MAT0511/101/0/2015
Tutorial Letter 101/0/2015
Access to Mathematics
MAT0511
Year module
Department of Mathematical Sciences
IMPORTANT INFORMATION:
This tutorial letter contains important
information about your module.
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univer
MAT0511/103/0/2015
Tutorial Letter 103/0/2015
Access to Mathematics
MAT0511
Year module
Department of Mathematical Sciences
IMPORTANT INFORMATION:
This tutorial letter contains revision
exercises
BAR CODE
Learn without limits.
university
of south africa
D
Summary:
Differentiation: By first principles
IEB + NSC (GDE)
In this lesson, you will be introduced to a branch of mathematics called calculus. In particular, we will be
studying a topic in calculus called differentiation. Calculus is probably the most i
Maths revision for COMPGC05/1004
Maths revision for algorithmic analysis
The course will assume familiarity with a small range of standard
mathematical functions, in particular powers (as in polynomials),
exponentials, and logarithms.
Power functions
Supp
Summary:
The Law of Cosines
IEB + NSC (GDE)
In this lesson, we will concern ourselves with the Law of Cosines. This will be applied so that angles in
triangles and the lengths of triangles' sides can be calculated.
To begin, we know that the Pythagorean T
LOGARITHMS
1
LESSON
The logarithm of a number to a given base is the exponent to which that base
must be raised in order to produce the number.
For example: What is the exponent that 5 must be raised to in order to produce
25?
The answer is 2 of course!
S
Summary:
Applications of the derivative
Part 1
IEB + NSC (GDE)
Applications of the derivative Part 1
Maths: Grade 12
We know how to find derivatives and we know that the derivative gives us the instantaneous rate of
change of a function. In this lesson, w
UNIVERSITY EXAMINATIONS UNIVERSITEITSEKSAMENS
U N I SA ‘
mm
MAT051 1 OctoberfNovember 2013
ACCESS TO MATHEMATICS
Duration . 3 Hours 125 Marks
EXAMINERS .
FIRST : MRS JC BEDEKER
SECOND MR DC iKPE
Closed book examination
This examination question paper
UNIVERSITY EXAMINATIONS UNIVERSITEITSEKSAMENS
U N I SA '
:1me
1 January/February 2011
ACCESS TO MATHEMATICS
Durauon 3 Hours 130 Marks
EXAMINERS
FIRST MRS JC BEDEKER
SECOND : MRS NH PENZHORN
and may not be removed from the examinatlon room.
TI‘HS p
UNIVERSITY EXAMINATIONS UNIVERSITEITSEKSAMENS
St
U N I SA mm
1 JanuarylFebrualy 2012
ACCESS TO MATHEMATICS
Duration 3 Hours 120 Marks
EXAMINERS :
FIRST MRS JC BEDEKER
SECOND MRS NH FENZF'IQRN
AMA _M_r_ _ _ g A M
This examination paper remains the p
UNIVERSITY EXAMINATIONS UNIVERSITEITSEKSAMENS
UNISA“
unwelsrty
of south afnca
1 OctoberlNovembe-r 2012
ACCESS TO MATHEMATICS
Duration 3 Hours 120 Marks
EXAMINERS
FIRST MRS JC BEDEKER
SECOND MRS NH PENZHORN
Closed book examination
This examination que
Logarithmic Functions
y=logax
x=ay (exponential form)
Properties of Logarithms
1. loga1=0 because a0=1
2. logaa=1 because a1=a
3. logaax=x and
=x
Inverse Property
4. If logax=logay then x=y One-to-one
Natural Logarithms
y=lnx if x=ey
Properties of Logarit
Summary:
Limits
IEB + NSC (GDE)
Limits
Maths: Grade 12
Limits are the building blocks of calculus
Notation
x
a means x tends to a
When considering x tending to a, we can think of selecting a number greater or less than a by a tiny
amount.
If f(x)
b as x
a
Summary:
The Hyperbolic Functions
IEB + NSC (GDE)
In this lesson, we will learn how to sketch hyperbolic functions. Furthermore, we will pay careful attention to
the properties of these functions, so that they may be applied to examination-type questions.
