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Edexcel FP2 Official 2016 Exam Thread - 8th June 2016

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Original post by EricPiphany
Show that the locus of z=x+yi,arg(z3iz5)=π4\displaystyle z=x+yi, \arg\left(\frac{z-3i}{z-5}\right)=\frac{\pi}{4}, has the cartesian equation (x1)2+(y+1)2=17\displaystyle (x-1)^2+(y+1)^2=17, subject to 5y+3x<15\displaystyle 5y+3x<15.

Spoiler



Unparseable latex formula:

\displaystyle[br]\begin{equation*} \frac{z-3i}{z-5} = \frac{x + (y-3)i}{(x-5) + iy} = \frac{(x +(y-3)i)((x-5) -iy) }{(x-5)^2 + y^2}



Doing this all on LaTeX, forgive the excessive working:

Unparseable latex formula:

\displaystyle [br]\begin{equation*}\frac{x(x-5) + y(y+3) - iyx + (y-3)(x-5)i}{(x-5)^2 + y^2} \end{equation*}



Imaginary and real parts need to be identical:

Unparseable latex formula:

\displaystyle[br]\begin{equation*}x^2 - 5x + y^2 + 3y = -5y - 3x + 15\end{equation*}



Completing the square:

Unparseable latex formula:

\displaystyle[br]\begin{equation*}(x-1)^2 + (y+1)^2 = 15 + 2 = 17\end{equation*}



As required.

Blah blah required conditions, pish posh. We require both the real and imaginary part to be positive, which gives us

x(x5)+y(y+3)>0\displaystyle x(x-5) + y(y+3) > 0 and 5y3x+15>0    5y+3x<15-5y - 3x + 15> 0 \iff 5y + 3x < 15.

I don't really see how this is above the syllabus. :dontknow:
Original post by Zacken
Unparseable latex formula:

\displaystyle[br]\begin{equation*} \frac{z-3i}{z-5} = \frac{x + (y-3)i}{(x-5) + iy} = \frac{(x +(y-3)i)((x-5) -iy) }{(x-5)^2 + y^2}



Doing this all on LaTeX, forgive the excessive working:

Unparseable latex formula:

\displaystyle [br]\begin{equation*}\frac{x(x-5) + y(y+3) - iyx + (y-3)(x-5)i}{(x-5)^2 + y^2} \end{equation*}



Imaginary and real parts need to be identical:

Unparseable latex formula:

\displaystyle[br]\begin{equation*}x^2 - 5x + y^2 + 3y = -5y - 3x + 15\end{equation*}



Completing the square:

Unparseable latex formula:

\displaystyle[br]\begin{equation*}(x-1)^2 + (y+1)^2 = 15 + 2 = 17\end{equation*}



As required.

Blah blah required conditions, pish posh. We require both the real and imaginary part to be positive, which gives us

x(x5)+y(y+3)>0\displaystyle x(x-5) + y(y+3) > 0 and 5y3x+15>0    5y+3x<15-5y - 3x + 15> 0 \iff 5y + 3x < 15.

I don't really see how this is above the syllabus. :dontknow:


Good. I feel bad you put so much work into the latex :smile:
They just don't ask these types of problem in the textbook.
Original post by EricPiphany
Good. I feel bad you put so much work into the latex :smile:
They just don't ask these types of problem in the textbook.


You're nicer than I am! Had I seen this problem, I'd have asked: Show that argzaizb=π4\arg \frac{z-ai}{z-b} = \frac{\pi}{4} has cartesian equation blah subject to by+ax<abby + ax < ab :rofl:
Original post by Zacken
You're nicer than I am! Had I seen this problem, I'd have asked: Show that argzaizb=π4\arg \frac{z-ai}{z-b} = \frac{\pi}{4} has cartesian equation blah subject to by+ax<abby + ax < ab :rofl:


Go for the full arg(z(a+bi)z(c+di))=θ\displaystyle \arg\left(\frac{z-(a+bi)}{z-(c+di)}\right)=\theta. lol
Original post by EricPiphany
Go for the full arg(z(a+bi)z(c+di))=θ\displaystyle \arg\left(\frac{z-(a+bi)}{z-(c+di)}\right)=\theta. lol


I wouldn't mind doing that one, but there's no way I'm doing it algebraically. :lol:
Original post by Zacken
I wouldn't mind doing that one, but there's no way I'm doing it algebraically. :lol:


At least it's one for all. You might have to make cases for which quadrant θ is in.

