TRIGONOMETRY
In this module you will learn about the following concepts.
A.
B.
C.
D.
E.
F.
G.
H.
I.
Measurement of arcs and rotation, angle measurement
The length of an arc and area of a sector
Trigonometry of right angles and trigonometric functions
Circ
Mathematical induction
Mathematical Induction (MI) is an extremely important tool in Mathematics.
MI is a way of proving math statements for all integers (perhaps excluding a
finite number.)
Statements proven by math induction all depend on an integer, sa
Interval Notation
From Wikipedia, the free encyclopedia
This article is about intervals of real numbers.
In mathematics, a (real) interval is a set of real numbers with the property that any number that lies
between two numbers in the set is also included
AbsoluteValues
In this module you will learn the different methods of solving equations and inequalities involving
absolute values. We first apply the definition of absolute value to deduce certain properties which
will be useful in solving problems .We t
Getting ready for the Differential Calculus
Now we turn our attention to all the inverse trigonometric
functions and their graphs. It is good to have a sense of these
graphs so that you know why there are restrictions on the values
that we find on our cal
:
RULES OF DIFFERENTIATION
Had enough? Enough of simplifying difference quotients to evaluate derivatives
from first principles, that is. There has to be a better way and there is. In the next
few topics we develop the rules that make differentiating much
INEQUALITIES
Rule
Description
1. a b a c b c
Adding the same quantity to each side of an
inequality gives an equivalent inequality.
2. a b a c b c
Subtracting the same quantity from each side
of an inequality gives an equivalent inequality.
3. If c 0 , th
Continuity Notes
1) lim x a f ( x) f (a) is the definition of continuity of
the function f(x) at a.
lim
x a
f ( x ) f (a )
is a definition which contains within itself the following
3 conditions:
1. f a
is defined, in other words there is a point a, f a
Fill in your student number in the box below.
Fill in your surname and initials in the box below.
Fill in your course code (MAM1010F or MAM1110F).
Department of Mathematics and Applied Mathematics
Mathematics MAM1010F/MAM1110F
Class Test 2 6 May 2013
Time
University of Cape Town
Department of Mathematics and Applied Mathematics
MAM1010F Class Test 1
19 March2014
Time: 75 minutes
Total marks: 53
Full Marks: 50
Answer the questions in the space provided on the Question sheets. If you run out
of space for an
Department of Mathematics and Applied Mathematics
Mathematics MAM1002W
Class Test 4 30th August 2007
Time: 1 hour 15 minutes
Full Marks: 50
Marks available: 53
Be careful to provide answers that we can read and make sense of at all
times. We will pay atte
Fill in your student number in the box below.
Fill in your surname and initials in the box below.
Fill in your course code (MAM1010F or MAM1110F).
Department of Mathematics and Applied Mathematics
Mathematics MAM1010F/MAM1110F
Class Test 1 20 March 2013
T
Department of Mathematics and Applied Mathematics
Mathematics MAM1002W
Class Test 4 30th August 2007
Solutions
1. A rough sketch:
2. (a)
10
dq
q+4
= 2000q 10q 2 q 3 + 10 ln |q + 4| + C
R(q) =
Z
2000 20q 3q 2 +
But R = 0 when q = 0, so 0 = 10 ln(4) + C, so
If you would like to access your examination script(s) please see the notice
board in the Mathematics Building for application details or alternatively go
to http:/www.mth.uct.ac.za .
Fill in your student number in the box below.
Fill in your surname and
Department of Mathematics and Applied Mathematics
Mathematics MAM102W
Class Test 4
8 August 2005
Time: 75 minutes
Full Marks: 50
This paper consists of 3 pages. Be careful to provide coherent answers at
all times. We will pay attention to the presentation
Fill in your student number in the box below.
Fill in your surname and initials in the box below.
Fill in your course code (MAM1010F or MAM1110F).
Department of Mathematics and Applied Mathematics
Mathematics MAM1010F/MAM1110F
Class Test 2 6 May 2013
Time
Department of Mathematics and Applied Mathematics
Mathematics MAM1002W
Class Test 2 8th May 2008
Time: 1 hour 15 minutes
Full Marks: 50
Be careful to provide answers that we can read and make sense of at all
times. We will pay attention to your presentati
Department of Mathematics and Applied Mathematics
Mathematics MAM1002W
Class Test 4 5th August 2008
Solutions
1. First find the intersection points of f and g. Solve x 2 = x2 4x + 2
to get x = 1 or x = 4. The area required is
Z1
(x2 4x + 2) (x 2) dx +
0
Z
If you would like to access your examination script(s) please see the notice
board in the Mathematics Building for application details or alternatively go
to http:/www.mth.uct.ac.za .
Fill in your student number in the box below.
Fill in your surname and
University of Cape Town
Department of Mathematics and Applied Mathematics
MAM1010F/ MAM1110F June Examination
2 June 2014
Time: 2 hours
Marks available: 94
Full Marks: 92
Answer the questions in the space provided on the question sheets. If you run out of
University of Cape Town
Department of Mathematics and Applied Mathematics
MAM1010F Class Test 2
6 May 2014
Time: 75 minutes
Total marks: 52
Full Marks: 50
Answer the questions in the space provided on the question sheets. If you run out of
space for an an
University of Cape Town
Department of Mathematics and Applied Mathematics
MAM1010F Class Test 2
6 May 2014
Time: 75 minutes
Total marks: 52
Full Marks: 50
Answer the questions in the space provided on the Question sheets. If you run out of
space for an an
University of Cape Town
Department of Mathematics and Applied Mathematics
MAM1010F Class Test 1
19 March2014
Time: 75 minutes
Total marks: 53
Full Marks: 50
Answer the questions in the space provided on the Question sheets. If you run out
of space for an
Department of Mathematics and Applied Mathematics
Mathematics MAM1002W
Class Test 5 2nd October 2007
Time: 1 hour 15 minutes
Full Marks: 50
Marks available: 51
Be careful to provide answers that we can read and make sense of at
all times. We will pay att
Fill in your student number in the box below.
Fill in your surname and initials in the box below.
Fill in your course code (MAM1010F or MAM1110F).
Department of Mathematics and Applied Mathematics
Mathematics MAM1010F/MAM1110F
Class Test 1 20 March 2013
T
2007 students: you wont be questioned on the stuff in Q5(b)
Department of Mathematics and Applied Mathematics
Mathematics MAM102W
Class Test 5
21 September 2005
Time: 75 minutes
Full Marks: 50
This paper consists of 4 pages. Be careful to provide coherent
UNIVERSITY OF CAPE TOWN
DEPARTMENT OF MATHEMATICS AND APPLIED MATHEMATICS
MAM1010F
TUTORIAL 1
Assume 1 year = 365 days.
Round the answers off to two decimal places.
1. Given the formulae:
a) = (1 + )
b) = (1 + )
c) = (1 )
d) = (1 ) .
In each one of them m
Department of Mathematics and Applied Mathematics
Mathematics MAM102W
Class Test 2
4 May 2005
Time: 75 minutes
Full Marks: 50
This paper consists of 3 pages. Be careful to provide coherent answers at all
times. We will pay attention to the presentation as