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Edexcel FP3 - 27th June, 2016

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I dont quite follow this: "there's one plane with equation r.(3,-4,2)=5 and r.(1,3,-1)=0 ---- this one is from taking out 3 from (3,9,-3) and using the dot product on (0,0,0)
after having the two equations, r.(3,-4,2)=5 and r(1,3,-1)=0 you do simultaneous equations from letting x=0, which would be -4x+2y=5, 3x-y=0 --- "

from the question we are told plane 1 has vector equation r.(3,-4,2)=5 and that plane 2 has vector equation r=lambda(2,1,5) + mu(1,-1,-2) -- we can assume from plane 2 that the position vector is (0,0,0) so r=(0,0,0) + lambda(2,15) + mu(1,-1,-2).

Then we want the plane 2 in the form r.n=p.
we then cross multiply (2,1,5) and (1,-1,-2) to give us (3,9,-3)
then r.(3,9,-3)=(0,0,0).(3,9,-3) = 0
r can then be written as r.(1.3,-1)=0 (dividing by 3)

now we have 2 equations r.(1,3,-1)=0 and r.(3,-4,2)=5
which can be written as x+3y-z=0 , 3x-4y+2z=5.
in the mark scheme they had let x=0 which gives us 2 simultaneous equations
3y-z=0, 4y+2z=5
you then solve these for the position vector of the 2 planes
and cross multiply (1,3,-1) and (3,-4,2) for the direction vector.
This may seem complicated due to the amount written but it's fairly simple

Reply 521

oinkk

Original post by Cookie2314

ImageUploadedByStudent Room1466875049.094976.jpg

When do I use the sin teetha formula? And what does it actually mean

Posted from TSR Mobile

This is the definition of the cross product between two vectors. Take care with the direction of n hat.

It is used to find the sine of the angle between two vectors. We tend to use the scalar product in this case though to find the cosine of the angle.

Reply 522

Major-fury

How is everyone feeling about the exam? is it weird i'm hoping for a hard paper :s-smilie:

Reply 523

Major-fury

Original post by the-anonymous-me

Thanks x

no problem will try helping if possible x

Reply 524

Maetras

Original post by Major-fury

How is everyone feeling about the exam? is it weird i'm hoping for a hard paper :s-smilie:

I'm hoping for hard paper. I love low grade boundaries.

Reply 525

Major-fury

Original post by target21859

I'm hoping for hard paper. I love low grade boundaries.

same xD It's much easier imo to do better in a hard paper rather than an easy paper because 1 mistake can be the difference between an A* and an A.

Reply 526

Maetras

Original post by Major-fury

same xD It's much easier imo to do better in a hard paper rather than an easy paper because 1 mistake can be the difference between an A* and an A.

Yeah true and I don't find them to be much harder. In fact I found June 2011 ( I think) to be the hardest paper and that's 70 for an A*. Tbh I only need a B in FP3 or S2 to get the A* anyway so I'm not too worried :biggrin:

. Although I am worried about physics as I haven't done any revision or past papers yet. I'm screwed :biggrin:

Reply 527

King Beast

Hey guys, can anyone post a link to all the formulas that need to be memorised especially for the vectors stuff it'd be really appreciated.

Reply 528

King Beast

Original post by target21859

. Although I am worried about physics as I haven't done any revision or past papers yet. I'm screwed :biggrin:

Nice man. I on the ohter hand need essentially 100 ums in S2 and FP3 for my A* :frown:

. And I havent even learnt unit 5 physics yet let alone done a past paper.

Reply 529

Major-fury

Original post by King Beast

Hey guys, can anyone post a link to all the formulas that need to be memorised especially for the vectors stuff it'd be really appreciated.

all in the fp3 book, check the summary of the chapter.

Reply 530

Major-fury

Could someone explain how big of a deal predicition grades are? because i know i'll do good in my exams but for my mocks i know they're gonna go badly because i'm trying to focus on my actual exams. Because i'm in my first year of sixth form but already have an A* in maths and have nearly gotten an A* in further maths ( fp3 last module).

Reply 531

Cookie2314

Original post by oinkk

Thanks! Is there any examples of questions when we have to find the sin of the angle instead of the cos and will they tell us or we have to recognise this

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Reply 532

Craig1998

Original post by King Beast

Hey guys, can anyone post a link to all the formulas that need to be memorised especially for the vectors stuff it'd be really appreciated.

