Condensed AQA Core 4 June 2011 Paper

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  • Created on: 07-06-13 16:28
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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
You may use a graphics calculator.
Time allowed
1 hour 30 minutes s
Use black ink or black ball-point pen. Pencil should only be used for
Fill in the boxes at the top of this page.
Answer all questions.
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
outside the box around each page.
Show all necessary working; otherwise marks for method may be
Do all rough work in this book. Cross through any work that you do
not want to be marked.
The marks for questions are shown in brackets.
The maximum mark for this paper is 75.
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

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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
(ii) Find an equation of the normal to the curve at the point where y ¼ . (4 marks)
(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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