Condensed AQA Core 4 Jan 2011 Paper

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  • Created on: 07-06-13 16:31
Preview of Condensed AQA Core 4 Jan 2011 Paper

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General Certificate of Education
Advanced Level Examination
January 2011
Mathematics MPC4
Unit Pure Core 4
Monday 24 January 2011 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.
P38267/Jan11/MPC4 6/6/6/ MPC4

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Express 2 sin x þ 5 cos x in the form R sinðx þ a Þ , where R > 0 and 0° < a < 90° .
Give your value of a to the nearest 0.1° . (3 marks)
(b) (i) Write down the maximum value of 2 sin x þ 5 cos x .…read more

Page 3

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A curve is defined by the parametric equations
x ¼ 3et , y ¼ e2t À eÀ2t
(a) (i) Find the gradient of the curve at the point where t ¼ 0 . (3 marks)
(ii) Find an equation of the tangent to the curve at the point where t ¼ 0 . (1 mark)
(b) Show that the cartesian equation of the curve can be written in the form
x2 k
y¼ À 2
k x
where k is an integer.…read more

Page 4

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Given that tan 2x þ tan x ¼ 0 , show that tan x ¼ 0 or tan2 x ¼ 3 . (3 marks)
(ii) Hence find all solutions of tan 2x þ tan x ¼ 0 in the interval 0° < x < 180° .…read more

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The coordinates of the points A and B are ð3, À 2, 4Þ and ð6, 0, 3Þ respectively.
2 3 2 3
3 2
The line l1 has equation r ¼ 4 À2 5 þ l 4 À1 5 .
4 3
!
(a) (i) Find the vector AB . (2 marks)
!
(ii) Calculate the acute angle between AB and the line l1 , giving your answer to the
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