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General Certificate of Education
Advanced Level Examination
January 2012

Mathematics MPC4
Unit Pure Core 4
Monday 23 January 2012 9.00 am to 10.30 am

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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2x þ 3 A B
1 (a) Express in the form þ , where A and B are integers. (3 marks)
4x 2 À 1 2x À 1 2x þ 1

12x 3 À 7x À 6 Dð2x þ 3Þ
(b) Express 2
in the form Cx þ ,…

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4 A scientist is testing models for the growth and decay of colonies of bacteria.

For a particular colony, which is growing, the model is P ¼ Ae 8 , where P is the
number of bacteria after a time t minutes and A is a constant.


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6 (a) Use the Factor Theorem to show that 4x À 3 is a factor of

16x 3 þ 11x À 15 (2 marks)

(b) Given that x ¼ cos y , show that the equation

27 cos y cos 2y þ 19 sin y sin 2y À 15…


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