MEI C1 May/June 17 Unofficial Mark Scheme

See attached image

8) proof of root of g(x)=6

I seemed to have gotten all of them except a couple. Anyone know what 12)iii) was out of? Messed that up. Also only got half the working of 11)iii) so wondering what that was out of too. Praying for around 64-67/72

Was out of 4 but I expect there is marks for substituting the 2 equations together and writing b^2-4ac < 0

Same about the workings out on 11, I could do the diving by (X+2) to get to the quadratic, but just for some reason couldn't show the first bit

k< -13 in the end

Defo -11

Urm I dont think the questions are in the right order in your thing but heres what I got:

1. Sketched y= -2x + 1 (0,1) and gradient was -2 (2 marks)
2.
i) (1 7/9)^-1/2 = 3/4 (3 marks)
ii) (6x^5y^2)^3/18y^10 = 12x^15/y^4 (2 marks)
3. 6-x > 5(x-3) = 6 - x > 5x - 15 = -6x > -21 = x< 21/6 (3 marks)
4. Intersection of 2x+5y=5 and x-2y = (10/3, -1/3) (4 marjs)
5. (x+2)^2 + (y-3)^2 = 5
i) radius is root 5, centre is (-2,3) (2 marks)
ii) Line parallel to 5x + y = 4 and touches centre is y= -5x-7 (2 marks)
6. r = root (v/a+b) - Make B the subject : Two possible answers are b = (v-ar^2)/r^2 or b = v/r^2 - a (4 marks)
7.
i) (5-2root7)/3+root7 = (29-11root7)/2 (3 marks)
ii) 12/root2 + root 98 = 13root2 (2 marks)
8. (a+bx)^5 x^3 coefficient is -1080, constant is 32. a^5 = 32, so a = 2. b= -3 (5 marks)
9. Three consecutive integers and n is the smallest (therefore n, n+1 and n+2) show difference between squares of smallest and largest is 4 * middle. (n+2)^2 - n^2 = 4n+4. 4n+4 = 4(n+1). (4 marks.

Section B

10. A(3,3) B (-2,-2) C (5,-1)
i) Show AB is BC. AB = ROOT 50, BC = ROOT 50 (2 marks)
ii)Line perpendicular to AC which passes by B
Grad of AC is -2, perp gradient is 1/2. Line is y= 1/2x-1 (4 marks)
iii) D is (10,4) because difference between B and C is 7, 1. Add 7 to x of A and 1 to y of A to get 10,4 (2 marks)
iv) 3.8 < 26/7. Find equation of lines and prove 8, 3.8 does not belong in them therefore it is outside rhombus (4 marks)
11. f(x) = (x-2)(2x-3)(x+5)
i) Sketch graph (3 marks)
ii) Show when (-3 0) occurs that g(x) is 2x^3 + 21x^2 + 43x + 24. You use f(x+3) and from that x+3 = 2, 3/2, -5
x = -1, -3/2, -8 are new roots
factors are (x+1)(2x+3)(x+8), multiply out to get the answer (3 marks)
iii)x = -2 is root of g(x)=6, prove this and find other roots. Other roots = (-17+-root217)/4 - Not sure of this (6 marks)
12.
i) Show y= x^2 + x + 3 as (x+a)^2 + b and it doesnt touch the x axis. Completed square is (x+1/2)^2 + 11/4 So minimum point is -1/2, 11/4 which is above x axis (4 marks)
ii) Intersection of x^2+x+3 and 2x^2-3x-9 are (6,45) and (-2,5) (4 marks)
iii) For what values of k is there no intersection of x^2 + x + k and 2x^2 - 3x- 9
Use b^2 - 4ac<0
k< -13

I have the official 2017 paper. took it from the exam with me