Mathematics for the international student : pre-Diploma SL and HL (MYP 5 Plus)

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Pre-Diploma SL and HL (MYP 5 Plus)
Foreword
Using the interactive CD
Areas of interaction
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
Summary of circle properties
Summary of measurement facts
Challenge sets
1. Sets and Venn diagrams
	Opening problem
	A - Number sets
		Exercise 1A
			Answers
	B - Interval notation
		Exercise 1B
			Answers
	C - Venn diagrams
		Exercise 1C
			Answers
	D - Union and intersection
		Exercise 1D.1
			Answers
		Exercise 1D.2
			Answers
	E - Problem solving with venn diagrams
		Exercise 1E
			Answers
	F - The algebra of sets (extension)
		Exercise 1F
			Answers
	Review set 1A
		Answers
	Review set 1B
		Answers
2. Algebraic expansion and factorisation
	A - Revision of expansion laws
		Exercise 2A
			Answers
	B - Revision of factorisation
		Exercise 2B
			Answers
	C - Further expansion
		Exercise 2C
			Answers
	D - The binomial expansion
		Investigation 1 - The binomial expansion of (a+b)³
		Exercise 2D
			Answers
	E - Factorising expressions with four terms
		Exercise 2E
			Answers
	F - Factorising quadratic trinomials
		Exercise 2F
			Answers
	G - Factorisation by splitting
		Investigation 2 - Factorisation by splitting the middle term
		Exercise 2G
			Answers
	H - Miscellaneous factorisation
		Exercise 2H
			Answers
	Review set 2A
		Answers
	Review set 2B
		Answers
3. Radicals and surds
	Historical note
	A - Basic operations with radicals
		Exercise 3A.1
			Answers
		Exercise 3A.2
			Answers
	B - Properties of radicals
		Investigation 1 - Properties of radicals
		Exercise 3B.1
			Answers
		Exercise 3B.2
			Answers
	C - Multiplication of radicals
		Exercise 3C
			Answers
	D - Division by radicals
		Exercise 3D
			Answers
	E - Equality of surds
		Exercise 3E
			Answers
		Investigation 2 - Continued square roots
	Review set 3A
		Answers
	Review set 3B
		Answers
4. Pythagoras' theorem
	Opening problem
	A - Pythagoras' theorem
		Exercise 4A
			Answers
	B - The converse of Pythagoras' theorem
		Exercise 4B.1
			Answers
		Exercise 4B.2
			Answers
		Investigation - Pythagorean triples spreadsheet
	C - Problem solving using Pythagoras' theorem
		Exercise 4C.1
			Answers
		Exercise 4C.2
			Answers
	D - Circle problems
		Exercise 4D
			Answers
	E - Three-dimensional problems
		Exercise 4E
			Answers
	F - More difficult problems (extension)
		Exercise 4F
			Answers
	Review set 4A
		Answers
	Review set 4B
		Answers
5. Coordinate geometry
	Historical note
		Opening problem
	A - Distance between two points
		Exercise 5A.1
			Answers
		Exercise 5A.2
			Answers
	B - Midpoints
		Exercise 5B
			Answers
	C - Gradient (or slope)
		Exercise 5C.1
			Answers
		Exercise 5C.2
			Answers
		Exercise 5C.3
			Answers
	D - Using coordinate geometry
		Exercise 5D
			Answers
	E - Equations of straight lines
		Exercise 5E.1
			Answers
		Exercise 5E.2
			Answers
		Exercise 5E.3
			Answers
		Exercise 5E.4
			Answers
	F - Distance from a point to a line
		Exercise 5F
			Answers
	G - 3-dimensional coordinate geometry (extension)
		Exercise 5G
			Answers
	Review set 5A
		Answers
	Review set 5B
		Answers
6. Congruence and similarity
	Opening problem
	A - Congruence of figures
		Exercise 6A
			Answers
	B - Constructing triangles
		Exercise 6B
			Answers
		Investigation - Constructing triangles
	C - Congruent triangles
		Exercise 6C.1
			Answers
		Exercise 6C.2
			Answers
		Exercise 6C.3
			Answers
	D - Similarity
		Discussion
		Exercise 6D
			Answers
	E - Areas and volumes of similar figures
		Exercise 6E
			Answers
	Review set 6A
		Answers
	Review set 6B
		Answers
7. Transformation geometry
	A - Translations
		Exercise 7A
			Answers
	B - Reflections
		Exercise 7B
			Answers
	C - Rotations
		Exercise 7C
			Answers
	D - Dilations
		Investigation 1 - Negative dilation factors
		Exercise 7D
			Answers
		Investigation 2 - Linear transformations
	Review set 7A
		Answers
	Review set 7B
		Answers
8. Univariate data analysis
	Historical note
		Opening problem 1
	A - Statistical terminology
		Exercise 8A.1
			Answers
		Exercise 8A.2
			Answers
	B - Quantitative (numerical) data
		Discussion
		Exercise 8B
			Answers
	C - Grouped discrete data
		Exercise 8C
			Answers
	D - Continuous data
