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Further Mathematics
� �
Advanced
PAPER 4A: Further Pure Mathematics 2
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.
• There are 9 questions in this question paper. The total mark for this paper is 75.
– use this as a guide as to how much time to spend on each question.
• Read each question carefully before you start to answer it.
• Check your answers if you have time at the end. Turn over
,1. The set S = {1, 3, 5, 9, 11, 13} forms the group G, under the operation multiplication
modulo 14
(a) Complete the Cayley table below for the group G
×14 1 3 5 9 11 13
1 1 3 5 9 11 13
3 3 9 1 13 5 11
5 5 1 11
9 9 13 11
11 11 5 9
13 13 11 1
A spare table can be found on page 5 if you need to rewrite your Cayley table.
(3)
(b) Write down a subgroup of G of order 2
(1)
The group H is defined by the Cayley table below.
* p q r s t u
p p q r s t u
q q t u r s p
r r u t q p s
s s r q p u t
t t s p u r q
u u p s t q r
(c) Show that G and H are isomorphic.
(3)
2
■■■■
,Question 1 continued
3
■■■■ Turn over
, Question 1 continued
4
■■■■
Number Number
Further Mathematics
� �
Advanced
PAPER 4A: Further Pure Mathematics 2
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.
• There are 9 questions in this question paper. The total mark for this paper is 75.
– use this as a guide as to how much time to spend on each question.
• Read each question carefully before you start to answer it.
• Check your answers if you have time at the end. Turn over
,1. The set S = {1, 3, 5, 9, 11, 13} forms the group G, under the operation multiplication
modulo 14
(a) Complete the Cayley table below for the group G
×14 1 3 5 9 11 13
1 1 3 5 9 11 13
3 3 9 1 13 5 11
5 5 1 11
9 9 13 11
11 11 5 9
13 13 11 1
A spare table can be found on page 5 if you need to rewrite your Cayley table.
(3)
(b) Write down a subgroup of G of order 2
(1)
The group H is defined by the Cayley table below.
* p q r s t u
p p q r s t u
q q t u r s p
r r u t q p s
s s r q p u t
t t s p u r q
u u p s t q r
(c) Show that G and H are isomorphic.
(3)
2
■■■■
,Question 1 continued
3
■■■■ Turn over
, Question 1 continued
4
■■■■
