IGCSE Cambridge International Mathematics (0607) Extended

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IGCSE Cambridge International Mathematics (0607) Extended
Foreword
Acknowledgements
Using the interactive CD
Symbols and notation used in this book
Table of contents
Graphics calculator instructions
A - Basic calculations
B - Basic functions
C - Secondary function and alpha keys
D - Memory
E - Lists
F - Statistical graphs
G - Working with functions
H - Two variable analysis
Assumed Knowledge (Number)
Assumed Knowledge (Geometry and graphs)
1. Algebra (Expansion and factorisation)
Opening problem
A - The distributive law
Exercise 1A
Answers
B - The product (a+b)(c+d)
Exercise 1B
Answers
C - Difference of two squares
Exercise 1C
Answers
Discovery 1 - The product of three consecutive integers
D - Perfect squares expansion
Exercise 1D
Answers
E - Further expansion
Exercise 1E
Answers
F - Algebraic common factors
Exercise 1F
Answers
Activity - Algebraic common factor maze
G - Factorising with common factors
Exercise 1G
Answers
H - Difference of two squares factorisation
Exercise 1H
Answers
I - Perfect squares factorisation
Exercise 1I
Answers
J - Expressions with four terms
Exercise 1J
Answers
K - Factorising x²+bx+c
Exercise 1K
Answers
L - Splitting the middle term
Discovery 2 - Splitting the middle term
Exercise 1L
Answers
M - Miscellaneous factorisation
Exercise 1M
Answers
Review set 1A
Answers
Review set 1B
Answers
2. Sets
Opening problem
A - Set notation
Exercise 2A
Answers
B - Special number sets
Exercise 2B
Answers
C - Interval notation
Exercise 2C
Answers
D - Venn diagrams
Exercise 2D
Answers
E - Union and intersection
Exercise 2E.1
Answers
Exercise 2E.2
Answers
F - Problem solving
Exercise 2F
Answers
Review set 2A
Answers
Review set 2B
Answers
3. Algebra (Equations and inequalities)
Opening problem
A - Solving linear equations
Exercise 3A.1
Answers
Exercise 3A.2
Answers
B - Solving equations with fractions
Exercise 3B
Answers
C - Forming equations
Exercise 3C
Answers
D - Problem solving using equations
Exercise 3D
Answers
E - Power equations
Exercise 3E
Answers
F - Interpreting linear inequalities
Exercise 3F
Answers
G - Solving linear inequalities
Exercise 3G
Answers
Review set 3A
Answers
Review set 3B
Answers
4. Lines, angles and polygons
Opening problem
A - Angle properties
Exercise 4A
Answers
B - Triangles
Discussion
Exercise 4B
Answers
C - Isosceles triangles
Exercise 4C
Answers
D - The interior angles of a polygon
Discovery 1 - Angles of an n-sided polygon
Exercise 4D
Answers
E - The exterior angles of a polygon
Discovery 2 - Exterior angles of a polygon
Exercise 4E
Answers
Review set 4A
Answers
Review set 4B
Answers
Challenge
Answers
5. Graphs, charts and tables
Opening problem
A - Statistical graphs
Exercise 5A
Answers
B - Graphs which compare data
Exercise 5B
Answers
C - Using technology to graph data
Discovery - Spreadsheets for graphing data
Exercise 5C
Answers
Review set 5A
Answers
Review set 5B
Answers
6. Exponents and surds
Opening problem
A - Exponent or index notation
Exercise 6A.1
Answers
Historical note
Exercise 6A.2
Answers
B - Exponent or index laws
Exercise 6B
Answers
C - Zero and negative indices
Exercise 6C
Answers
D - Standard form
Exercise 6D.1
Answers
Exercise 6D.2
Answers
E - Surds
Historical note
Exercise 6E
Answers
F - Properties of surds
Discovery - Properties of surds
Exercise 6F
Answers
G - Multiplication of surds
Exercise 6G
Answers
H - Division by surds
Exercise 6H
Answers
Review set 6A
Answers
Review set 6B
Answers
Discovery - Continued square roots
Challenge
Answers
7. Formulae and simultaneous equations
Opening problem
A - Formula substitution
Exercise 7A
Answers
Activity - Pizza pricing
B - Formula rearrangement
Exercise 7B.1
Answers
Exercise 7B.2
Answers
C - Formula derivation
Exercise 7C
Answers
D - More difficult rearrangements
Exercise 7D
Answers
