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