MATH132 S1, 2013
Mathematics IA (Advanced)
FACULTY OF SCIENCE
Week 5 tutorial exercises
2x + 2
and h(x) = |x| for
2x + 1
every x Z , and by g (x) = x for every x R . Here x denotes the greatest integer not exceeding x ,
so that, for example, 5 = 5, 4 1 =
DEPARTMENT OF
MATHEMATICS
MATH132 S113
NAME: Patel Aanand
Student Id: 43291562
Mathematics IA
(Advanced)
Tutorial Group: C1, Thu 12:00, C5A 313
FACULTY OF SCIENCE
Tutor: Leung Poon
Assignment 2
Due 12:00 05/04 2013
Please sign the declaration below, and s
MATH132 S1, 2013
Mathematics IA (Advanced)
FACULTY OF SCIENCE
Week 7 tutorial exercises
1. Consider the system of linear equations
2x 1 + 5x 2 + 8x 3 = 2,
x 1 + 2x 2 + 3x 3 = 4,
3x 1 + 4x 2 + 4x 3 = 1.
a) Write down the augmented matrix for this system.
b
1
0
0
0
2
1
0
0
0
3
0
0
3
1
1
0
5
3
.
4
0
1
2
1
0
a) Which are the pivot variables and which are the free variables?
b) Determine all the solutions of the system of linear equations.
MATH132 S1, 2013
Mathematics IA (Advanced)
9. Consider the system of li
DEPARTMENT OF
MATHEMATICS
MATH132 S113
NAME: Patel Aanand
Student Id: 43291562
Tutorial Group: C1, Thu 12:00, C5A 313
FACULTY OF SCIENCE
Tutor: Leung Poon
Mathematics IA
(Advanced)
Assignment 3
Due 12:00 03/05 2013
Please sign the declaration below, and s
MATH132 S1, 2013
Mathematics IA (Advanced)
FACULTY OF SCIENCE
Week 9 tutorial exercises
1. Suppose that
3 2 7
M = 6 5 4
0 4 9
6 2 4
N = 0 1 3 .
7 7 5
and
Let c be the third column of M N and d the third column of N M . Calculate c, d , and c d .
2. Simpl
DEPARTMENT OF
MATHEMATICS
MATH132 S113
NAME: Patel Aanand
Student Id: 43291562
Tutorial Group: C1, Thu 12:00, C5A 313
FACULTY OF SCIENCE
Tutor: Leung Poon
Mathematics IA
(Advanced)
Assignment 4
Due 12:00 17/05 2013
Please sign the declaration below, and s
MATH132 S1, 2013
Mathematics IA (Advanced)
FACULTY OF SCIENCE
Week 10 tutorial exercises
0.2 0.2 0
4000000
1. Solve the equation x = C x + d, where C = 0.1 0 0.2 and d = 8000000. This means that you
0.3 0.1 0.3
6000000
need to nd the inverse of I 3 C and
MATH132 S1, 2013
Mathematics IA (Advanced)
FACULTY OF SCIENCE
Week 4 tutorial exercises
1. [R EPEATED FROM LAST WEEK ]
For each of the following sets S, determine if S is bounded above, bounded below or neither, and nd
the supremum and/or inmum of S where
DEPARTMENT OF
MATHEMATICS
MATH132 S113
NAME: Patel Aanand
Student Id: 43291562
Tutorial Group: C1, Wed 12:00, C5A 313
FACULTY OF SCIENCE
Mathematics IA
(Advanced)
Tutor: Leung Poon
Assignment 1
Due 12:00 22/03 2013
Please sign the declaration below, and s
MACQUARIE UNIVERSITY
MID-YEAR EXAMINATIONS 2011
Unit:
MATH 132 Mathematics IA ADVANCED
Date and Time:
16 June 2011 at 8:50
Time Allowed:
Three (3) hours plus ten (10) minutes reading time
Number of Questions:
Six (6)
Instructions:
1. This paper contains v
MACQUARIE UNIVERSITY
MID-YEAR EXAMINATIONS 2009
Unit:
MATH 132 Mathematics IA ADVANCED
Date and Time:
15 June 2009 at 13:50
Time Allowed:
Three (3) hours plus ten (10) minutes reading time
Number of Questions:
Six (6)
Instructions:
1. This paper contains
MACQUARIE UNIVERSITY
MID-YEAR EXAMINATIONS 2010
Unit:
MATH 132 Mathematics IA ADVANCED
Date and Time:
18 June 2010 at 13:50
Time Allowed:
Three (3) hours plus ten (10) minutes reading time
Number of Questions:
Six (6)
Instructions:
1. This paper contains
MACQUARIE UNIVERSITY MID-YEAR EXAMINATIONS 2008
Unit: Date and Time: Time Allowed: Number of Questions: Instructions:
MATH 132 Mathematics IA ADVANCED Wed 18 June 2008 at 13:50 Three (3) hours plus ten (10) minutes reading time Six (6)
1. This paper conta
MATH132 S1, 2013
Mathematics IA (Advanced)
FACULTY OF SCIENCE
Week 1 tutorial exercises
1. Factorize 12x 2 x 6 .
2. Simplify the expression
x 2 y 2
.
x 1 y 1
3. Suppose that f (t ) = a b t , for constants a and b and variable t . Find a and b so that f (2
MATH132 S1, 2013
Mathematics IA (Advanced)
FACULTY OF SCIENCE
Week 2 tutorial exercises
1. Let be the set = a, b, c, d . How many elements does have? Find all the subsets of . How
many subsets does have? Can you nd a general expression for the number of s
MATH132 S1, 2013
Mathematics IA (Advanced)
FACULTY OF SCIENCE
Week 3 tutorial exercises
1. Let w = 512i . Calculate w+|w| and (w + |w|)2 . Find the positive real number t for which (w + |w|)2 = t w.
Calculate = (w + |w|) / t and check that 2 = w.
2.
a) Fi
DEPARTMENT OF
MATHEMATICS
MATH132 S113
NAME: Patel Aanand
Student Id: 43291562
Tutorial Group: C1, Thu 12:00, C5A 313
Tutor: Leung Poon
FACULTY OF SCIENCE
Mathematics IA
(Advanced)
Assignment 5
Due 12:00 31/05 2013
Please sign the declaration below, and s