MATHS108 Test Solutions 2012
Summer School
Semester Two
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(G
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THE UNIVERSITY OF AUCKLAND
MATHS 108
2012 SEMESTER 1 TEST
MATHEMATICS
General Mathematics 1
(Time allowed: 60 MINUTES)
NOTE:
This test will begin with 5 minutes of reading time.
You may not write anything or use a calculator in this time.
This
Lecture 1 a few things to try!
1. Describe the set of all real numbers whose square is 1.
2. Write down all of the sets that are subsets of cfw_1, 2, 3.
3. Describe the elements of the following sets:
a) cfw_0, 2 (0, 2) cfw_1, 2, 3
b) (2, 1] N \ [1, )
MATHS 108 Test Solutions 2015
Summer School
Semester Two
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Department of Mathematics
MATHS 108
Study Guide for Semester Two 2016
This is an important document containing a lot of information about the course. Please refer to
this study guide before emailing your lecturer with course related questions; you may fin
MATHS 108 Test Solutions 2014
Summer School
Semester Two
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Markers Comments Question 12
Note: this is NOT a model answer!
This was a fairly challenging question but a perfect answer was not expected in order to get
full marks. In fact there were many acceptable ways to tackle it.
A basic look at the question woul
Department of Mathematics
MATHS 108
Tutorial 6
1. Write down the augmented matrix for the following system of linear equations and solve the system.
3x1 7x2 + 4x3 = 10
x1 2x2 + 3x3 = 1
x1 + x2 + 2x3 = 8
2. Below is the augmented
1 1 0 0 1
0 1 2 1
A= 0
0
0
Maths 108
The University of Auckland
Assignment 1
Due: Wednesday, August 17th, before 4pm
Semester 2, 2016
Hand your completed assignment in to the correct box in the Student Resource Centre (G38 Building
301) before the due date. Please use a Mathematics
Department of Mathematics
Tutorial 8
MATHS 108
1 3 5
1. Find the determinant of A = 2 1 1 . Is A invertible?
3 4 6
2. Use the cross product to find the general equation of the plane through the points A(1, 3, 5),
B(3, 1, 5) and C(6, 1, 6). Start by findin
VERSION 1
THE UNIVERSITY OF AUCKLAND
MATHS 108
2014 SEMESTER 2 TEST
MATHEMATICS
General Mathematics 1
(Time allowed: 60 MINUTES)
NOTE:
This test will begin with 5 minutes of reading time.
You may not write anything or use a calculator in this time.
This
MATHS 108 Test Solutions 2013
Summer School
Semester Two
Version 1
(Yellow)
Version 2
(Pink)
Version 3
(Green)
Version 4
(Blue)
Version 1
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Version 2
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Section D: Intellectual Property
What is intellectual Property?-Creations of the mind
E.G. Ideas, inventions (patents), books, music, poetry, films (copyright) and signs
(trademark)
What are the two meanings of property?-*Ownership (title)
*Property = the
Section C: law in the Operation of Business
What is the definition of a contract?-A set of promises that the law will enforce
Do all contracts have to be in writing?-No. Contracts can be either fully written,
fully oral or partially written and partially
Department of Mathematics
Tutorial 4
MATHS 108
1. Let u = (1, 1, 0, 2, 1) and v = (2, 8, 6, 0, 6).
(a) Find the angle between the vectors u and v.
(b) Find constants a and b such that au + bv = (1, 2, 3, 4, 5).
2. Given any two vectors u and v show that t
Maths 108
The University of Auckland
Assignment 2
Due: Wednesday, September 28th, before 4pm
Semester 2, 2016
Hand your completed assignment in to the correct box in the Student Resource Centre (G38, Building
301) before the due date. Please use a Mathema
Tutorial Three
COMLAW 101
Law in a business environment
Second Semester 2016
Week A beginning Monday 12th September
Week B beginning Monday 19th September
Tutorial 3
Part A
1.
Brenda, a student, notices an advertisement in the newspaper. The
advertisement
Section D: Trusts
What are 'Legal' interests?-Property rights recognised by common law
Between Legal interests and Equitable interests, which of the two is superior?-Legal Interests
What is a "Trust"?-An equitable obligation that arises when one or more p
Section D: Concepts of Property and Ownership, Trusts
What are the/some of the four Laws of Property?-* Legal relationship between
persons and things
E.G. Your rights to your phones
* "Property" rights enforced against a 'thing' or "property object"
*Not
Department of Mathematics
Tutorial 10
MATHS 108
d
|x|
1. (a) Let f (x) = sin(|x|). Use the Chain Rule and the fact that
(|x|) =
to find the
dx
x
derivative of f , for x 6= 0.
(b) Rewrite f (x) as a piecewise function not involving the absolute value funct
THE UNIVERSITY OF AUCKLAND
BUSINESS SCHOOL
DEPARTMENT OF COMMERCIAL LAW
COMLAW 101
LAW IN A BUSINESS ENVIRONMENT
2016 Second Semester
FINAL EXAMINATION INFORMATION
1. Format of the Examination Paper
The time allowed is TWO hours plus 10 minutes reading ti
Lecture 2 a few things to try!
1. Graph* the following functions.
a(x) = 1/x
b(x) = -x2
c(x) = ln(-x)
d(x) = e1-x
e(x) = (x2+2)/(x2-2)
*Best would be to be able to sketch them by hand
2. Identify their domain and the range of the previous function
MATHS108 Exam Solutions 2013
Semester One
Summer School
Semester Two
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Section C: Fiduciary obligations
What is a Fiduciary Obligation about?-Where fiduciaries serve the interests of
others
i.e. Selflessness rather than selfishness
Which law creates Fiduciary Obligations?-Law of Equity
What are some remedies for a breach in
VERSION 1
MATHS 108
THE UNIVERSITY OF AUCKLAND
SEMESTER ONE, 2015
Campus: City
MATHEMATICS
General Mathematics 1
(Time allowed: TWO hours)
NOTE:
This exam contains 40 questions on pages 3 to 10. Attempt ALL questions.
To answer, fill in the appropriate
VERSION 1
MATHS 108
THE UNIVERSITY OF AUCKLAND
SUMMER, 2012
Campus: City
MATHEMATICS
General Mathematics 1
(Time allowed: TWO hours)
NOTE:
This exam contains 40 questions. Attempt all questions.
Write all answers on the Teleform sheet provided.
Use pen
Department of Mathematics
MATHS 108
Tutorial 3
1. A student defines the function f by: f (x) =
2x + 1 if x 1
.
3x2 1 if x < 1
She thinks she can make f continuous at x = 1 by changing the coefficient of x2 . What value(s) could she
change it to, to make f