Edexcel Maths FP1 UNOFFICIAL Mark Scheme 19th May 2017

I got 8f(k) + 19(3^3k+blah). There are loads of different methods for it.

what question was the p=20 one?

you know the last part of the series question i got 910=sigma k(2^r-1) and couldnt do the rest how many mark do you think that'll get? and how many marks was that last part of the question if any1 knows?

Do you remember your working for the question? None of my classmates including me were able to do this question, a few of them are still trying to work it out right now. Any help?

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) $p=\frac{3}{2}$ , $\frac{15}{2}$

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) (a) (5 marks)
(b) $\frac{2}{9}$ (4 marks)

9) two proofs questions, each worth 6 marks

For the Area FXD question:
tangent has equation yq= x+ aq^2
at directrix, x= -a so yq = -a + aq^2 so y = (-a + aq^2)/q
F(a,0) X(-0.25a,0) D(-a, (-a + aq^2)/q)
Area of FXD = 1/2 x base x height = 0.5 x (a+0.25a) x modulus of ((aq^2 - a)/q)

Lets suppose the y coordinate of D is -5, length is 5, so times y coordinate of D by -1 to give magnitude.

Area = 0.5 x (1.25a) x ((a - aq^2)/q) = 0.625 x q^-1 x (a^2 - (a^2 x q^2))
I got it all in terms of q, as q is a parameter and everything in the question is algebra

I got fisted by the proof but the rest went well

For the Area FXD question:
tangent has equation yq= x+ aq^2
at directrix, x= -a so yq = -a + aq^2 so y = (-a + aq^2)/q
F(a,0) X(-0.25a,0) D(-a, (-a + aq^2)/q)
Area of FXD = 1/2 x base x height = 0.5 x (a+0.25a) x modulus of ((aq^2 - a)/q)

Lets suppose the y coordinate of D is -5, length is 5, so times y coordinate of D by -1 to give magnitude.

Area = 0.5 x (1.25a) x ((a - aq^2)/q) = 0.625 x q^-1 x (a^2 - (a^2 x q^2))
I got it all in terms of q, as q is a parameter and everything in the question is algebra

What were proof questions?

How did everyone do the first proof by induction question? Was I wrong to prove true for n=k+1 and n=k+2?

one was $19 \mid 3^{3n-2}-2^{3n+1}$ for all n in natural set

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

Also for the matrix question where it was AB +2A= kI, me and my friends got p=3/2, k=15/2

I consider this half-answer neither sufficient nor helpful

Question 5 Matrices
i.) a.) ((12-5p) (4p-10))
..........((6p-15) (12-5p)) [2]
b.) p=1.5, k=7.5 [4]
ii.) a=4.5 [5]