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Edexcel FP1 Thread - 20th May, 2016

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Any predictions then?

I think divisibility will (unfortunately) come up, the other induction proofs are quite a bit easier. I think edexcel might throw in an r=0 series but that's been covered so many times in this thread it's simple now. Also I think we'll get a harder than usual /obscure complex numbers question and probably a parabola question with a lot of letters and algebra.

Reply 581

Yunique

If I carried on that Iast Iine with:

Unparseable latex formula:

k^2 -2k + 3 -(\frac{1}{2})^k^+^1 + k^2 + 2k + 1

Unparseable latex formula:

= 2k^2 +4 - (\frac{1}{2})^k^+^1

Unparseable latex formula:

= 2(k+1)^2 - 4(k+1) + 6 -(\frac{1}{2})^k^+^1

WouId I get aII the marks for that inductive step?

(edited 7 years ago)

Reply 582

Zacken

Original post by Yunique

If I carried on that Iast Iine with:

Unparseable latex formula:

k^2 -2k + 3 -(\frac{1}{2})^k^+^1 + k^2 + 2k + 1

Unparseable latex formula:

= 2k^2 +4 - (\frac{1}{2})^k^+^1

Unparseable latex formula:

= 2(k+1)^2 - 4(k+1) + 6 -(\frac{1}{2})^k^+^1

WouId I get aII the marks for that inductive step?

Yes.

Reply 583

Zacken

Original post by yesyesyesno

I think edexcel might throw in an r=0 series but that's been covered so many times in this thread it's simple now.

Oh god, I've answered the same question like 7/8 times on this thread. :lol:

Reply 584

NotNotBatman

For divisibility tests, is the conclusion different from true for n=k, k+1,n =1, so all n. Do you have to state since f(k) divisible by n, so f(k+1) is divisible by n etc.

Reply 585

NotNotBatman

If we were to find a point on a parabola that is equidistant from a point on the directrix and the focus, would the line joining the points always be perpendicular to the directrix?

Reply 586

SB0073

Original post by Zacken

Oh god, I've answered the same question like 7/8 times on this thread. :lol:

Ahh want to make it 8/9 Pleeeease! Just incase :smile:

I remember seeing this in a past paper last question just cant find it anymore! :O Didn't understand it fully at the time

If I had to predict something coming up I think a proof by induction of Un+2=... type of question may come up!

Reply 587

justalawyer1998

Why do some mark schemes say 'all n and nEZ+'. Surely it's just the latter? (induction)

Reply 588

justalawyer1998

Original post by SeanFM

it'd be a bit nasty in that the sum of n terms would be going from r=0 to r=n-1. I wouldn't put it past them but it seems needlessly complicated.

In this case you would prove n = 0 (instead of n = 1) right?

Reply 589

Louisb19

Original post by Nikhilm

Why do some mark schemes say 'all n and nEZ+'. Surely it's just the latter? (induction)

How you state it using set theory is

\forall n, n \in \mathbb{Z}^+

.

This reads as "for all n where n is an element of

\mathbb{Z}^+

Reply 590

justalawyer1998

Mathematical induction Q:

say if you have a summation formula, 1 to n, for (2n + r^2 + 4r). I.e. the n is within the equation. It would be impossible to prove an equality by mathematical induction right? Because the actual equation would change when you have k or k+1?

@Zacken

Reply 591

NotNotBatman

So, matrix multiplication is not commutative, but for the induction questions it is, because (where

\mathbf A

is a matrix)

Unparseable latex formula:

\mathbf{A}^k^+^1 = \mathbf{A}^k\cdot \mathbf{A}^1

and

Unparseable latex formula:

\mathbf{A}^k^+^1 = \mathbf{A}^1\cdot \mathbf{A}^k

due to index laws, so does it matter what way around we multiply it in the in inductive proof?

Reply 592

Eshanth

Anyone know any good tips on how to work out the transformations of a matrix?

Reply 593

maruchan

Original post by Eshanth

Anyone know any good tips on how to work out the transformations of a matrix?

for rotations find the inverse of it using your calculator and the formula in the booklet

Reply 594

LukeB98

Not sure if this has been brought up before but I noticed there was one proof by induction question in the textbook that had a factorial in it and I was wondering the best way to go about these problems if it were to come up in the exam tomorrow.

Reply 595

economicss

Original post by Don John

The determinant of the product of two square and equal dimension matrices is equal to the product of both matrix's determinants. Also, the determinant of the inverse of a matrix is equal to the inverse of the determinant of the original matrix.

So if the determinant of the inverse is a third, what does that tell you about