Malawi University of Science and Technology
Malawi Institute of Technology
Algebra and Trigonometry
MATH 111
Module Writer:
Symon Bilesi Chibaya
Module Reviewer:
(Full name of the reviewer)
Date
March 2015
, Malawi University of Science & Technology Algebra & Trigonometry Module
Copyright
This material is a property of the Malawi University of Science and Technology
This material is not to be sold.
2015
All rights are reserved. No part of this publication may be reproduced, stored in a
retrieval system or transmitted in any form or by any means, electronic or mechanical,
including photocopying, recording or otherwise without copyright clearance from
Malawi University of Science and Technology.
Malawi University of Science and Technology
P.O. Box 5196
Limbe
Malawi
Tel: (265)
Fax: (265)
Copyright Page ii
,Malawi University of Science and Technology 2015
Acknowledgements
(MUST will provide, acknowledging contributions made by others
Acknowledgements Page iii
, Malawi University of Science & Technology Algebra & Trigonometry Module
Table of Contents
Copyright ............................................................................................................ ii
Acknowledgements ............................................................................................. iii
Table of Contents................................................................................................ iv
Module Overview ............................................................................................... ix
Unit: 1 ................................................................................................................. 1
Factorisation and Expansion ................................................................................. 1
1.0 Introduction ................................................................................................... 1
1.1 Objectives of the Unit...................................................................................... 1
1.2 Key Terms ...................................................................................................... 1
1.3 Factorisation of difference of two cubes........................................................... 1
1.4 Factorisation of sum of two cubes ................................................................... 2
1.5 Expansion ....................................................................................................... 3
1.5.1 How is Pascals triangle constructed? ........................................................... 4
1.5.2 Points to remember when expanding binomial terms ................................ 4
1.6 Unit Summary ............................................................................................. 5
1.7 Unit Test..................................................................................................... 5
Unit: 2 ................................................................................................................ 6
Permutation and Combinations ............................................................................ 6
2.0 Introduction ................................................................................................... 6
2.1 Objectives of the Unit ..................................................................................... 6
2.2 Key Terms ...................................................................................................... 6
2.3 Factorial Notation .......................................................................................... 6
2.4 Permutations .................................................................................................. 7
2.5 Combinations................................................................................................. 9
2.6 Application of Combinations: The Binomial theorem ..................................... 11
2.7 Unit Summary .............................................................................................. 12
2.8 Unit Test ...................................................................................................... 12
Unit: 3 ...............................................................................................................13
Set Theory ......................................................................................................... 13
3.0 Introduction ................................................................................................. 13
3.1 Objectives of the Unit ................................................................................... 13
3.2 Key Terms .................................................................................................... 13
3.3 Notation and Terminology ........................................................................... 13
3.4 Subsets ......................................................................................................... 15
3.5 Union and Intersection of Sets ...................................................................... 16
3.5.1 Union of Sets .......................................................................................... 16
Table of Contents Page iv
Malawi Institute of Technology
Algebra and Trigonometry
MATH 111
Module Writer:
Symon Bilesi Chibaya
Module Reviewer:
(Full name of the reviewer)
Date
March 2015
, Malawi University of Science & Technology Algebra & Trigonometry Module
Copyright
This material is a property of the Malawi University of Science and Technology
This material is not to be sold.
2015
All rights are reserved. No part of this publication may be reproduced, stored in a
retrieval system or transmitted in any form or by any means, electronic or mechanical,
including photocopying, recording or otherwise without copyright clearance from
Malawi University of Science and Technology.
Malawi University of Science and Technology
P.O. Box 5196
Limbe
Malawi
Tel: (265)
Fax: (265)
Copyright Page ii
,Malawi University of Science and Technology 2015
Acknowledgements
(MUST will provide, acknowledging contributions made by others
Acknowledgements Page iii
, Malawi University of Science & Technology Algebra & Trigonometry Module
Table of Contents
Copyright ............................................................................................................ ii
Acknowledgements ............................................................................................. iii
Table of Contents................................................................................................ iv
Module Overview ............................................................................................... ix
Unit: 1 ................................................................................................................. 1
Factorisation and Expansion ................................................................................. 1
1.0 Introduction ................................................................................................... 1
1.1 Objectives of the Unit...................................................................................... 1
1.2 Key Terms ...................................................................................................... 1
1.3 Factorisation of difference of two cubes........................................................... 1
1.4 Factorisation of sum of two cubes ................................................................... 2
1.5 Expansion ....................................................................................................... 3
1.5.1 How is Pascals triangle constructed? ........................................................... 4
1.5.2 Points to remember when expanding binomial terms ................................ 4
1.6 Unit Summary ............................................................................................. 5
1.7 Unit Test..................................................................................................... 5
Unit: 2 ................................................................................................................ 6
Permutation and Combinations ............................................................................ 6
2.0 Introduction ................................................................................................... 6
2.1 Objectives of the Unit ..................................................................................... 6
2.2 Key Terms ...................................................................................................... 6
2.3 Factorial Notation .......................................................................................... 6
2.4 Permutations .................................................................................................. 7
2.5 Combinations................................................................................................. 9
2.6 Application of Combinations: The Binomial theorem ..................................... 11
2.7 Unit Summary .............................................................................................. 12
2.8 Unit Test ...................................................................................................... 12
Unit: 3 ...............................................................................................................13
Set Theory ......................................................................................................... 13
3.0 Introduction ................................................................................................. 13
3.1 Objectives of the Unit ................................................................................... 13
3.2 Key Terms .................................................................................................... 13
3.3 Notation and Terminology ........................................................................... 13
3.4 Subsets ......................................................................................................... 15
3.5 Union and Intersection of Sets ...................................................................... 16
3.5.1 Union of Sets .......................................................................................... 16
Table of Contents Page iv