Summary:
Sketching Parabolic Functions
IEB + NSC (GDE)
In this section we will look at how we can sketch accurately functions of the form f(x) = ax2 + bx + c. These
functions are knows as parabolas or parabolic functions and generally look like this:
To s
Summary:
Co-Functions
IEB + NSC (GDE)
In this lesson, we will look at co-functions. Co-functions are trigonometric functions that are related to one
another by the angles (90 ) and (270 ). The following angles are co-functions of one another:
Because the
Summary:
Applications of the derivative
Part 2
IEB + NSC (GDE)
Applications of the derivative Part 2
Maths: Grade 12
Concavity
If the curve f(x) lies below its tangents, we say it is concave down.
If the curve lies above its tangents, we say it is concave
UNIVERSITY EXAMINATIONS UNIVERSITEITSEKSAMENS
UNISAEQ:
1 JanuaryIFebruary 2014
ACCESS TO MATHEMATICS
Duration 3 Hours 100 Marks
EXAMINERS '
FIRST MRS JC BEDEKER
SECOND MR DC IKPE
Closed book examination
This examination question paper remains the prope
UNIVERSITY EXAMINATIONS UNIVERSITEITSEKSAMENS
U N I SA m “
ofmuth mu
1 JanuarylFebruary 2013
ACCESS TO MATHEMATICS
Duration . 3 Hours 120 Marks
EXAMINERS .
FIRST : MRS JC BEDEKER
SECOND MRS NH PENZHORN
Closed book examination
This examination questio
UNIVERSITY EXAMINATIONS UNIVERSITEITSEKSAMENS
UNISA“
arrive
at southmtl'rn
1 OctoberlNovember 2011
ACCESS TO MATHEMATICS
Duration 3 Hours 135 Marks
EXAMINERS .
FIRST MRS JC BEDEKER
SECOND MRS NH PENZHORN
Thrs mammarmn paper remains the property of the
Algebra I
Click to add text
Definitions
Variable A variable is a letter
or symbol that represents a
number (unknown quantity).
8 + n = 12
Definitions
A variable can use any letter of
the alphabet.
n+5
x7
w - 25
Definitions
Algebraic expression a grou
Question 1
In a given time Sandra can only paint half the area that Joseph can paint. Joseph takes 45 minutes to
paint one-quarter of the room.
1.1. How long will it take each of Joseph and Sandra to paint the whole room on her own?
1.2. How long will it
Worksheet #3 (Parallel Lines Cut by a Transversal)
Name: _ Date: _ Period: _
Use the figure at the right to answer problems 1- 8.
Classify each pair of angles as one of the following:
(a) alternate interior angles
(b) corresponding angles
(c) alternate ex
Surds
05/03/14
1
Contents
Simplifying a Surd
Rationalising a Surd
Conjugate Pairs
05/03/14
2
Starter Questions
Use a calculator to find the values
of :
36
3
8
=
6
144
=
3
4
2 1.41
3
16
=
12
=
2
21 2.76
What is a Surd ?
These roots have exact values and
ar
Metric System Basics
Metric System
The metric system is based on a base
unit that corresponds to a certain kind
of measurement
Length = metre
Volume = litre
Weight (Mass) = gramme
Prefixes plus base units make up the
metric system
Example:
Centi +
Numbers
1.
0.13
To prove that
0.1313 .(1)
Let x =
100 x=1313
99 x=13
x=
0.13
.(2)
(Subtracting, 2 -1)
13
99
x=0.131313 .
This is recurring decimal; therefore it is a rational number
0.13=
13
100
0.13
But
2.To prove that
is also rational number
0.12
0.13
EXERCISE 2.2
1. Suppose 7 less than four fifths of a number is 5. What is the number.
Let the number be x
4
x7=5
5
4
x=7+5
5
4
x=12
5
4
4 x =60
Checking: 5
x=15
157=5
127=5
2. Suppose the length of a rectangle is
4 cm more than one and half times the widt
EXERCISE 4.2
Q 1a Sketch on separate axes without using table values the following parabola
(a)
(i)
y=4( x +1)2+1
(b)
y=4( x +1)2
(e)
2
y=4( x +1) +1
Axis of symmetry
(ii)
TP (h, k) = (-1,1)
(iii)
y- Intercept implies
x=1
x=0
y=(4)2 +1
y=4+1
y=5
(iv)
(0,