E - Simultaneous equations
Discovery - The coin problem
Exercise 7E.1
Answers
Exercise 7E.2
Answers
Exercise 7E.3
Answers
F - Problem solving
Exercise 7F
Answers
Review set 7A
Answers
Review set 7B
Answers
Challenge
Answers
8. The theorem of Pythagoras
Opening problem
A - Pythagoras’ theorem
Exercise 8A.1
Answers
Exercise 8A.2
Answers
Discovery - Pythagorean triples spreadsheet
B - The converse of Pythagoras’ theorem
Exercise 8B
Answers
C - Problem solving
Exercise 8C
Answers
Exercise 8D
Answers
E - Three-dimensional problems
Exercise 8E
Answers
Review set 8A
Answers
Review set 8B
Answers
Challenge
Answers
9. Mensuration (length and area)
Opening problem
A - Length
Exercise 9A
Answers
B - Perimeter
Exercise 9B
Answers
C - Area
Exercise 9C.1
Answers
Exercise 9C.2
Answers
D - Circles and sectors
Exercise 9D
Answers
Review set 9A
Answers
Review set 9B
Answers
Challenge
Answers
10. Topics in arithmetic
Opening problem
A - Percentage
Exercise 10A
Answers
B - Profit and loss
Exercise 10B.1
Answers
Exercise 10B.2
Answers
C - Simple interest
Exercise 10C.1
Answers
Exercise 10C.2
Answers
Activity - Simple interest calculator
D - Reverse percentage problems
Exercise 10D
Answers
E - Multipliers and chain percentage
Exercise 10E.1
Answers
Exercise 10E.2
Answers
F - Compound growth
Exercise 10F
Answers
G - Speed, distance and time
Exercise 10G
Answers
H - Travel graphs
Exercise 10H
Answers
Review set 10A
Answers
Review set 10B
Answers
Challenge
Answers
11. Mensuration (solids and containers)
Opening problem
A - Surface area
Exercise 11A.1
Answers
Exercise 11A.2
Answers
B - Volume
Exercise 11B.1
Answers
Exercise 11B.2
Answers
C - Capacity
Exercise 11C.1
Answers
Exercise 11C.2
Answers
D - Mass
Exercise 11D
Answers
E - Compound solids
Exercise 11E
Answers
Discovery 1 - Making cylindrical bins
Discovery 2 - Constructing a lampshade
Discovery 3 - The turkey problem
Review set 11A
Answers
Review set 11B
Answers
12. Coordinate geometry
Opening problem
Historical note
A - Plotting points
Exercise 12A
Answers
B - Distance between two points
Exercise 12B.1
Answers
Exercise 12B.2
Answers
C - Midpoint of a line segment
Exercise 12C
Answers
D - Gradient of a line segment
Exercise 12D.1
Answers
Exercise 12D.2
Answers
E - Gradient of parallel and perpendicular lines
Exercise 12E.1
Answers
Exercise 12E.2
Answers
F - Using coordinate geometry
Exercise 12F
Answers
Review set 12A
Answers
Review set 12B
Answers
Challenge
Answers
13. Analysis of discrete data
Historical note
Opening problem
A - Variables used in statistics
Exercise 13A
Answers
B - Organising and describing discrete data
Exercise 13B.1
Answers
Exercise 13B.2
Answers
C - The centre of a discrete data set
Exercise 13C
Answers
D - Measuring the spread of discrete data
Exercise 13D
Answers
E - Data in frequency tables
Exercise 13E
Answers
F - Grouped discrete data
Exercise 13F
Answers
G - Statistics from technology
Exercise 13G
Answers
Review set 13A
Answers
Review set 13B
Answers
14. Straight lines
Opening problem
A - Vertical and horizontal lines
Discovery 1 - Vertical and horizontal lines
Exercise 14A
Answers
B - Graphing from a table of values
Exercise 14B
Answers
Discovery 2 - Graphs of the form y=mx+c
C - Equations of lines (gradient-intercept form)
Exercise 14C
Answers
D - Equations of lines (general form)
Exercise 14D.1
Answers
Exercise 14D.2
Answers
E - Graphing lines from equations
Exercise 14E
Answers
F - Lines of symmetry
Exercise 14F
Answers
Review set 14A
Answers
Review set 14B
Answers
15. Trigonometry
Opening problem
A - Labelling sides of a right angled triangle
Exercise 15A
Answers
Discovery 1 - Ratio of sides of right angled triangles
B - The trigonometric ratios
Exercise 15B.1
Answers
Exercise 15B.2
Answers
Discovery 2 - Hipparchus and the universe
C - Problem solving
Exercise 15C
Answers
D - The first quadrant of the unit circle
Exercise 15D.1
Answers
Exercise 15D.2
Answers
E - True bearings
Exercise 15E
Answers
F - 3-dimensional problem solving
Exercise 15F.1
Answers
Exercise 15F.2
Answers
Exercise 15F.3
Answers
Review set 15A
Answers
Review set 15B
Answers
16. Algebraic fractions
Opening problem
A - Simplifying algebraic fractions
Exercise 16A.1
Answers
Exercise 16A.2
Answers
B - Multiplying and dividing algebraic fractions
Exercise 16B
Answers
C - Adding and subtracting algebraic fractions
Exercise 16C
Answers
D - More complicated fractions
Exercise 16D.1
Answers
Exercise 16D.2
Answers
Review set 16A
Answers
Review set 16B
Answers
17. Continuous data
Opening problem
A - The mean of continuous data
Exercise 17A
Answers
B - Histograms
Exercise 17B
Answers
C - Cumulative frequency
Exercise 17C
Answers
Review set 17A
Answers
Review set 17B
Answers
18. Similarity
Opening problem
A - Similarity
Discussion
Exercise 18A
Answers
B - Similar triangles
Exercise 18B.1
Answers
Exercise 18B.2
Answers
C - Problem solving
Exercise 18C
Answers
D - Area and volume of similar shapes
Exercise 18D
Answers
Review set 18A
Answers
Review set 18B
Answers
Challenge
Answers
19. Introduction to functions
Opening problem
A - Mapping diagrams
Exercise 19A
Answers
B - Functions
Exercise 19B.1
Answers
Exercise 19B.2
Answers
C - Function notation
Exercise 19C
Answers
Discovery 1 - Fluid filling functions
D - Composite functions
Exercise 19D
Answers
E - Reciprocal functions
The family of curves y=k/x, k≠0
Exercise 19E
Answers
F - The absolute value function
Discovery 3 - The absolute value function
Exercise 19F.1
Answers
Exercise 19F.2
Answers
Review set 19A
Answers
Review set 19B
Answers
20. Transformation geometry
Opening problem
A - Translations
Exercise 20A
Answers
B - Rotations
Exercise 20B
Answers
C - Reflections
Exercise 20C
Answers
D - Enlargements and reductions
Exercise 20D
Answers
E - Stretches
Exercise 20E
Answers
Discussion - Invariant points
F - Transforming functions
Discovery
Exercise 20F
Answers
G - The inverse of a transformation
Exercise 20G
Answers
H - Combinations of transformations
Exercise 20H
Answers
Review set 20A
Answers
Review set 20B
Answers
21. Quadratic equations and functions
Opening problem
A - Quadratic equations
Exercise 21A
Answers
B - The Null Factor law
Exercise 21B.1
Answers
Exercise 21B.2
Answers
C - The quadratic formula
Exercise 21C.1
Answers
Exercise 21C.2
Answers
D - Quadratic functions
Exercise 21D
Answers
E - Graphs of quadratic functions
Exercise 21E.1
Answers
Discovery 1 - Graphs of quadratic functions
Exercise 21E.2
Answers
Exercise 21E.3
Answers
F - Axes intercepts
Discovery 2 - Axes intercepts
Exercise 21F.1
Answers
Exercise 21F.2
Answers
G - Line of symmetry and vertex
Discovery 3 - Line of symmetry and vertex
Exercise 21G
Answers
H - Finding a quadratic function
Exercise 21H
Answers
I - Using technology
Exercise 21I
Answers
J - Problem solving
Exercise 21J
Answers
Review set 21A
Answers
Review set 21B
Answers
Challenge
Answers
22. Two variable analysis
Opening problem
A - Correlation
Exercise 22A
Answers
B - Line of best fit by eye
Exercise 22B
Answers
C - Linear regression
Exercise 22C
Answers
Review set 22A
Answers
Review set 22B
Answers
23. Further functions
Opening problem
A - Cubic functions
Discovery - Cubic functions
Exercise 23A.1
Answers
Exercise 23A.2
Answers
B - Inverse functions
Exercise 23B
Answers
C - Using technology
Exercise 23C.1
Answers
Exercise 23C.2
Answers
D - Tangents to curves
Exercise 23D
Answers
Review set 23A
Answers
Review set 23B
Answers
24. Vectors
Opening problem
A - Directed line segment representation
Exercise 24A
Answers
B - Vector equality
Exercise 24B
Answers
C - Vector addition
Exercise 24C
Answers
D - Vector subtraction
Exercise 24D
Answers
E - Vectors in component form
Exercise 24E.1
Answers
Exercise 24E.2
Answers
F - Scalar multiplication
Exercise 24F
Answers
G - Parallel vectors
Exercise 24G
Answers
