ACC2022F MANAGEMENT ACCOUNTING 1
FINAL EXAMINATION 13 JUNE 2014
150 Marks
180 Minutes
PLEASE READ THE FOLLOWING INSTRUCTIONS VERY CAREFULLY:
1.
Please fill in the attendance slip and complete your personal details on the exam answer books
before the start

2IA Introductory Algebra
18,19 September 2014
Tutorial 7
Lagranges Theorem, the RSA cryptosystem, group homomorphisms
(For all questions show your working.)
1. For each of the following statements say whether it is true or false. Do this quickly,
but try

2IA Introductory Algebra
21, 22 August 2014
Tutorial 4
Subgroups
(For all questions show your working.)
1. The set G = cfw_z C : z 6= 0 of all non-zero complex numbers is a group under
multiplication. (You may assume this.) For each of the following subse

2LA 2015
Tutorial 11
1. Let B = cfw_e1 , e2 , e3 be the standard basis for R3 and B = cfw_e1 , e2 , e3 its dual basis in (R3 ) .
It is easy to check that
C = cfw_v1 = (1, 0, 1) = e1 e3 , v2 = (0, 1, 1) = e2 + e3 , v3 = (2, 1, 0) = 2e1 e2
is another bas

2LA 2015
Tutorial 12
1. Let V be an inner product space and suppose that u, v and w are vectors such that
hu, vi = 2, hv, wi = 3, hu, wi = 5, kuk = 1, kvk = 2, kwk = 7
Evaluate each of the following using this information:
(a) hu + v, v + wi
(b) hu v 2w,

i
Department of Mathematics and Applied Mathematics
University of Cape Town
Linear Algebra
(MAM2000W Module 2LA)
Written by John Frith and Anneliese Schauerte
Revised version by Jurie Conradie
2009
Contents
Introduction
v
1 Systems of Equations, Matrices

NOTES FOR SECOND YEAR LINEAR ALGEBRA
JESSE RATZKIN
1. Introduction and Background
We begin with some motivational remarks and then outline a list (not necessarily
complete!) of things you should already know.
1.1. Motivations. In these notes we will explo

NOTES FOR SECOND YEAR DIFFERENTIAL EQUATION
PART III: FIRST ORDER ORDINARY SYSTEMS
JESSE RATZKIN
1. Introduction
A first order system of differential equations is a system of n first order ODEs.
In general, these can be coupled together. Here are some exa

NOTES FOR SECOND YEAR DIFFERENTIAL EQUATION
PART II: FIRST ORDER ORDINARY DIFFERENTIAL
EQUATIONS
JESSE RATZKIN
1. Definitions
An ordinary differential equation of order k has the form
dy d2 y
dk y
(1)
F x, y, , 2 , . . . , k = 0,
dx dx
dx
where F is a fun

NOTES FOR SECOND YEAR DIFFERENTIAL EQUATION
PART IV:SECOND ORDER, LINEAR ODES
JESSE RATZKIN
1. Introduction
In this set of notes we examine linear, second order ODEs, concentrating on
those with constant coefficients. Our ODEs will have the general form
a

NOTES FOR SECOND YEAR DIFFERENTIAL EQUATION
PART VI: FOURIER SERIES AND THE HEAT EQUATION
JESSE RATZKIN
1. Introduction
In this set of notes we introduce Fourier series and use them to solve the heat
equation.
The heat equation is your first example of a

2IA Introductory Algebra
25,26 September 2014
Tutorial 8
Group homomorphisms and isomorphisms
(For all questions show your working.)
1. For each of the following statements say whether it is true or false. Do this quickly,
but try to get consensus in your

2IA Introductory Algebra
2,3 October 2014
Tutorial 9
Homomorphisms and quotient groups
1. The Chinese Remainder Theorem tells us that
(Z45 , +45 )
= (Z5 , +5 ) (Z9 , +9 )
under the isomorphism f (x) = (x mod 5, x mod 9). Find x cfw_0, 1, . . . , 44 such

2IA Introductory Algebra
28, 29 August 2014
Tutorial 5
Cyclic groups and subgroups
1. Read the following theorem and its proof and then answer the questions that follow.
Theorem: Let G be a cyclic group of order n with generator x, and suppose 0
k < n. T

Solution June Exam 2014
Question 1
1 Standard costing has many objectives.
It can be used for costing one production unit and this information can be used for internal and external reporting.
It is also used for planning and control. Standards can be used

ACC2022S MANAGEMENT ACCOUNTING 1
CLASS TEST 2 28 September 2015
75 Marks
PLEASE READ THE FOLLOWING INSTRUCTIONS VERY CAREFULLY:
90 Minutes
1.
Please fill in the attendance slip and complete your personal details on the test answer books before
the start o

ACC2022S MANAGEMENT ACCOUNTING 1 DETAILED PROGRAMME 2015 SECOND SEMESTER
Notes on the Detailed Programme
1. Submission tutorials are supplied with the modules. They comprise a series of questions based on your textbook readings
together with moderately di

ACC2022S MANAGEMENT ACCOUNTING 1
Tutorial Submission Declaration
TUTORIAL GROUP NO
TUTORS NAME
DAY & TIME
STUDENT NO
SURNAME
FIRST NAMES
Declaration
I declare that all the submissions for this course represent my attempt and I
have not copied this work fr

2IA Introductory Algebra
31 July, 1 August 2014
Tutorial 1
Properties of the integers
(For all questions show your working.)
1. Let a, b, c, d N+ . Show that
(a) If a divides b and b divides c then a divides c.
(b) If d divides both a and b, then d divide

Department of Mathematics and Applied Mathematics
Course: Real Analysis: MAM 2000W 2RA
Sequencies and Limits
Tutorial N3
Some solutions and hints
August 16, 2014
1. Let cfw_xn
1 be a real sequence. Show using the definition of a limit that:
(a) xn x if a

2IA Introductory Algebra
11,12 September 2014
Tutorial 6
Equivalence relations, partitions and cosets
(For all questions show your working.)
1. Let X = N+ N+ and define a relation ' on X by
(n, m) ' (p, q) nq = mp.
(a) Prove that ' is an equivalence relat

Name & Surname:
Student ID:
2DE Exam
11 November 2014
Instructions: You have two hours to complete this test. It is a closed book, closed notes test and
there are 100 marks possible. Please write your answers directly on this question paper.
You may use a

CARD RESPONSES FOR 2DE
JESSE RATZKIN
Below your questions appear in italics and my responses appear in plain text. If
you still have a question, you can either knock on my door (M307) or send me an
email ([email protected]).
How does one determine

2LA 2015
Tutorial 1
1. Let T : R2 R2 be given by
T (x, y) = A
x
y
for some 2 2 matrix A, and suppose T maps the unit square S = cfw_0 x 1, 0 y 1
to the parallelogram P with corners (0, 0), (1, 2), (3, 1), and (4, 1).
(a) Show that T (0, 0) = (0, 0).
(b) I

2LA 2015
Tutorial 2
1. Let A be an m n matrix. (That is, A has m rows and n columns.) Under what conditions
are each of A2 , At A, and AAt defined? In each case that the product is defined, state how
many rows and columns it has.
2. Let
1 2 0
A = 0 1 0 ,

DEPARTMENT OF MATHEMATICS AND APPLIED MATHEMATICS
Mathematics II
Advanced Calculus (2AC)
Tutorial Sheet 3
3rd and 4th March 2016
1. Sketch the level lines and the graphs of the following functions:
(a) f (x, y) =
x2
1
;
+ y2
(b) f (x, y) = x2 + 3y 2 ;
(c)

DEPARTMENT OF MATHEMATICS AND APPLIED MATHEMATICS
Mathematics II
Advanced Calculus (2AC)
Tutorial Sheet 2
25 and 26 February 2016
1. Consider the curve C parameterized by: r(t) = (et sin t, e2t cos t, 2),
t [0, 2] .
(a) Show that C is a regular curve.
(b)