OCR C4 2017 Unofficial Community Markscheme
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- i) Binomial Expansion
(3 marks)
ii) Range of x values:
( -⅛<x<⅛ also allowed) (1 mark)
2. Vectors. Find intersection of lines.
Point (8,5,17) (4 marks)
3. Show 
Sub in limits of 1 & 0 to get 
(5 marks)
4. Partial fractions? I think I got 2, 5 and -3 as numerators Something like 2/(1-x) + 5/(3-x)? -3/(1+2x) ?
5. i) Quotient: 3x^2 -3 Remainder: x+1
+c
ii) Integrate = 18 + 0.25ln(31)
6.
The graph
+ 
y - 8 =0 meets the line y=1,twice, calc. dy/dx for these points.
⅔ and -⅔
7. Pond Question
dA/dt = 0.48, at A=10, t=0
Area = 250 however A does tend towards 250, not quite reaching it though. True Does anyone have a reason / working for the area? - A=(250e^kt)/(24+e^kt), as e^kt tends towards infinity A tends towards 250 - water approaches area asymptotically, but area = 250
(1/A + 1/(250-A).da/dt = k
Think I got A=(250e^kt)/(1+24e^kt)
i) Express A in terms or k and t.
A=
ii) Value of k=1/20
A=250/24e^-kt + 1 as t tends towards infinity a tends towards 250
iii) Pond area. = 250
8.i) y=ln((1+sin4x)/cos4x)
Show that dy/dx = 4/cos4x: turn to y=ln(sec4x + tan4x), then differentiate to get
(sec4xtan4x + sec^2(4x))/(sec4x + tan4x), simplifies to required form
Or
y=ln(u)
dy/du=1/u = cos4x/1+sin4x
u=1+sin4x/cos4x
Quotient rule; 4cos^2(4x)-(-4sin^2(4x)-4sin4x)/cos^2(4x)
=4(cos^2(4x)+sin^2(4x))+4sin(4x)/cos^2(4x)
=4(1+sin4x)/cos^2(4x)
dy/dx=4/cos(4x)
ii) Integral of ((sin2x)/sin2x+cos2x) + (cos2x/(sin2x - cos2x)) Something like that
0.25ln((1+sin4x)/cos4x) +c
9. Integration by sub u=1+lnx+x
I ended up with 6ln(1+lnx+x) -3(1+lnx+x) + c
10. Vectors
i) Equation of line AB: (5,1,9) + t(3,6,6) ? think (5,1,9) + s(1,2,2) is also valid
A (5,1,9), B (8,7,15)
(4 marks)
ii) Prove Isosceles & calculate angle. P (5 ,-2 ,15)
|AP| = 9
|AB| = 9
Isosceles as |AB|=|AP|
Or use angle formula to find that 2 of the angles are 58.2
Angle is 63.1 (cos(theta) = 4/9)
cos(theta)*hypotenuse= 4/9*|AP| = 4/9*9 = ½|AD| = 4
|AD|=8 |AB|=9
|AD| = 8/9|AB|
(5,1,9) + 8/9(3,6,6) = D
Coords of D are: (23/3,19/3,43/3) (4 marks)
11. Parametric Equations
i) Find dy/dx = 2(3t^2-3)(t-2)^3/2
(3 marks)
ii) Find and classify stat point (4 marks)
Solutions are t^2 -1 = 0 and something else but two of them are out of range for t
t = -1 or 1 ,1 isn’t in the range -2<t<=0
(1, 2) is stat point. (Using old-school left right diff) nature: Maximum point
iii) (Range of x and y) x>=1/sqrt2 -2<y<=2 (2 marks)
iv) Draw graph (asymptote at y=-2), crosses x axis at 1/sqrt2 and sqrt3 (1 mark)
Predicted Grade Boundaries:
100UMS = 63/72
90UMS = 57/72
80UMS = 50/72
70UMS = 43/72
The grade boundaries above are ridiculous.
Comparing to previous years I assume:
90UMS= 57 (June 2014 an A was 51 marks, and that was relatively easy compared to this paper)
80UMS= 53
70UMS=48
9 marks between 70 and 90 seems a little steep, i think the first is more reasonable
To help you recover from the misery that this exam is, here are some amusing C4 tweets: