MAS111
SCHOOL OF MATHEMATICS AND STATISTICS
Sample exam 2012-2013
Mathematics Core II
2 hours
Attempt all the questions. The allocation of marks is shown in brackets.
Section A
A1
Solve the following inequalities:
(i)
(2 marks)
(ii)
A2
j4x 3j < 5;
1
2
x
MAS111 Strand 1: Solutions to Week 1 Problems
Spring Semester 2013-2014
Week 1 (Review)
1. Let A = B = x to get cos(2x) = cos2 x sin2 x. So
cos(2x) = (cos2 x + sin2 x) 2 sin2 x
= 1 2 sin2 x
and
cos(2x) = 2 cos2 x (cos2 x + sin2 x)
= 2 cos2 x 1.
Rearrangin
MAS111 Strand 1 Solutions to Problems: Week 7
Spring Semester 2013-2014
1.
z
z x z y
z
z
=
+
=
+
,
u
x u y u
x y
z
z x z y
z
z
=
+
=
.
v
x v
y v
x y
Multiplying gives the result.
2. Dierentiate both sides with respect to x to give
2xy + x2
So
dy
dy
+ cos(
MAS111
SCHOOL OF MATHEMATICS AND STATISTICS
Spring Semester
20122013
Mathematics Core II
2 hours
Attempt all the questions. The allocation of marks is shown in brackets.
Section A
A1
(2 marks)
(ii)
A2
Solve the following inequalities:
(i)
|2x 5| < 7;
(2 m