, 2016, 02:02:17 pm by RuiAce »

katherine123

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #36 on: February 19, 2016, 05:27:21 pm »
0
hi how do u integrate (x+1)/(x^2+x+1)^1/2

RuiAce

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #37 on: February 19, 2016, 06:53:04 pm »
+3
hi how do u integrate (x+1)/(x^2+x+1)^1/2





RuiAce

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #38 on: February 19, 2016, 07:04:59 pm »
+4





Neutron

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #39 on: February 20, 2016, 05:20:47 pm »
0
Hello! Me again :P Heh so I was trying to complete some 4U curve sketching when I came across a few silly problems I realised I haven't fully understood. The question is as follows:

Sketch the graph of y=lxl-lx-4l . Use this graph to solve the inequality lxl-lx-4l>2

So I managed to sketch it by plotting points and I was wondering whether there's an easier method? Like how would you know whether the absolute value graph resembles a backwards Z like this one or one that looks more like \_/ ? And secondly, I tried solving
2=|x|-|x-4| to find the x coordinate but I kept getting the answer as -1 when the real answer is 3.. Could you please show me how to solve these equations ^^'' heh sorry this is kinda dumb

Neutron

RuiAce

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #40 on: February 20, 2016, 06:05:07 pm »
+1
Hello! Me again :P Heh so I was trying to complete some 4U curve sketching when I came across a few silly problems I realised I haven't fully understood. The question is as follows:

Sketch the graph of y=lxl-lx-4l . Use this graph to solve the inequality lxl-lx-4l>2

So I managed to sketch it by plotting points and I was wondering whether there's an easier method? Like how would you know whether the absolute value graph resembles a backwards Z like this one or one that looks more like \_/ ? And secondly, I tried solving
2=|x|-|x-4| to find the x coordinate but I kept getting the answer as -1 when the real answer is 3.. Could you please show me how to solve these equations ^^'' heh sorry this is kinda dumb

Neutron






katherine123

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #41 on: February 20, 2016, 06:43:50 pm »
0
how to integrate x^2sinx  thanks :)

Happy Physics Land

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #42 on: February 20, 2016, 07:18:15 pm »
+4
how to integrate x^2sinx  thanks :)

Hey Katherine:

For this question you would be required to use IBP (integration by parts) which is an integration technique that you learn from extension 2 mathematics. The technique is actually derived from the production rule that we use when we differentiate. Anyways, this question would require double applications of IBP and if you have any further questions or doubts please dont hesitate to ask!




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she0071

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #43 on: February 20, 2016, 09:43:38 pm »
0
hi! There's this question I don't really understand:
'A cuboid tank is open at the top and the internal dimensions of its base are xm and 2xm. The height is hm. The volume of the tank is Vm^3 and the volume is fixed. Let S m^2 denote the internal surface area of the tank.'

hence find S in terms of V and x

Thanks a lot in advance! :)

Happy Physics Land

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #44 on: February 20, 2016, 10:16:55 pm »
+2
hi! There's this question I don't really understand:
'A cuboid tank is open at the top and the internal dimensions of its base are xm and 2xm. The height is hm. The volume of the tank is Vm^3 and the volume is fixed. Let S m^2 denote the internal surface area of the tank.'

hence find S in terms of V and x

Thanks a lot in advance! :)

Hey Ms She:

To deal with these questions, the most immediate things I would have done are to find the surface area in terms of x and h and the volume in terms of x and h. Because the question asks us to find S in terms of V and x, we know that we need to substitute h with an expression in terms of V and x in order to eliminate the h from the surface area equation. anyways, you can check out what l mean through observing my working out below. If you have any further questions dont hesitate to ask me! :)



Best Regards
Happy Physics Land
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