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Pearson Edexcel GCE Advanced Subsidiary Level Further Mathematics (8FM0)
Paper 22 Further Pure Mathematics 2
Afternoon
Further Mathematics
■ ■
Advanced Subsidiary
Further Mathematics options
22: Further Pure Mathematics 2
(Part of option A only)
Candidates may use any calculator allowed by Pearson regulations. Calculators
must not have the facility for symbolic algebra manipulation, differentiation
and integration, or have retrievable mathematical formulae stored in them.
Instructions
• If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
centre number and candidate number.
Answer all questions and ensure that your answers to parts of questions are
clearly labelled.
Answer the questions in the spaces provided
– there may be more space than you need.
You should show sufficient working to make your methods clear. Answers without
working may not gain full credit.
Inexact answers should be given to three significant figures unless
otherwise stated.
• The total mark for this part of the examination is 40. There are 5 questions.
– 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. Turn over
,1. (i) The table below is a Cayley table for the group G with operation °
° a b c d e f
a d c b a f e
b e f a b c d
c f e d c b a
d a b c d e f
e b a f e d c
f c d e f a b
(a) State which element is the identity of the group.
(1)
(b) Determine the inverse of the element (b°c)
(2)
(c) Give a reason why the set {a, b, e, f } cannot be a subgroup of G. You must
justify your answer.
(1)
(d) Show that the set {b, d, f } is a subgroup of G.
(2)
(ii) Given that H is a group with an element x of order 3 and an element y of
order 6 satisfying
yx = xy5
show that y3xy3x2 is the identity element.
(3)
, Question 1 continued
Number Number
Pearson Edexcel GCE Advanced Subsidiary Level Further Mathematics (8FM0)
Paper 22 Further Pure Mathematics 2
Afternoon
Further Mathematics
■ ■
Advanced Subsidiary
Further Mathematics options
22: Further Pure Mathematics 2
(Part of option A only)
Candidates may use any calculator allowed by Pearson regulations. Calculators
must not have the facility for symbolic algebra manipulation, differentiation
and integration, or have retrievable mathematical formulae stored in them.
Instructions
• If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
centre number and candidate number.
Answer all questions and ensure that your answers to parts of questions are
clearly labelled.
Answer the questions in the spaces provided
– there may be more space than you need.
You should show sufficient working to make your methods clear. Answers without
working may not gain full credit.
Inexact answers should be given to three significant figures unless
otherwise stated.
• The total mark for this part of the examination is 40. There are 5 questions.
– 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. Turn over
,1. (i) The table below is a Cayley table for the group G with operation °
° a b c d e f
a d c b a f e
b e f a b c d
c f e d c b a
d a b c d e f
e b a f e d c
f c d e f a b
(a) State which element is the identity of the group.
(1)
(b) Determine the inverse of the element (b°c)
(2)
(c) Give a reason why the set {a, b, e, f } cannot be a subgroup of G. You must
justify your answer.
(1)
(d) Show that the set {b, d, f } is a subgroup of G.
(2)
(ii) Given that H is a group with an element x of order 3 and an element y of
order 6 satisfying
yx = xy5
show that y3xy3x2 is the identity element.
(3)
, Question 1 continued
