Condensed AQA Core 4 June 2011 Paper

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  • Created on: 07-06-13 16:28
Preview of Condensed AQA Core 4 June 2011 Paper

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General Certificate of Education
Advanced Level Examination
June 2011
Mathematics MPC4
Unit Pure Core 4
Thursday 16 June 2011 1.30 pm to 3.00 pm
For this paper you must have:
the blue AQA booklet of formulae and statistical tables. d
e
*
You may use a graphics calculator.
Time allowed
*
1 hour 30 minutes s
Instructions
*
n
Use black ink or black ball-point pen. Pencil should only be used for
*
*
drawing.
Fill in the boxes at the top of this page.
Answer all questions.
e
*
margin. d
Write the question part reference (eg (a), (b)(i) etc) in the left-hand
You must answer the questions in the spaces provided. Do not write
n
*
outside the box around each page.
*
Show all necessary working; otherwise marks for method may be
*
lost.
o
Do all rough work in this book. Cross through any work that you do
not want to be marked.
Information
*
*
C
The marks for questions are shown in brackets.
The maximum mark for this paper is 75.
Advice
*
Unless stated otherwise, you may quote formulae, without proof,
from the booklet.
P38710/Jun11/MPC4 6/6/6/6/ MPC4

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The polynomial f ðxÞ is defined by f ðxÞ ¼ 4x 3 À 13x þ 6 .
(a) Find f ðÀ2Þ . (1 mark)
(b) Use the Factor Theorem to show that 2x À 3 is a factor of f ðxÞ . (2 marks)
2x 2 þ x À 6
(c) Simplify . (4 marks)
f ðxÞ
2 The average weekly pay of a footballer at a certain club was £80 on 1 August 1960.
By 1 August 1985, this had risen to £2000 .…read more

Page 3

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A curve is defined by the parametric equations x ¼ 3 cos 2y , y ¼ 2 cos y .
dy 1
(i) Show that ¼ , where k is an integer. (4 marks)
dx k cos y
p
(ii) Find an equation of the normal to the curve at the point where y ¼ . (4 marks)
3
ðp
4
(b) Find the exact value of sin2 x dx .…read more

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A giant snowball is melting. The snowball can be modelled as a sphere whose
surface area is decreasing at a constant rate with respect to time. The surface area of
the sphere is A cm2 at time t days after it begins to melt.
(a) Write down a differential equation in terms of the variables A and t and a constant k ,
where k > 0 , to model the melting snowball.…read more

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