FP3 pretty much has all the formulae in the formula booklet. It takes out 4 pages for FP3 compared to 1 for FP2.
Hyperbolics:
sinhx = (e^x - e^-x)/2
coshx = (e^x + e^-x)/2
tanhx = (e^x - e^-x)/(e^x + e^-x)
cosh(A+B) = coshAcoshB + sinhAsinhB
sinh(A+B) = coshAsinhB + coshbsinhA

Available in the review of hyperbolics in the FP3 book are more, but those are the main ones not on the second page of the formula booklet.

Coordinate systems:
Nothing really here which isn't in the formula booklet. Ensure you know trig/hyperbolic trig identities for locus questions, but no formulae.

Integration/differentiation:
Again, nothing really. Results are in the formula booklet, the by parts formula for integration is in c4, and the formulae are in the formula booklet. Differentiation usually asks for some knowledge from C3/C4 (e.g. d/dx (yx) = xdy/dx + y).

Vectors:
Most formulae are in the formula booklet, even with some you never even use.
Area of triangle = 1/2 |axb|
Area of parallelogram = |axb|
Volume of parallelepiped = |a.(bxc)|
Volume of tetrahedron = 1/6 |a.(bxc)|

Matrices:
If you're stuck with the matrices stuff, ask me. As much as I want to help, I'm not bothering writing out the formula for cofactor matrices, inverses etc. It's also much better to remember the process, rather than where the numbers go.
Just remember you've got:
- Inverse matrices (covers cofactor matrix and determinant of 3x3 matrix, if you're using them).
- What makes a matrix singular, orthogonal, diagonal.
- Combining matrices with vectors to see where the matrix transforms it.
- Finding eigenvalues/eigenvectors.
- Any FP1 stuff on matrices, like the manipulation of matrices (using inverses etc.).

Also worth remembering:
C1, C2, C3, C4, FP1, FP2 stuff (don't think anything from applied modules will appear).
- Proof by induction HAS come up (I know in FP2 it has, don't remember seeing it in FP3). Go over the method, n=1, assume true for n=k, n=k+1.
- Again, fp1 matrix stuff could come up, aswell as fp1/fp2 complex numbers.
- C4 vectors knowledge forms the basis of a lot of FP3 vectors knowledge.
- Known differentials/integrals are in the formula booklet under c3, c4 and fp3.
- This exam is intended to be hard. If your working reaches an impass, clear your mind by moving onto the next question. When you get back to that question, consider using a new method or manipulating something right at the start (this happens with me a lot, there'll be something right at the start that I miss).

(edited 7 years ago)

Reply 533

oinkk

Original post by Cookie2314

Thanks! Is there any examples of questions when we have to find the sin of the angle instead of the cos and will they tell us or we have to recognise this

Posted from TSR Mobile

We tend to use the cosine over the sine as there is an ambiguity problem for obtuse angles (that is to say, once we've found the value of

sin\theta

, is the angle we're actually looking for greater than or equal to

\frac{\pi}{2}

— this is much like the ambiguous case with the sine rule from C2. Might be with a Google cos we don't actually get taught this).

This is the definition of a vector cross product. We can use either or for finding angles. We get the same result. But we almost always prefer use the dot product as cosine does not have this extra ambiguity.

(edited 7 years ago)

Reply 534

blahblah21

Hows everyone feeling about this exam lol?

Reply 535

ThatGuy153

Original post by blahblah21

Hows everyone feeling about this exam lol?

totally ****ed only started revising it today. i covered it all about 3 months ago was happy with it and now i've forgotten most of it.

Reply 536

Anon-

hey guys, could someone help me out on this ellipse question?

https://3a14597dd5c7aa2363f0675717665774b02557b0.googledrive.com/host/0B1ZiqBksUHNYQWE5bVRTVE9BLW8/June%202015%20QP%20-%20FP3%20Edexcel.pdf

q8 part b. i can get to e(PN1+PN2) but I don't see why this is equal to e*N1*N2? cheers

Reply 537

Major-fury

Original post by Anon-

I let P = (2costheta,sin theta)
and then proceeded to just find the distance of pf1 and pf2 and it cancels out to 4.

Reply 538

blahblah21

Original post by ThatGuy153

totally ****ed only started revising it today. i covered it all about 3 months ago was happy with it and now i've forgotten most of it.

haha tell me about it, i need a solid B to get an A but ill be lucky if I get a D lol

Reply 539

Craig1998

Need somewhere in the region of 70-80 to get an A in further maths (thanks M2). I'd need about 92-96 to get an A*. I really hope this is as much a breeze as C4 was.

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Edexcel FP3 - 27th June, 2016

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