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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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
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
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
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
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
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
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:
Number Sequences 02
IEB + NSC (GDE)
Number Sequences 02
In this lesson, we are going to be introduced to:
Ways to identify patterns in number sequences.
Ways to represent a pattern using specific notation.
Let us look at some notation.
T1 = 16
T2
MAT0511/207/0/2015
Tutorial Letter 207/0/2015
ACCESS TO MATHEMATICS
MAT0511
Year module
Department of Mathematical Sciences
IMPORTANT INFORMATION:
This tutorial letter contains solution to
assignement 07.
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MAT0511/104/0/2015
Tutorial Letter 104/0/2015
Access to Mathematics
MAT0511
Year module
Department of Mathematical Sciences
IMPORTANT INFORMATION:
This tutorial letter contains essential
formulas and facts and guidance
through the study guide
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Lea
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
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university
of south africa
D
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
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
Graphs of Linear Functions
When we are working with a new function, it is useful to know as much as we can about
the function: its graph, where the function is zero, and any other special behaviors of the
function. We will begin this exploration of linear
MENSURATION (solutions)
eTutoring Activity 18 October 2013
1.1.1
Total surface area = 2x3+2x3-(
1.1.2
Remaining volume = 3x2x2 1/3 x
2
+2(2x2)+2(3x2) = 32-(13/16)
2
x2 = 12 (13 )/24
1.2.1 volume of B = 2 x volume of A
b3 = 2a3
1.2.2 Volume of sphere
= (1
Linear Functions
As you hop into a taxicab in New York, the meter will
immediately read $3.30; this is the drop charge made
when the taximeter is activated. After that initial fee, the
taximeter will add $2.40 for each mile the taxi drives. In
this scenar
Modeling with Linear Functions
When modeling scenarios with a linear function and solving problems involving quantities changing
linearly, we typically follow the same problem solving strategies that we would use for any type of
function:
Problem solving
Important Notes on Graphs
Horizontal and Vertical Lines
Horizontal lines have equations of the form f ( x) b
Vertical lines have equations of the form x = a
Example 6
Write an equation for the horizontal line graphed below.
This line would have equation f
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