Condensed AQA Core 4 June 2012 Paper

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  • Created on: 07-06-13 16:19
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General Certificate of Education
Advanced Level Examination
June 2012
Mathematics MPC4
Unit Pure Core 4
Thursday 14 June 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 each question in the space provided for that
n
*
question. If you require extra space, use an AQA supplementary
answer book; do not use the space provided for a different question.
o
Do not write outside the box around each page.
*
*
Show all necessary working; otherwise marks for method may be
lost.
Do all rough work in this book. Cross through any work that you do
C
*
not want to be marked.
Information
*
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.
P50339/Jun12/MPC4 6/6/6/ MPC4

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À 6 A B
1 (a) (i) Express in the form þ . (2 marks)
xðx À 3Þ x xÀ3
ð
5x À 6
(ii) Find dx . (2 marks)
xðx À 3Þ
(b) (i) Given that
4x 3 þ 5x À 2 ¼ ð2x þ 1Þð2x 2 þ px þ qÞ þ r
find the values of the constants p, q and r. (4 marks)
ð
4x 3 þ 5x À 2
(ii) Find dx .…read more

Page 3

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The value, £V , of an initial investment, £P, at the end of n years is given by the
formula
r n
V ¼P 1þ
100
where r % per year is the fixed interest rate.
Mr Brown invests £1000 in Barcelona Bank at a fixed interest rate of 3% per year.
(a) (i) Find the value of Mr Brown's investment at the end of 5 years. Give your value to
the nearest £10 .…read more

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The line l1 has equation r ¼ 4 À2 5 þ l 4 0 5 , where q is an integer.
q À1
2 3 2 3
8 2
The line l2 has equation r ¼ 3 þ m 5 5 .
4 5 4
5 4
The lines l1 and l2 intersect at the point P.
(a) Show that q ¼ 4 and find the coordinates of P. (3 marks)
(b) Show that l1 and l2 are perpendicular.…read more

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