		Exercise 8D
			Answers
	E - Measuring the centre
		Exercise 8E.1
			Answers
		Discussion
		Exercise 8E.2
			Answers
	F - Cumulative data
		Exercise 8F
			Answers
	G - Measuring the spread
		Exercise 8G
			Answers
	H - Box-and-whisker plots
		Exercise 8H.1
			Answers
		Exercise 8H.2
			Answers
	I - Statistics from technology
		Exercise 8I.1
			Answers
		Exercise 8I.2
			Answers
	J - Standard deviation
		Exercise 8J.1
			Answers
		Exercise 8J.2
			Answers
	K - The normal distribution
		Exercise 8K
			Answers
	Review set 8A
		Answers
	Review set 8B
		Answers
9. Quadratic equations
	Opening problem
	A - Quadratic equations of the form x²=k
		Exercise 9A
			Answers
	B - Solution by factorisation
		Exercise 9B.1
			Answers
		Exercise 9B.2
			Answers
	C - Completing the square
		Exercise 9C
			Answers
	D - Problem solving
		Exercise 9D
			Answers
		Historical note - Babylonian algebra
	E - The quadratic formula
		Exercise 9E.1
			Answers
		Exercise 9E.2
			Answers
		Exercise 9E.3
			Answers
	Review set 9A
		Answers
	Review set 9B
		Answers
10. Trigonometry
	Historical note - Astronomy and trigonometry
		Opening problem
	A - Trigonometric ratios
		Investigation 1 - Complementary angles
		Exercise 10A.1
			Answers
		Exercise 10A.2
			Answers
		Investigation 2 - Hipparchus and the universe
	B - Trigonometric problem solving
		Exercise 10B.1
			Answers
		Exercise 10B.2
			Answers
	C - 3-dimensional problem solving
		Exercise 10C.1
			Answers
		Exercise 10C.2
			Answers
	D - The unit circle
		Exercise 10D
			Answers
	E - Area of a triangle using sine
		Exercise 10E
			Answers
		Investigation 3 - Sine and cosine rules
	F - The sine rule
		Exercise 10F
			Answers
	G - The cosine rule
		Exercise 10G
			Answers
	H - Problem solving with the sine and cosine rules
		Exercise 10H
			Answers
	I - Trigonometric identities
		Exercise 10I.1
			Answers
		Exercise 10I.2
			Answers
	Review set 10A
		Answers
	Review set 10B
		Answers
11. Probability
	Historical note
		Opening problem
	A - Experimental probability
		Exercise 11A
			Answers
	B - Probabilities from tabled data
		Exercise 11B
			Answers
	C - Representing combined events
		Exercise 11C
			Answers
	D - Theoretical probability
		Exercise 11D
			Answers
	E - Compound events
		Exercise 11E.1
			Answers
		Exercise 11E.2
			Answers
	F - Using tree diagrams
		Exercise 11F
			Answers
	G - Sampling with and without replacement
		Exercise 11G
			Answers
	H - Mutually exclusive and non-mutually exclusive events
		Exercise 11H
			Answers
	I - Venn diagrams and conditional probability
		Exercise 11I.1
			Answers
		Exercise 11I.2
			Answers
	Review set 11A
		Answers
	Review set 11B
		Answers
12. Algebraic fractions
	A - Simplifying algebraic fractions
		Exercise 12A.1
			Answers
		Exercise 12A.2
			Answers
	B - Multiplying and dividing algebraic fractions
		Exercise 12B
			Answers
	C - Adding and subtracting algebraic fractions
		Exercise 12C
			Answers
	D - More complicated fractions
		Exercise 12D.1
			Answers
		Exercise 12D.2
			Answers
	Review set 12A
		Answers
	Review set 12B
		Answers
13. Formulae
	A - Formula substitution
		Exercise 13A
			Answers
		Investigation - Pizza pricing
	B - Formula rearrangement
		Exercise 13B.1
			Answers
		Exercise 13B.2
			Answers
	C - Formula construction
		Exercise 13C
			Answers
	D - Formulae by induction
		Exercise 13D
			Answers
	E - More difficult rearrangements
		Exercise 13E
			Answers
	Review set 13A
		Answers
	Review set 13B
		Answers
14. Relations, functions and sequences
	Opening problem
	A - Relations and functions
		Exercise 14A
			Answers
	B - Functions
		Exercise 14B
			Answers
	C - Function notation
		Exercise 14C.1
			Answers
		Exercise 14C.2
			Answers
		Investigation 1 - Fluid filling functions
	D - Composite functions
		Exercise 14D
			Answers
	E - Transforming y=f(x)
		Exercise 14E
			Answers
	F - Inverse functions
		Investigation 2 - Inverse functions
		Exercise 14F
			Answers
	G - The modulus function
		Investigation 3 - The modulus function
		Exercise 14G.1
			Answers
		Exercise 14G.2
			Answers
	H - Where functions meet
		Exercise 14H
			Answers
	I - Number sequences
		Exercise 14I.1
			Answers
		Exercise 14I.2
			Answers
	J - Recurrence relationships
		Exercise 14J
			Answers
		Investigation 4 - Sequences in finance
