AQA A2 Mathematics MPC4 Core 4 - 9th June 2015 [Discussion & unofficial markscheme]

What are you aiming for? That could be enough for an A*?


Posted from TSR Mobile

Aiming for an a* but seems to be hopeless.But I check 2012 and 2013 grade boundaries, I can just hopefully get an a* if this year's boundary follows the trade Can forgive myself making tones of silly mistakes.


Posted from TSR Mobile

Easily! What about 73 in Core 3 and 65 in Core 4?


Posted from TSR Mobile

I reckon the grade boundaries for C3 will cap at about 70/71, so you probably have 100 in C3 and I reckon it'll be about 58 for an A in C4 so you'll have your 180 UMS average. thanks for responding!

I'm sure this year's boundaries will follow the trend. Hard to say until results day!


Posted from TSR Mobile

UNOFFICIAL MARK SCHEME

1.

A) Express f(x) = (19x-2)/(5-x)(1+6x) in the form:

f(x) = A/(5-x) + B/(1+6x):



A=3 B=-1 (3 marks)



B) Find Integral between x = 4 and x = 0 of f(x). Show it equals pln5.



= 8/3ln5 (6 marks)



2.

A) Express 2cosx - 5sinx in the form Rcos(x+alpha), R>0, 0<alpha<pi/2

√29cos(x+1.19) (3 Marks)



B) Find value of x in interval 0<x<2pi where 2cosx - 5sinx is at a maximum.

(i). x=5.09 (2 Marks)

(ii) Solve equation 2cosx - 5sinx + 1 = 0

x=0.567, 3.34 (3 Marks)



3.

A) g(x) = 8x^3 - 12x^2 - 2x + d

Given when g(x) is divided by (2x+1) the remainder is -2, find d.

d=1 (2 Marks)



B) Given x = -0.5 is a solution of g(x)=0, express g(x) as 3 linear factors.

g(x) = (2x+1)(2x-1)(2x+3) (3 marks)



C) h(x) is given by 4x^2 - 1 / f(x). Simplify h(x), showing it is a decreasing function.



h(x) = 1/(2x+3), h'(x) = -2(2x+3)^-2 this is always negative, therefore it is a decreasing function (4 Marks)



4.

A) Find the binomial expansion of (1+5x)^(1.5):

= 1 + x - 2(x^2) (2 Marks)

B) Expand (8 + 3x)^(-2/3)

(i). 1/4 - (1/16)x + (5/256)x^2 (3 Marks)

(ii) Find an estimate for Cube root of 1/81.

0.2313 (2 Marks)



5. x = cos2t, y = sint

A) Find the gradient at t = pi/6.

dy/dx= -1/2 (3 Marks)



B) Equation of normal at t=pi/6

y=2x-1/2 (2 Marks)



C) Normal cuts curve at Q(cos2q, sinq). Set up a quadratic in sinq to find where the normal cuts the curve again. Then find the x co-ordinate of Q.

cos2q = -1/8 (5 Marks)



6. A = (3,2,10), B = (5,-2, 4)

Line l passes through A and has equation:

r = [3,2,10] + lambda[x,y,z]



A) Find angle between line l and AB.

Theta = 60 degrees (4 Marks)

B) C(15, 6, 2) (4 Marks)

C) E(11, 0, 0) and (23, 3, 0) (4 Marks)



7. y^3 + 2e^(-3x)y + x = k

Find k given point P (ln2, 0.5) lies on curve.

A) k=1/4 - ln2 (1 Mark)

B). Find the gradient at P:

dy/dx = 11/8 (6 Marks)



8. dx/dt = (4+5x)^0.5/5(1+t)^2

A) Given t=0 when x=0 find x in terms of t.

x=9/20-1/2(t+1)-1/20(1+t)^2

OR

x = 1/5[(-1/2(1+t)^-1 + 5/2)^2 - 4]



(7 marks)



B) Another pond models a circle of radius r. Rate of change of radius is inversely proportional to pond surface area. Write a differential equation to model this situation.

(i) dr/dt = k/(pir^2) (3 Marks)



(ii) The rate of change of radius is 4.5 when the radius is 1. Find the radius when the rate is 0.5.

r=3 metres (2 Marks)



Date: 9th June 2015

Time: 09:00am

Duration: 1h 30m

Thanks! Don't know what happened to me in that core 4 paper


Posted from TSR Mobile

Think I at least got 65/75 on c3 and 50/75 on core 4. Please tell me that's enough for a B
I'll probably get close to 70/75 on the decision exam (fingers crossed)


Posted from TSR Mobile

Probably an A

Hi! Love the work, I'm confident on everything except the formulation of a differential equation and the final trig question (not the parametric one).

Your +C in your differential equation solution, was that meant to be +1?

Is it Question 8(a)?

If so could you let me know where I've gone wrong, I have just checked it and got C=5 again - in a previous post somebody said it should be 5

Thanks

Is it Question 8(a)?

If so could you let me know where I've gone wrong, I have just checked it and got C=5 again - in a previous post somebody said it should be 5

Thanks