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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…

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1 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…

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4 (a) 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…

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7 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…


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