Edexcel Maths FP1 UNOFFICIAL Mark Scheme 19th May 2017

Ffs, i thought the k series one was kr(2^(r-1)) not k(2^(r-1))

Hopefully this helps.

U have to prove true for n=k+2 by induction and assume true for n=k and n=k+1

I believe this is correct too.

Oh... We weren't taught that you could do multiple f(k) :/

Am i the only one who forgot the sum for 2 to the power of r-1 from c2 so manually wrote out all 12 terms such mathematical elegance

How did you solve this one, tbh I just added it 12 times

You have to test n=1 and n=2, assume it's true for n = k and n = k + 1 then test if it's true for n = k + 2

Use the assumption of k with k-1 to get answer and factorise it into 3^k+1((k+1)+1)

have to use geometric series formula from c2.
Also in the determinant question there is another solution, a = -27/2 as well as -9/2 as both of these satisfy mod(detM) = 18. Great job for putting up this mark scheme with the latex and stuff

ffs, that was a sneaky one. I always seem to forget to consider the negative case.

Sorry, I'll use English,

The question was to prove that 19 divides $3^{3n-2}-2^{3n+1}$ where n is a natural number (positive, non zero integer), which I'm sure you can easily do yourself.

I cannot remember the other one, but it was a sequence of some sort.

Must a Cartesian equation be written with y as the subject, as I had written xy=16 and not y=16/x.

Must a Cartesian equation be written with y as the subject, as I had written xy=16 and not y=16/x.

Must a Cartesian equation be written with y as the subject, as I had written xy=16 and not y=16/x.

These are my answers, looking for mild confirmation, here also are the marks:

1) This was a newton r $f(x)=\frac{1}{3}x^2+\frac{4}{x^2}-2x-1$

a) Prove root [6,7] Change of sign (2 marks)
b) Find first newton approx starting at 6 to 2dp , 6.45 (5 marks)

2) some matrix question:
$A=\begin{bmatrix} 2 & -1 \\ 4 & 3 \end{bmatrix}$
(a) $A^{-1} = \frac{1}{10}\begin{bmatrix} 3 & 1 \\ -4 & 2 \end{bmatrix}$ (2 marks)

$P=\begin{bmatrix} 3 & 6 \\ 11 & -8 \end{bmatrix}$

(b) Given AB=P find B $B = \begin{bmatrix} 2 & 1 \\ 1 & -4 \end{bmatrix}$ (3 marks)

3)
$x=4t$ , $x=\frac{4}{t}$
a) Find a line perpendicular to line between points $t=\frac{1}{4}$ and $t=2$ that goes through origin. Ans: $y=\frac{1}{2}x$ (3 marks)
b) cart equation $y=\frac{16}{x}$

c) Points of intersection $(4\sqrt{2},2\sqrt{2})$ and $(-4\sqrt{2},-2\sqrt{2})$ (3 marks)

4) Complex Numbers, horra.
i) $w=\frac{p-4i}{2-3i}$
a) a+bi form : $\frac{2p+12}{13}+\frac{3p+8}{13}i$ (3 marks)
$arg(w) = \frac{\pi}{4}$
b) p=20 (2 marks)
ii) $z=(1-\lambda i)(4+3i)$ , $\mid z \mid = 45$

$\lambda = \pm 4\sqrt{5}$ (2 marks)

5) i)
$A= \begin{bmatrix} p & 2 \\ 3 & p \end{bmatrix}$ , $B= \begin{bmatrix} -5 & 4 \\ 6 & -5 \end{bmatrix}$
(a) Find AB (2)
$AB + 2A = kI$
find $k$ and $p$
(b) $p=\frac{3}{2}$ , $k = \frac{15}{2}$

ii) I forget what the question was but $a=\frac{9}{2}$ (5 marks)

6 (a) -2-3i (1)
$(x-4)(x+2-3i)(x+2+3i)$
(b) a=2 b=-11 (5 marks)
7 (a) (4 marks)
(b) (4 marks)
(c) $\frac{15}{16}a^2$ (2 marks)

8) Proof involving sums:
(a) (5 marks)
(b) $\frac{2}{9}$ and $\frac{-27}{2}$ (4 marks)

9) two proofs questions, each worth 6 marks


Thanks To:
- @k.russell for 8 b second answer

Shame you couldn't have typeset it properly so that text was a consistent size.