Edexcel FP3 - 27th June, 2016

Anyone got any tips on how to go about reduction formulae questions? Most of them just require basic parts but alot of the exam q's I see require more than that.

Like how would you spot certain clues to 'make it work?

Like this one for example (Jun 15)

I did this paper and attempted to use 1 as one part and the sin ^n x as the other but the mark scheme advises you to split it into

Sin^n-1 x sin ^ x which makes sense but it's a case of how would I know to do that?

I see the result has a n-2 in it which might indicate doing that as it'll differentiate to n-2 but so would doing parts twice on my initial method, which isn't uncommon.

So yeah long story short, how'd you go about this.

Oh and part (b)...what the hell

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Reply 228

Original post by CALI1198

Anyone got any tips on how to go about reduction formulae questions? Most of them just require basic parts but alot of the exam q's I see require more than that..

It's most intuition you gain from practice, for example - you see that the integral has a

n-2

in it and that should immediately get you thinking of two things:

(i) IBP twice.
(ii) split into x^(n-1) x.

The latter case is motivated when you have something of the form

x^n f(x)

where

f(x)

is annoying and/or hard to integrate but

xf(x)

is stupendously easy to integrate.

Furthermore to this, you have a

(n-1)I_{n-2}

, this should also alert you to the usage of splitting into x^(n-1) x^{n} instead of IBP twice, since with IBP twice you would expect something like

(n-1)(n-2)I_{n-2}

or

(n-2)I_{n-2}

.

part (b) is just placing limits on your answer to part (a). The bottom limit is just obviously 0, the upper limit you need to remember is n is an odd number, so you need to stop at I_1. Then it's just a matter of plugging in x=pi/2 into your answer to part (a).

Part (c) is just rewriting

\cos^2 x = 1 - \sin^2 x

and using the answer to (b) in two different cases with sin^5 and sin^7.

Reply 229

Argh, either Tapatalk or tsr has put Smiley's in there haha. I sort of get ya, plan to sit down and just work through loads of similar types

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Reply 230

Original post by CALI1198

Argh, either Tapatalk or tsr has put Smiley's in there haha. I sort of get ya, plan to sit down and just work through loads of similar types

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Cheers, it should be viewable properly if you open TSR on your mobile browser instead of an app. Let me know if you need any help.

Reply 231

anndz3007

2

I have a few problems with vector actually, i can do the exercise and get it right but im not really sure how it works. So my skill only work if im lucky enough to get a straight forward question but not the complicated one. any tips ?

Reply 232

Original post by anndz3007

I have a few problems with vector actually, i can do the exercise and get it right but im not really sure how it works. So my skill only work if im lucky enough to get a straight forward question but not the complicated one. any tips ?

Some videos online might help as they'll probably give you an actual visual as to what is happening. Eg two planes intersecting, showing why the cross product of the two normals gives you the line of intersection.

Vectors, the visual is the key to understanding it IMO.

If possible, ask your teacher to help you with visualising. Might help you to appreciate the concepts more

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Reply 233

EricPiphany

17

Non syllabus stuff below.
Does anyone know how to do intrinsic equations questions?
For example, Q7 from this, http://old.antonymale.co.uk/s/download.php?file=ext%2FExam+Papers+and+Mark+Schemes%2FEdexcel+Maths%2FP5%2FP5B.pdf.
I can do part (a), it's just the derivative,

\rho = \dfrac{\mathrm{d}s}{\mathrm{d} \Phi}

.

(edited 7 years ago)

Reply 234

Original post by EricPiphany

Non syllabus stuff below.
Does anyone know how to do intrinsic equations questions?
For example, Q7 from this, http://old.antonymale.co.uk/s/download.php?file=ext%2FExam+Papers+and+Mark+Schemes%2FEdexcel+Maths%2FP5%2FP5B.pdf.
I can do part (a), it's just the derivative,

\rho = \dfrac{\mathrm{d}s}{\mathrm{d} \Phi}

.

\displaystyle \frac{\mathrm{d}y}{\mathrm{d} \psi} = \frac{\mathrm{d}y}{\mathrm{d}s} \times \frac{\mathrm{d}s}{\mathrm{d} \psi} = \cdots

(edited 7 years ago)

Reply 235

username1162972

18

Original post by EricPiphany

Non syllabus stuff below.
Does anyone know how to do intrinsic equations questions?
For example, Q7 from this, http://old.antonymale.co.uk/s/download.php?file=ext%2FExam+Papers+and+Mark+Schemes%2FEdexcel+Maths%2FP5%2FP5B.pdf.
I can do part (a), it's just the derivative,

\rho = \dfrac{\mathrm{d}s}{\mathrm{d} \Phi}

.

It is old syllabus, I have the P5 book so I will send all the notes on it when i get home tmmrw :smile:

it used to come up in M6 aswell, well applications of it

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Reply 236

Original post by Zacken

Cheers, it should be viewable properly if you open TSR on your mobile browser instead of an app. Let me know if you need any help.

I ended up pulling the solution bank from PMT and attempting the questions on there. I've sort of got a method where I try splitting it first and if that fails, I try splitting something.

Seems to have worked. That question I posted here makes perfect sense now! Cheers for the help

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Reply 237

EricPiphany

17

Original post by Zacken

\displaystyle \frac{\mathrm{d}y}{\mathrm{d} \psi} = \frac{\mathrm{d}y}{\mathrm{d}s} \times \frac{\mathrm{d}s}{\mathrm{d} \psi} = \cdots

Aha. And for the last part

\displaystyle x=\int \frac{\mathrm{d}x}{\mathrm{d}y} \,\mathrm{d}y = \int \cot(\psi) \, \mathrm{d}y = \int \cot(y) \, \mathrm{d}y

. Does that look reasonable?

Original post by physicsmaths

It is old syllabus, I have the P5 book so I will send all the notes on it when i get home tmmrw :smile:

it used to come up in M6 aswell, well applications of it

.Posted from TSR Mobile

Thanks.

(edited 7 years ago)

Reply 238

Original post by EricPiphany

Aha. And for the last part

\displaystyle x=\int \frac{\mathrm{d}x}{\mathrm{d}y} \,\mathrm{d}y = \int \cot(\psi) \, \mathrm{d}y = \int \cot(y) \, \mathrm{d}y

. Does that look reasonable?

Yep, that's precisely correct.

Reply 239