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
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.
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

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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
nearest 0.1°.…read more


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