Condensed AQA Core 4 Jan 2012 Paper

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  • Created on: 07-06-13 16:25
Preview of Condensed AQA Core 4 Jan 2012 Paper

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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
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.
You do not necessarily need to use all the space provided.
P46341/Jan12/MPC4 6/6/6/ MPC4

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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 , where C and D are integers.…read more

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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.
(a) This growing colony consists initially of 500 bacteria. Calculate the number of
bacteria, according to the model, after one hour. Give your answer to the nearest
thousand.…read more

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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 ¼ 0
can be written in the form
16x 3 þ 11x À 15 ¼ 0 (4 marks)
(c) Hence show that the only solutions of the equation
27 cos y cos 2y þ 19 sin y sin…read more


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