About the Book

Year Published: 2011
Page Count: 152
ISBN: 978-1-921500-16-9 (9781921500169)

Table of Contents

Cambridge IGCSE International Mathematics (0607) Extended EXAM PREPARATION & PRACTICE GUIDE

Table of contents

1 NUMBER 6
    Number sets 6
    Primes and composites 6
    Other terms 6
    Order of operations 6
    Rounding numbers 6
    Absolute value 6
    Fractions 6
    Time 6
    Speed, distance and time 6
    Surds and radicals 6
    Exponents and indices 7
    Exponents and radicals 7
    Standard form 7
    Ratio and proportion 7
    Percentage 7
    Simple interest 7
    Compound interest 7
    Skill practice 7
       
2 ALGEBRA 9
    Expansion laws 9
    Factorisation 9
    Algebraic fractions 9
    Linear equations 9
    Simultaneous linear equations 10
    Problem solving using equations 10
    Formulae 10
    Quadratic equations 10
    Power equations 10
    Exponential equations 10
    Direct variation 10
    Inverse variation 10
    Variation modelling 10
    Linear inequalities 11
    Other one-variable inequalities 11
    Number sequences 11
    Skill practice 11
       
3 FUNCTIONS 15
    Mappings 15
    Functions 16
    Reciprocal functions 16
    Absolute value function 16
    Quadratic functions 16
    Cubic functions 16
    Exponential functions 17
    Logarithms 17
    Trigonometric functions 17
    Using technology 17
    Transforming functions 17
    Skill practice 17
       
4 GEOMETRY 21
    Lines and line segments 21
    Symmetry 21
    Angles 22
    Triangles 22
    Polygons 22
    Pythagoras 22
    Congruence 23
    Similarity 23
    Circles 23
    Circle theorems 23
    Theorems involving arcs 24
    Cyclic quadrilaterals 24
    Cyclic quadrilateral theorems 24
    Skill practice 24
       
5 TRANSFORMATIONS IN TWO DIMENSIONS 29
    Vectors 29
    Transformations 29
    Skill practice 30
       
6 MENSURATION 33
    Units 33
    Length 33
    Area 33
    Surface area 33
    Volume 34
    Capacity 34
    Mass 34
    Skill practice 34
       
7 COORDINATE GEOMETRY 37
    The number plane 37
    Distance between two points 37
    Midpoint of a line segment 37
    Gradient 37
    Straight lines 37
    Linear inequality regions 37
    Skill practice 38
       
8 TRIGONOMETRY 40
    Right angled triangles 40
    The unit circle 40
    Area of a triangle using sine 41
    The sine rule 41
    The cosine rule 41
    Trigonometric graphs 41
    Skill practice 42
       
9 SETS 44
    Venn diagrams 45
    Skill practice 45
       
10 PROBABILITY 46
    Experimental probability 46
    Expectation 46
    Sample space 46
    Theoretical probability 46
    Complementary events 46
    Independent events 46
    Dependent events 46
    Mutually exclusive events 46
    Skill practice 46
       
11 STATISTICS 48
    Variables 48
    Statistical graphs 48
    Census or sample 49
    The distribution of a data set 49
    The centre of a discrete data set 49
    Measuring the spread of discrete data 49
    Frequency tables 49
    Grouped discrete data 49
    Using technology 49
    Continuous data 49
    Correlation 50
    Line of best fit 50
    Skill practice 50
       
  PRACTICE EXAM 1 54
    Paper 2: 45 minutes / 40 marks 54
    Paper 4: 2 hours 15 minutes / 120 marks 55
    Paper 6: 1 hour 30 minutes / 40 marks 56
       
  PRACTICE EXAM 2 57
    Paper 2: 45 minutes / 40 marks 57
    Paper 4: 2 hours 15 minutes / 120 marks 58
    Paper 6: 1 hour 30 minutes / 40 marks 59
       
  PRACTICE EXAM 3 61
    Paper 2: 45 minutes / 40 marks 61
    Paper 4: 2 hours 15 minutes / 120 marks 61
    Paper 6: 1 hour 30 minutes / 40 marks 63
       
  SOLUTIONS 65
    Topic 1: Number 65
    Topic 2: Algebra 68
    Topic 3: Functions 81
    Topic 4: Geometry 94
    Topic 5: Transformations in two dimensions 102
    Topic 6: Mensuration 108
    Topic 7: Coordinate geometry 112
    Topic 8: Trigonometry 118
    Topic 9: Sets 124
    Topic 10: Probability 126
    Topic 11: Statistics 129
    Practice exam 1 136
    Paper 2 136
    Paper 4 137
    Paper 6 139
    Practice exam 2 140
    Paper 2 140
    Paper 4 141
    Paper 6 144
    Practice exam 3 146
    Paper 2 146
    Paper 4 146
    Paper 6 149

Authors

Author

Keith Black

Author

Alison Ryan

Author

James Foley

Author

Katie Richer

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.