pearson edexcel international gcse further pure mathematics
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P46901A©2016 Pearson Education Ltd.
1/1/1/
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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
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)
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Question 1 continued
(Total for Question 1 is 5 marks)
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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)
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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)
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4 The n tn
n Sn
S t2 5
2
3= S
4 = t
(5)
Sp
Sp
p
(3)
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Question 4 continued
(Total for Question 4 is 8 marks)
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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
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Question 5 continued
(Total for Question 5 is 9 marks)
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6
x
(2)
(7y
(2)
a a
(3)
b 7 b
(5)
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Question 6 continued
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Question 6 continued
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Question 6 continued
(Total for Question 6 is 12 marks)
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7 y x
x 1
y 4
(2)
y x x
(2)
7
(3)
x + x = x
(4)
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Question 7 continued
–
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–
–
–
–
–
–
–
–
O
1
4
5
1– – – – – –
y
x
Turn over for a spare grid if you need to redraw your graph.
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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
–
–
–
–
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1
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1
– – – – – –y
x
(Total for Question 7 is 11 marks)
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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)
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Question 8 continued
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Question 8 continued
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Question 8 continued
(Total for Question 8 is 13 marks)
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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)
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Question 9 continued
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Question 9 continued
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Question 9 continued
(Total for Question 9 is 16 marks)
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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)
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Question 10 continued
Turn over
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Question 10 continued
(Total for Question 10 is 13 marks)
TOTAL FOR PAPER IS 100 MARKS