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# Pearson Edexcel International GCSE Further Pure Mathematics

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1/1/1/

*P46901A0132*

Further Pure MathematicsPaper 1

Tuesday 14 June 2016 – Morning

Time: 2 hours 4PM0/01

Calculators may be used.

Instructions

• Use black ink or ball-point pen.

centre number and candidate number.

• Without sufficient working, correct answers may be awarded no marks.

• Answer the questions in the spaces provided

– there may be more space than you need.

Information

• The total mark for this paper is 100.

• The marks for each question are shown in brackets

– use this as a guide as to how much time to spend on each question.

Pearson Edexcel

International GCSE

2

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You must write down all the stages in your working.

1 f ( )x x x= − +3 7 6

(a) Show that (x x)

(2)

x)

(3)

3

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Question 1 continued

(Total for Question 1 is 5 marks)

4

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2 1 3 21

3+( )−

x x x

x6

(3)

f ( )

( )

xkx

x

=−

+

1

1 3

2

2

1

3

k

x x

x4

(3)

x x −5

k

(1)

5

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Question 2 continued

(Total for Question 2 is 7 marks)

6

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3 ABCDE ABCD

AE

(3)

ABE

ABCD

(3)

7

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Question 3 continued

(Total for Question 3 is 6 marks)

8

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4 The n tn

n Sn

S t2 5

2

3= S

4 = t

(5)

Sp

Sp

p

(3)

9

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Question 4 continued

(Total for Question 4 is 8 marks)

10

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5

A + B A B A B

tansin

cosA

A

A=

x + x )

x = 4 tan

(5)

y y y

(4)

11

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Question 5 continued

12

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Question 5 continued

13

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Question 5 continued

(Total for Question 5 is 9 marks)

14

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6

x

(2)

(7y

(2)

a a

(3)

b 7 b

(5)

15

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Question 6 continued

16

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Question 6 continued

17

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Question 6 continued

(Total for Question 6 is 12 marks)

18

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7 y x

x 1

y 4

(2)

y x x

(2)

7

(3)

x + x = x

(4)

19

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Question 7 continued

O

1

4

5

1– – – – – –

y

x

Turn over for a spare grid if you need to redraw your graph.

20

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Question 7 continued

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Question 7 continued

Only use this grid if you need to redraw your graph

O

1

4

5

1

– – – – – –y

x

(Total for Question 7 is 11 marks)

22

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8

A

BDO

E

NOT

Figure 1

OA = a OB = b OD = 2

3b

a b

(5)

F OA OF = F E B

(5)

OFB

p

qp q

(3)

23

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Question 8 continued

24

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Question 8 continued

25

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Question 8 continued

(Total for Question 8 is 13 marks)

26

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9 x x x

x

x

andα β

β α

(6)

(5)

x A(x + B ) + C A B C

(3)

x

(2)

27

*P46901A02732* Turn over

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Question 9 continued

28

*P46901A02832*

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Question 9 continued

29

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Turn over

Question 9 continued

(Total for Question 9 is 16 marks)

30

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10 A B

C AB

C

(2)

D

(b) Show that DC AB

(3)

DC py = x + q

(2)

E DCE DC = CE.

E

(2)

(4)

31

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Question 10 continued

Turn over

32

*P46901A03232*

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Question 10 continued

(Total for Question 10 is 13 marks)

TOTAL FOR PAPER IS 100 MARKS