Spoiler

Hi, could anyone explain how to do question 3b on this paper please? https://8dedc505ac3fba908c50836f59059ccce5cd0f1e.googledrive.com/host/0B1ZiqBksUHNYdHIxUkJmdndfMlE/June%202010%20QP%20-%20FP2%20Edexcel.pdf I'm confused how the modulus changes things? Thanks :smile:
Original post by economicss
Hi, could anyone explain how to do question 3b on this paper please? https://8dedc505ac3fba908c50836f59059ccce5cd0f1e.googledrive.com/host/0B1ZiqBksUHNYdHIxUkJmdndfMlE/June%202010%20QP%20-%20FP2%20Edexcel.pdf I'm confused how the modulus changes things? Thanks :smile:


Sketch the graph and you'll see
Flopped my FP2 mock today :lol:
Original post by Student403
Flopped my FP2 mock today :lol:


:console:

Sorry about your 74
Original post by Kvothe the arcane
:console:

Sorry about your 74


No seriously :rofl: I ain't Zain lol

Reason being we do a joint FP2-FP3 (I think the maths department wanted to kill us) and it's impossible to revise for both of them the night before :cry2:
Original post by Student403
Flopped my FP2 mock today :lol:


It'll be alright on the night :wink:
Original post by SeanFM
It'll be alright on the night :wink:


Hope so mate - thanks :biggrin:

How was your test today?
Original post by Student403
Hope so mate - thanks :biggrin:

How was your test today?


:lol: good memory, PRSOM (I see we are both really close to 11 gems...)

It was alright, not sure if I've met my GYG goal but we shall see :borat:
Original post by SeanFM
:lol: good memory, PRSOM (I see we are both really close to 11 gems...)

It was alright, not sure if I've met my GYG goal but we shall see :borat:


:biggrin: I'm sure it was alright!

And holy cow.. Yeah :eek:
Please can anyone explain why the limits aren't between 0 and pi/6 on question 4b of this paper https://8dedc505ac3fba908c50836f59059ccce5cd0f1e.googledrive.com/host/0B1ZiqBksUHNYdHIxUkJmdndfMlE/January%202006%20QP%20-%20FP2%20Edexcel.pdf and how you know to subtract a shape from the area? Thanks :smile:
Capture.PNG
Original post by economicss
Please can anyone explain why the limits aren't between 0 and pi/6 on question 4b of this paper https://8dedc505ac3fba908c50836f59059ccce5cd0f1e.googledrive.com/host/0B1ZiqBksUHNYdHIxUkJmdndfMlE/January%202006%20QP%20-%20FP2%20Edexcel.pdf and how you know to subtract a shape from the area? Thanks :smile:
Reply 197
Original post by Zacken
Unparseable latex formula:

\displaystyle[br]\begin{equation*} \frac{z-3i}{z-5} = \frac{x + (y-3)i}{(x-5) + iy} = \frac{(x +(y-3)i)((x-5) -iy) }{(x-5)^2 + y^2}



Doing this all on LaTeX, forgive the excessive working:

Unparseable latex formula:

\displaystyle [br]\begin{equation*}\frac{x(x-5) + y(y+3) - iyx + (y-3)(x-5)i}{(x-5)^2 + y^2} \end{equation*}



Imaginary and real parts need to be identical:

Unparseable latex formula:

\displaystyle[br]\begin{equation*}x^2 - 5x + y^2 + 3y = -5y - 3x + 15\end{equation*}



Completing the square:

Unparseable latex formula:

\displaystyle[br]\begin{equation*}(x-1)^2 + (y+1)^2 = 15 + 2 = 17\end{equation*}



As required.

Blah blah required conditions, pish posh. We require both the real and imaginary part to be positive, which gives us

x(x5)+y(y+3)>0\displaystyle x(x-5) + y(y+3) > 0 and 5y3x+15>0    5y+3x<15-5y - 3x + 15> 0 \iff 5y + 3x < 15.

I don't really see how this is above the syllabus. :dontknow:


Whaaat is this in FP2? tbh we have done all the chapters except end of 3 :frown: this looks horrible :frown:

edit I just went through it again and its not that bad :biggrin:
Original post by Cpj16
Whaaat is this in FP2? tbh we have done all the chapters except end of 3 :frown: this looks horrible :frown:

edit I just went through it again and its not that bad :biggrin:


Glad to hear that, it seems fairly standard to me but mileage varies; don't be worried if you weren't able to do it. :smile:
Reply 199
Help Maths.PNG

Hi can someone pls explain this integration, I don't understand it

thanks

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