About the Book

Year Published: 2013
Page Count: 152
ISBN: 978-1-921972-13-3 (9781921972133)

Table of Contents

Mathematics HL Core EXAM PREPARATION & PRACTICE GUIDE (3rd edition)

1 ALGEBRA 6
    Sequences and series 6
    Exponentials and logarithms 6
    Counting and the binomial theorem 6
    Mathematical induction 6
    Complex numbers 6
    Systems of linear equations 7
    Skill builder questions 7
       
2 FUNCTIONS AND EQUATIONS 10
    Functions f : x ↦ f(x) or y = f(x) 10
    Graphs of functions 10
    Exponential and logarithmic functions 11
    Quadratics 11
    Real polynomials 11
    Inequalities in one variable 12
    Skill builder questions 12
       
3 CIRCULAR FUNCTIONS AND TRIGONOMETRY 14
    The general sine function 14
    Other trigonometric functions 14
    Trigonometric identities 14
    Trigonometric equations 14
    Skill builder questions 15
       
4 VECTORS 16
    The scalar or dot product of two vectors 16
    The vector or cross product of two vectors 16
    Lines 16
    Planes 17
    Intersection of planes 17
    Skill builder questions 17
       
5 STATISTICS AND PROBABILITY 18
    Descriptive statistics 19
    Probability 19
    Discrete random variables 19
    Continuous random variables 20
    Skill builder questions 20
       
6 CALCULUS 22
    Limits 22
    Differentiation 22
    Properties of curves 23
    Kinematic problems 23
    Optimisation problems 23
    Integration 23
    Solids of revolution 24
    Skill builder questions 24
       
  EXAMINATION PRACTICE SETS 25
  1 No calculators 25
  2 Calculators 26
  3 No calculators 27
  4 Calculators 28
  5 No calculators 30
  6 Calculators 31
  7 No calculators 32
  8 Calculators 33
  9 No calculators 34
  10 Calculators 35
  11 No calculators 36
  12 Calculators 37
       
  TRIAL EXAMINATIONS 39
    Trial examination 1 - No calculator 39
    Trial examination 1 - Calculator 40
    Trial examination 2 - No calculator 41
    Trial examination 2 - Calculator 42
    Trial examination 3 - No calculator 44
    Trial examination 3 - Calculator 45
       
  SOLUTIONS 47
    Topic 1 (Algebra) 47
    Topic 2 (Functions and equations) 57
    Topic 3 (Circular functions and trigonometry) 63
    Topic 4 (Vectors) 68
    Topic 5 (Statistics and probability) 73
    Topic 6 (Calculus) 76
    Examination practice set 1 83
    Examination practice set 2 86
    Examination practice set 3 89
    Examination practice set 4 93
    Examination practice set 5 97
    Examination practice set 6 101
    Examination practice set 7 104
    Examination practice set 8 108
    Examination practice set 9 112
    Examination practice set 10 115
    Examination practice set 11 119
    Examination practice set 12 123
    Trial examination 1 - No calculator 127
    Trial examination 1 - Calculator 131
    Trial examination 2 - No calculator 134
    Trial examination 2 - Calculator 138
    Trial examination 3 - No calculator 141
    Trial examination 3 - Calculator 145

Authors

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 ....

Author

Robert Haese

Author

David Martin

Features

Fully worked solutions are included for every question.