Kings College London
UNIVERSITY OF LONDON
This paper is part of an examination of the College counting towards the award of a degree.
Examinations are governed by the College Regulations under the authority of the Academic
Boazd. , 9- _
B'SCIEXAMINATION
Kings College London
UNIVERSITY OF LONDON
This paper is part of an examination of the College counting towards the award _of a. degree.
Exa'nl'lathIlS are governed by the College Regulations under the authority of the Academic
" ' ATTACH THIS PAPER
Kings College London
University Of London
This paper is part of an examination of the College counting towards the award of a degree.
Examinations are governed by the College Regulations under the authority of the Academic
Board.
ATTACH this paper to your
CM121A, Abstract Algebra
May 2010 Exam
Solutions
A1. Find all solutions with , to the equation 20 + 34 = 10.
Solution:Apply the Euclidean algorithm to 20 and 34:
34 = 1 20 + 14,20 = 1 14 + 6,14 = 2 6 + 2,6 = 3 2
so gcd(20, 34) = 2 and the equation has sol
IngS College London
UNIVERSITY OF LONDON
paper is part of an examination of the College counting towards the award of a degree.
ATTACH THIS PAPER TO YOUR SCRIPT USING THE STRING PROVIDED
Candidate N o: . : .' .
BSC EXAMINATION
. CM241X PROBABILI
CM121A, Abstract Algebra
A1.
May 2009 Exam
Solutions
a) Find all x Z satisfying the congruence 19x 401 mod 10.
Solution:This is the same as x 1 mod 10,
so the solution is
x 1 mod 10, or x = 1 + 10k with k Z.
b) Find all solutions with x, y Z to the linear
Kings College London
University Of London
This paper is part of an examination of the College counting towards the award of a degree
Examinations are governed by the College Regulations under the authority of the Academic
Board.
ATTACH this paper to your
Kings College London
University Of London
This paper is part of an examination of the College counting towards the award of a degree.
Examinations are governed by the College Regulations under the authority of the Academic
Board.
ATTACH this paper to your
5CCM121A/6CCM121B
May 2011 Exam Solutions
A1. Recall that denotes the set cfw_[] : of residue classes modulo
and that this set forms a group under the operation of addition of residue
classes. Find the orders of the elements [49]98 and [38]98 in the gro
Kings College London
University Of London
This paper is part of an examination of the College counting towards the award of a degree.
Examinations are governed by the College Regulations under the authority of the Academic
Board.
ATTACH this paper to your
Kings College London
University Of London
This paper is part of an examination of the College counting towards the award of a degree.
Examinations are governed by the College Regulations under the authority of the Academic
Board.
ATTACH this paper to your
CM241X SOLUTIONS 2008
A1. (i) fX (x) = C
fY (y) = C
(ii) 1 =
R1
0
R1
y/3
R 3x
0
xdx =
xdy = 3Cx2
C 2 1
2 x |y/3
=
C
2 (1
y 2 /9)
3Cx2 dx = C = C = 1
(iii) f (x|y) = f (x, y)/fY (y) = 2x/(1
y2
9 )
1
f (x|y = 13 ) = 2x(1 81
) = 81
40 x
The line y = 13 int
Kings College London
University Of London
This paper is part of an examination of the College counting towards the award of a degree.
Examinations are governed by the College Regulations under the authority of the Academic
Board.
ATTACH this paper to your
5CCM241A/6CCM241B Solutions 2015
Note that the total number of marks available to a candidate is 200. The raw marks were converted
to percentages but, as the rubric indicates, how this was done was not quite the same for the two
versions of the exam. Ive
Kings College London
University Of London
This paper is part of an examination of the College counting towards the award of a degree.
Examinations are governed by the College Regulations under the authority of the Academic
Board.
ATTACH this paper to your
Kings College London
University Of London
This paper is part of an examination of the College counting towards the award of a degree.
Examinations are governed by the College Regulations under the authority of the Academic
Board.
ATTACH this paper to your