Complete Mathematics for Cambridge IGCSE® Student Book (Extended)

Stretching support for the latest Cambridge IGCSE Mathematics syllabus (0580)

Author David Rayner, Author Ian Bettison, and Author Mathew Taylor

Suitable for:  Students of Cambridge IGCSE Mathematics (0580)

Price:  £31.99

ISBN: 978-0-19-842507-6
Publication date: 19/04/2018
Paperback: 504 pages
Dimensions: 246x189mm

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Build confidence for the Extended part of the latest Cambridge IGCSE syllabus (0580) with the trusted and rigorous approach of Complete Mathematics, now in its Fifth Edition. From renowned author David Rayner, the practice-based approach ensures top Cambridge IGCSE results.


  • Be confident of full syllabus support with a comprehensive mapping grid drawn directly from the latest syllabus, for examination from 2020.
  • Get students ready for their exams with a wealth of practice material and careful question progression
  • Support students' learning with additional practice and revision checklists available on the accompanying support site
  • Ensure thorough comprehension with worked examples that demonstrate how problems are solved
  • Strengthen foundations for further study with clear explanations that build understanding
  • Engage students with a full colour design and plenty of international examples

This page was last updated on 04 July 2022 at 04:30 GMT


  • Of the 33 students in one of our IGCSE Extended Maths class last year, 25 got A passes (including 8 A*'s and one student on 100%) which is a credit to the comprehensive quality of the Rayner (Complete Mathematics) textbook. - Mathematics Teacher, New Zealand
  • This is the best Maths book for Cambridge IGCSE Extended. My son was struggling with Maths and was getting about 35% in Core Maths tests. After working through this book he is now scoring above 80% for Extended Maths tests. Any type of question you can possibly imagine could be asked in an exam is in this book. - Parent review, Amazon
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Table of Contents

Syllabus matching grid
1 Number
1.1: Arithmetic
1.2: Number facts and sequences
1.3: Approximations and estimation
1.4: Standard form
1.5: Ratio and proportion
1.6: Percentages
1.7: Speed, distance and time
1.8: Mixed problems
1.9: Calculator
Revision exercise 1A
Examination-style exercise 1B
2 Algebra 1
2.1: Negative numbers
2.2: Directed numbers
2.3: Formulae
2.4: Brackets and simplifying
2.5: Linear equations
2.6: Problems solves by linear equations
2.7: Simultaneous equations
2.8: Problems solved by simultaneous equations
2.9: Factorising
2.10: Quadratic equations
2.11: Problems solved by quadratic equations
2.12: Non-linear simultaneous equations
Revision exercise 2A
Examination-style exercise 2B
3 Mensuration
3.1: Area
3.2: The circle
3.3: Arc length and sector area
3.4: Chord of a circle
3.5: Volume
3.6: Surface area
Revision exercise 3A
Examination-style exercise 3B
4 Geometry
4.1: Fundamental results
4.2: Pythagoras' theorem
4.3: Symmetry
4.4: Similarity
4.5: Congruence
4.6: Circle theorems
4.7: Constructions
4.8: Nets
Revision exercise 4A
Examination-style exercise 4B
5 Algebra 2
5.1: Algebraic fractions
5.2: Changing the subject of a formula
5.3: Variation
5.4: Indices
5.5: Inequalities
5.6: Linear programming
Revision exercise 5A
Examination-style exercise 5B

6 Trigonometry
6.1: Right-angled triangles
6.2: Scale drawing
6.3: Three-dimensional problems
6.4: Sine, cosine and tangent for any angle
6.5: The sine rule
6.6: The cosine rule
Revision exercise 6A
Examination-style exercise 6B
7 Graphs
7.1: Drawing accurate graphs
7.2: Gradients
7.3: The form y = mx + c
7.4: Plotting curves
7.57.5: Interpreting graphs
7.6: Graphical solution of equations
7.7: Distance-time graphs
7.8: Speed-time graphs
7.9: Differentiation
Revision exercise 7A
Examination-style exercise 7B
8 Sets, vectors and functions
8.1: Sets
8.2: Logical problems
8.3: Vectors
8.4: Column vectors
8.5: Vector geometry
8.6: Functions
8.7: Simple transformations
8.8: Combined transformations
Revision exercise 8A
Examination-style exercise 8B
9 Statistics
9.1: Data display
9.2: Mean, median and mode
9.3: Scatter graphs
9.4: Box-and-whisker plots
9.5: Cumulative frequency
9.6: Comparing data sets
Revision exercise 9A
Examination-style exercise 9B
10 Probability
10.1: Simple probability
10.2: Relative frequency
10.3: Exclusive and independent events
10.4: Tree diagrams
10.5: Probability from Venn diagrams
10.6: Conditional probability
Revision exercise 10A
Examination-style exercise 10B
11 Investigations, practical problems, puzzles
11.1: Investigations
11.2: Practical problems
11.3: Puzzles and experiments
12 Revision tests
Examination-style Paper 2
Examination-style Paper 4