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Page 1

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For Examiner's Use
Centre Number Candidate Number

Surname

Other Names
Examiner's Initials

Candidate Signature


Pages Mark

Level 2 Certificate in Further Mathematics 3
June 2013
4­5

6­7
Further Mathematics 8360/1 8­9

10 ­ 11
Level 2 12 ­ 13
Paper 1 Non-Calculator 14 ­ 15

Wednesday 19 June 2013 1.30…

Page 2

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2


Formulae Sheet


Volume of sphere ¼ 4 p r 3
3

Surface area of sphere ¼ 4p r 2




Volume of cone ¼ 1 p r 2 h
3

Curved surface area of cone ¼ p rl




In any triangle ABC


Area of triangle ¼ 1 ab sin C…

Page 3

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Answer all questions in the spaces provided.



dy
1 A curve has gradient function ¼ 9 À x3
dx

1 (a) Work out the gradient of the curve when x ¼ À1

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Answer.............................................................................. (2 marks)



1 (b) Work out the value…

Page 4

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2 A is ðÀ4, 3Þ and B is ð2, 11Þ

AB is a diameter of the circle.

y
Not drawn
accurately
P

B




A



O x


2 (a) Work out the coordinates of the centre of the circle.





Centre ¼ ................ , ................…

Page 5

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2 (b) Work out the radius of the circle.

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Radius ¼ ....................................................... (2 marks)



2 (c) Write down the equation of the circle.


Answer ............................................................................. (1 mark)



2 (d) P is another point on the circle.
The gradient of the…

Page 6

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3 ABC is a right-angled triangle.
P is a point on AB.

A

x Not drawn
accurately




P


4 cm

x
B C


BP ¼ 4 cm and tan x ¼ 2
3

3 (a) Work out the length of BC.

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Page 7

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pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
pffiffiffi ffi
4 Solve ð33 þ xÞ ¼ 6

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Answer x ¼ ............................................................. (3 marks)




5 (a) Show that ðx þ 7Þ2 À ðx À 3Þ2 simplifies to 20ðx þ 2Þ

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Page 8

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6 Simplify ð3xy 5 Þ4

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Answer.............................................................................. (2 marks)




7 Expand and simplify ðy 2 À 5y þ 2Þð2y À 3Þ

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Answer.............................................................................. (3 marks)




(08)
P61254/Jun13/8360/1

Page 9

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8 A curve has equation y ¼ x 4 À 5x 2 þ 9
dy
8 (a) Work out
dx




dy
Answer ¼ ............................................................ (2 marks)
dx



8 (b) Work out the equation of the tangent to the curve at the point where…

Page 10

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9 Solve x 2 þ 6x þ 7 ¼ 0
pffiffiffi
Give your answer in the form a Æ b , where a and b are integers.

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Answer.............................................................................. (4 marks)




a þ 2x
10…

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