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Centre Number Candidate Number Write your name here Surname Other names Total Marks Paper Reference Turn over P46901A ©2016 Pearson Education Ltd. 1/1/1/ *P46901A0132* Further Pure Mathematics Paper 1 Tuesday 14 June 2016 – Morning Time: 2 hours 4PM0/01 Calculators may be used. Instructions Use black ink or ball-point pen. Fill in the boxes at the top of this page with your name, centre number and candidate number. Answer all questions. 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. Advice Read each question carefully before you start to answer it. Check your answers if you have time at the end. Pearson Edexcel International GCSE

Pearson Edexcel International GCSE Further Pure Mathematics

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Page 1: Pearson Edexcel International GCSE Further Pure Mathematics

Centre Number Candidate Number

Write your name here

Surname Other names

Total Marks

Paper Reference

Turn over

P46901A©2016 Pearson Education Ltd.

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.

• Fill in the boxes at the top of this page with your name,

centre number and candidate number.

• Answer all questions.

• 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.

Advice

• Read each question carefully before you start to answer it.

• Check your answers if you have time at the end.

Pearson Edexcel

International GCSE

Page 2: Pearson Edexcel International GCSE Further Pure Mathematics

2

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Answer all TEN questions.

Write your answers in the spaces provided.

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)

Page 3: Pearson Edexcel International GCSE Further Pure Mathematics

3

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Question 1 continued

(Total for Question 1 is 5 marks)

Page 4: Pearson Edexcel International GCSE Further Pure Mathematics

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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)

Page 5: Pearson Edexcel International GCSE Further Pure Mathematics

5

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Question 2 continued

(Total for Question 2 is 7 marks)

Page 6: Pearson Edexcel International GCSE Further Pure Mathematics

6

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3 ABCDE ABCD

AE

(3)

ABE

ABCD

(3)

Page 7: Pearson Edexcel International GCSE Further Pure Mathematics

7

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Question 3 continued

(Total for Question 3 is 6 marks)

Page 8: Pearson Edexcel International GCSE Further Pure Mathematics

8

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4 The n tn

n Sn

S t2 5

2

3= S

4 = t

(5)

Sp

Sp

p

(3)

Page 9: Pearson Edexcel International GCSE Further Pure Mathematics

9

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Question 4 continued

(Total for Question 4 is 8 marks)

Page 10: Pearson Edexcel International GCSE Further Pure Mathematics

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)

Page 11: Pearson Edexcel International GCSE Further Pure Mathematics

11

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Question 5 continued

Page 12: Pearson Edexcel International GCSE Further Pure Mathematics

12

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Question 5 continued

Page 13: Pearson Edexcel International GCSE Further Pure Mathematics

13

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Question 5 continued

(Total for Question 5 is 9 marks)

Page 14: Pearson Edexcel International GCSE Further Pure Mathematics

14

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6

x

(2)

(7y

(2)

a a

(3)

b 7 b

(5)

Page 15: Pearson Edexcel International GCSE Further Pure Mathematics

15

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Question 6 continued

Page 16: Pearson Edexcel International GCSE Further Pure Mathematics

16

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Question 6 continued

Page 17: Pearson Edexcel International GCSE Further Pure Mathematics

17

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Question 6 continued

(Total for Question 6 is 12 marks)

Page 18: Pearson Edexcel International GCSE Further Pure Mathematics

18

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7 y x

x 1

y 4

(2)

y x x

(2)

7

(3)

x + x = x

(4)

Page 19: Pearson Edexcel International GCSE Further Pure Mathematics

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.

Page 20: Pearson Edexcel International GCSE Further Pure Mathematics

20

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Question 7 continued

Page 21: Pearson Edexcel International GCSE Further Pure Mathematics

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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)

Page 22: Pearson Edexcel International GCSE Further Pure Mathematics

22

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8

A

BDO

E

NOT

Figure 1

OA = a OB = b OD = 2

3b

E AD

a b

AD OE BE

(5)

F OA OF = F E B

(5)

OFB

OAD

p

qp q

(3)

Page 23: Pearson Edexcel International GCSE Further Pure Mathematics

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Question 8 continued

Page 24: Pearson Edexcel International GCSE Further Pure Mathematics

24

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Question 8 continued

Page 25: Pearson Edexcel International GCSE Further Pure Mathematics

25

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Question 8 continued

(Total for Question 8 is 13 marks)

Page 26: Pearson Edexcel International GCSE Further Pure Mathematics

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)

Page 27: Pearson Edexcel International GCSE Further Pure Mathematics

27

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Question 9 continued

Page 28: Pearson Edexcel International GCSE Further Pure Mathematics

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Question 9 continued

Page 29: Pearson Edexcel International GCSE Further Pure Mathematics

29

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Turn over

Question 9 continued

(Total for Question 9 is 16 marks)

Page 30: Pearson Edexcel International GCSE Further Pure Mathematics

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)

ADBE

(4)

Page 31: Pearson Edexcel International GCSE Further Pure Mathematics

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Question 10 continued

Turn over

Page 32: Pearson Edexcel International GCSE Further Pure Mathematics

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Question 10 continued

(Total for Question 10 is 13 marks)

TOTAL FOR PAPER IS 100 MARKS