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Core 4: Parametric Equations, Help with exam question!

Hi everyone!

So I am just reviewing a past paper that I have done and am having trouble understanding the solution to a question.

For reference the question is 4(b) on the AQA Core 4 January 2013 Paper.

Question:
http://filestore.aqa.org.uk/subjects/AQA-MPC4-QP-JAN13.PDF#page=8
Answer:
http://filestore.aqa.org.uk/subjects/AQA-MPC4-W-MS-JAN13.PDF#page=8

So my issue is that I do not understand why when each of the parametric equations are square, 4 and -4 are introduced into the equations, my understanding was that then 2/t was squared it results in 4/t2 and when t was squared it simply results in t2. Im not sure if my question is clear or not so if any further clarification is needed please ask!

Thanks for any help and support!
Oh and have a happy NUT strike day tomorrow!
question.png12.0KB
answer.png16.0KB
Reply 1
Avatar for nerak99
nerak99
13
I think that maybe you are just forgetting the cross terms in the multiplication of the brackets.

e.g. -2ab in this expansion. (a-b)^2=a^2-2ab+b^2
(edited 8 years ago)
Reply 2
Avatar for Zacken
Zacken
22
Original post by Jonsmith98
Hi everyone!


Do you know how to expand brackets of the form (a+b)2(a+b)^2? If not - this is how: (a+b)2=(a+b)(a+b)=a(a+b)+b(a+b)=a2+ab+ab+b2=a2+2ab+b2(a+b)^2 = (a+b)(a+b) = a(a+b) + b(a+b) = a^2 + ab + ab + b^2 = a^2 + 2ab + b^2

In this case, for xx, for example, we have:

(t+2t)2=t2+2×t×2t+(2t)2\displaystyle \left(t + \frac{2}{t}\right)^2 = t^2 + 2 \times t \times \frac{2}{t} + \left(\frac{2}{t}\right)^2

And 2×t×2t=4tt=42 \times t \times \frac{2}{t} = \frac{4t}{t} = 4.

Can you do the same for yy?
Reply 3
Avatar for Jonsmith98
Jonsmith98
OP
11
Original post by nerak99
I think that maybe you are just forgetting the cross terms in the multiplication of the brackets.

e.g. -2ab in this expansion. (a-b)^2=a^2-2ab+b^2


Original post by Zacken
Do you know how to expand brackets of the form (a+b)2(a+b)^2?


*Face hits desk*
Thanks guys for the help, I had a feeling it was something frustratingly obvious. I think its just a new format that im not used to that caught me out.

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