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
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.
*
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

Page 3

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A scientist is testing models for the growth and decay of colonies of bacteria.
1t
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

Page 4

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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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