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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…

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1 (a) 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…

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4 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…

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6 (a) (i) 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° .…

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8 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…

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