H - Vectors in geometry
Exercise 24H
Answers
Review set 24A
Answers
Review set 24B
Answers
Challenge
Answers
25. Probability
Opening problem
A - Introduction to probability
Exercise 25A
Answers
B - Estimating probability
Activity - Rolling a pair of dice
Exercise 25B
Answers
C - Probabilities from two-way tables
Exercise 25C
Answers
D - Expectation
Exercise 25D
Answers
E - Representing combined events
Exercise 25E
Answers
F - Theoretical probability
Exercise 25F
Answers
G - Compound events
Exercise 25G.1
Answers
Exercise 25G.2
Answers
H - Using tree diagrams
Exercise 25H
Answers
I - Sampling with and without replacement
Exercise 25I
Answers
J - Mutually exclusive and non-mutually exclusive events
Exercise 25J
Answers
K - Miscellaneous probability questions
Exercise 25K
Answers
Review set 25A
Answers
Review set 25B
Answers
26. Sequences
Opening problem
A - Number sequences
Exercise 26A
Answers
B - Algebraic rules for sequences
Discussion - Properties of sequences
Exercise 26B
Answers
C - Geometric sequences
Exercise 26C
Answers
D - The difference method for sequences
Discovery - The difference method
Exercise 26D
Answers
Review set 26A
Answers
Review set 26B
Answers
27. Circle geometry
Opening problem
A - Circle theorems
Discovery 1 - Properties of circles
Exercise 27A.1
Answers
Discovery 2 - Theorems involving arcs
Exercise 27A.2
Answers
B - Cyclic quadrilaterals
Exercise 27B.1
Answers
Exercise 27B.2
Answers
Review set 27A
Answers
Review set 27B
Answers
28. Exponential functions and equations
Opening problem
A - Rational exponents
Discovery 1 - Rational exponents
Exercise 28A
Answers
B - Exponential functions
Discovery 2 - Graphs of simple exponential functions
Exercise 28B
Answers
C - Exponential equations
Exercise 28C.1
Answers
Discovery 3 - Solving exponential equations graphically
Exercise 28C.2
Answers
D - Problem solving with exponential functions
Exercise 28D
Answers
E - Exponential modelling
Exercise 28E
Answers
Review set 28A
Answers
Review set 28B
Answers
29. Further trigonometry
Opening problem
A - The unit circle
Exercise 29A.1
Answers
Exercise 29A.2
Answers
B - Area of a triangle using sine
Exercise 29B
Answers
C - The sine rule
Exercise 29C.1
Answers
Exercise 29C.2
Answers
D - The cosine rule
Exercise 29D
Answers
Exercise 29E
Answers
Exercise 29F
Answers
G - Trigonometric graphs
Exercise 29G.1
Answers
Exercise 29G.2
Answers
H - Graphs of y=a sin(bx) and y=a cos(bx)
Discovery - The families y=a sin(bx) and y=a cos(bx)
Exercise 29H
Answers
Review set 29A
Answers
Review set 29B
Answers
Challenge
Answers
30. Variation and power modelling
Opening problem
A - Direct variation
Exercise 30A.1
Answers
Exercise 30A.2
Answers
B - Inverse variation
Exercise 30B
Answers
C - Variation modelling
Discussion - Possible models
Exercise 30C
Answers
Discovery - The pendulum
D - Power modelling
Exercise 30D
Answers
Discovery - The pendulum
Review set 30A
Answers
Review set 30B
Answers
Challenge
Answers
31. Logarithms
Opening problem
A - Logarithms in base a
Exercise 31A
Answers
B - The logarithmic function
Exercise 31B
Answers
C - Rules for logarithms
Exercise 31C
Answers
D - Logarithms in base 10
Discovery - Logarithms
Exercise 31D.1
Answers
Exercise 31D.2
Answers
E - Exponential and logarithmic equations
Exercise 31E
Answers
Review set 31A
Answers
Review set 31B
Answers
Challenge
Answers
32. Inequalities
Opening problem
A - Solving one variable inequalities with technology
Exercise 32A
Answers
B - Linear inequality regions
Discovery - Linear inequalities of the form ax+byd
Exercise 32B
Answers
C - Integer points in regions
Exercise 32C
Answers
D - Problem solving (extension)
Exercise 32D
Answers
Review set 32A
Answers
Review set 32B
Answers
33. Multi-Topic Questions
Questions
Answers
34. Investigation and modelling questions
A - Investigation questions
Answers
B - Modelling questions
Answers
Answers
Index