About the Book

Year Published: 2014
Page Count: 344
ISBN: 978-1-921972-35-5 (9781921972355)
Online ISBN: 978-1-921972-60-7 (9781921972607)

Table of Contents

Further Mathematics HL: Linear Algebra and Geometry

  SYMBOLS AND NOTATION USED IN THIS BOOK 7
       
1 LINEAR ALGEBRA 9
  A Systems of linear equations 11
  B Gaussian elimination 15
  C Matrix structure and operations 25
  D Matrix multiplication 32
  E Matrix transpose 39
  F Matrix determinant and inverse 41
  G Solving systems of linear equations using matrices 49
  H Elementary matrices 55
  I Vector spaces 60
  J Linear transformations 83
  K Geometric transformations 100
  L Eigenvalues and eigenvectors 113
    THEORY OF KNOWLEDGE (REPRESENTING SPACE) 124
       
2 GEOMETRY 127
    THEORY OF KNOWLEDGE (EUCLID'S POSTULATES) 129
  A Similar triangles 133
  B Congruent triangles 138
  C Proportionality in right angled triangles 141
  D Circle geometry 145
  E Concyclic points, cyclic quadrilaterals 156
  F Intersecting chords and secants theorems 163
  G Centres of a triangle 167
  H Euclid's angle bisector theorem 172
  I Apollonius' circle theorem 176
  J Ptolemy's theorem for cyclic quadrilaterals 178
  K Theorems of Ceva and Menelaus 182
  L The equation of a locus 190
  M The coordinate geometry of circles 194
  N Conic sections 200
  O Parametric equations 216
  P Parametric equations for conics 219
  Q The general conic equation 223
       
  WORKED SOLUTIONS 231
       
  INDEX 342

Authors

Author

Catherine Quinn

Author

Peter Blythe

Author

Robert Haese

Author

Michael Haese

Michael completed a Bachelor of Science at the University of Adelaide, majoring in Infection and Immunity, and Applied Mathematics. He studied laminar heat flow as part of his Honours in Applied Mathematics, and finished a PhD in high speed fluid flows in 2001. He has been the principal editor for Haese Mathematics since 2008.

 

What motivates you to write mathematics books?

My passion is for education as a whole, rather than just mathematics. In Australia I think it is too easy to take education for granted, because it is seen as a right but with too little appreciation for the responsibility that goes with it. But the more I travel to places where access to education is limited, the more I see children who treat it as a privilege, and the greater the difference it makes in their lives. But as far as mathematics goes, I grew up with mathematics textbooks in pieces on the kitchen table, and so I guess it continues a tradition.

 

What do you aim to achieve in writing?

I think a few things:

  • I want to write to the student directly, so they can learn as much as possible from the text directly. Their book is there even when their teacher isn't.
  • I therefore want to write using language which is easy to understand. Sure, mathematics has its big words, and these are important and we always use them. But the words around them should be as simple as possible, so the meaning of the terms can be properly explained to ESL (English as a Second Language) students.
  • I want to make the mathematics more alive and real, not by putting it in contrived "real-world" contexts which are actually over-simplified and fake, but rather through its history and its relationship with other subjects.

 

What interests you outside mathematics?

Lots of things! Horses, show jumping and course design, alpacas, badminton, running, art, history, faith, reading, hiking, photography ....

Features

Fully worked solutions are included for every question.

This book is available on electronic devices through our Snowflake learning platform. This book includes 27 months of Snowflake access, featuring a complete electronic copy of the textbook.

Where relevant, Snowflake features include interactive geometry, graphing, and statistics software, demonstrations, games, spreadsheets, and a range of printable worksheets, tables, and diagrams. Teachers are provided with a quick and easy way to demonstrate concepts, and students can discover for themselves and re-visit when necessary.

Theory of Knowledge is a core requirement in the International Baccalaureate Diploma Programme.

Students are encouraged to think critically and challenge the assumptions of knowledge. Students should be able to analyse different ways of knowing and kinds of knowledge, while considering different cultural and emotional perceptions, fostering an international understanding.

Graphics calculator instructions for Casio fx-9860G Plus, Casio fx-CG20, TI-84 Plus, and TI-nspire are included with this textbook. The textbook will either have comprehensive instructions at the start of the book, specific instructions available from icons located throughout, or both. The extensive use of graphics calculators and computer packages throughout the book enables students to realise the importance, application, and appropriate use of technology.

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