	Review set 14A
		Answers
	Review set 14B
		Answers
15. Vectors
	Opening problem
	A - Directed line segment representation
		Exercise 15A
			Answers
	B - Vector equality
		Exercise 15B
			Answers
	C - Vector addition
		Exercise 15C
			Answers
	D - Vector subtraction
		Exercise 15D
			Answers
	E - Vectors in component form
		Exercise 15E.1
			Answers
		Exercise 15E.2
			Answers
	F - Scalar multiplication
		Exercise 15F
			Answers
	G - Vector equations
		Exercise 15G
			Answers
	H - Parallelism of vectors
		Exercise 15H
			Answers
	I - The scalar product of two vectors
		Exercise 15I.1
			Answers
		Exercise 15I.2
			Answers
		Exercise 15I.3
			Answers
	J - Vector proof (extension)
		Exercise 15J
			Answers
	Review set 15A
		Answers
	Review set 15B
		Answers
16. Exponential functions and logarithms
	Opening problem
	A - Index laws
		Exercise 16A
			Answers
	B - Rational (fractional) indices
		Investigation 1 - Rational indices
		Exercise 16B
			Answers
	C - Exponential functions
		Exercise 16C
			Answers
		Investigation 2 - Solving exponential equations graphically
	D - Growth and decay
		Exercise 16D
			Answers
	E - Compound interest
		Exercise 16E
			Answers
	F - Depreciation
		Exercise 16F
			Answers
	G - Exponential equations
		Exercise 16G
			Answers
	H - Expansion and factorisation
		Exercise 16H.1
			Answers
		Exercise 16H.2
			Answers
		Investigation 3 - Logarithms
		Exercise 16I.1
			Answers
		Exercise 16I.2
			Answers
		Exercise 16I.3
			Answers
		Research
		Exercise 16I.4
			Answers
		Exercise 16I.5
			Answers
	Review set 16A
		Answers
	Review set 16B
		Answers
17. Quadratic functions
	Opening problem
	A - Quadratic functions
		Exercise 17A
			Answers
	B - Graphs of quadratic functions
		Exercise 17B.1
			Answers
		Investigation 1 - Graphs of quadratic functions
		Exercise 17B.2
			Answers
		Exercise 17B.3
			Answers
		Exercise 17B.4
			Answers
	C - Axes intercepts
		Investigation 2 - Axes intercepts
		Exercise 17C.1
			Answers
		Exercise 17C.2
			Answers
	D - Axis of symmetry and vertex
		Investigation 3 - Axis of symmetry and vertex
		Exercise 17D
			Answers
	E - Quadratic optimisation
		Exercise 17E
			Answers
	Review set 17A
		Answers
	Review set 17B
		Answers
18. Advanced trigonometry
	Opening problem
	A - Radian measure
		Exercise 18A
			Answers
	B - Trigonometric ratios from the unit circle
		Exercise 18B
			Answers
	C - The multiples of 30° and 45°
		Exercise 18C.1
			Answers
		Exercise 18C.2
			Answers
	D - Graphing trigonometric functions
		Investigation - Families of trigonometric functions
		Exercise 18D
			Answers
	E - Modelling with sine functions
		Exercise 18E
			Answers
	F - Trigonometric equations
		Exercise 18F
			Answers
	G - Negative and complementary angle formulae
		Exercise 18G
			Answers
	H - Addition formulae
		Exercise 18H
			Answers
	Review set 18A
		Answers
	Review set 18B
		Answers
19. Inequalities
	Opening problem
	A - Sign diagrams
		Exercise 19A
			Answers
	B - Interval notation
		Exercise 19B
			Answers
	C - Inequalities
		Exercise 19C
			Answers
	D - The arithmetic mean-geometric mean inequality (extension)
		Investigation - Arithmetic and geometric means
		Exercise 19D
			Answers
	Review set 19A
		Answers
	Review set 19B
		Answers
20. Matrices and linear transformations
	Opening problem
	A - Introduction to matrices
		Exercise 20A
			Answers
	B - Operations with matrices
		Exercise 20B.1
			Answers
		Exercise 20B.2
			Answers
		Exercise 20B.3
			Answers
	C - Matrix multiplication
		Exercise 20C
			Answers
	D - The determinant of a matrix
		Exercise 20D
			Answers
	E - Multiplicative identity and inverse matrices
		Investigation - Discovering A^(-1)
		Exercise 20E
			Answers
	F - Simultaneous equations
		Exercise 20F.1
			Answers
		Exercise 20F.2
			Answers
	G - Linear transformations
		Exercise 20G.1
			Answers
		Exercise 20G.2
			Answers
		Exercise 20G.3
			Answers
		Exercise 20G.4
			Answers
		Exercise 20G.5
			Answers
	H - Proofs with 2×2 matrices (extension)
		Exercise 20H
			Answers
	Review set 20A
		Answers
	Review set 20B
		Answers
21. Deductive geometry
	Historical note
		Opening problem
	A - Circle theorems
		Exercise 21A
			Answers
	B - Further circle theorems
		Investigation 1 - Circle theorems
		Exercise 21B
			Answers
	C - Geometric proof
		Exercise 21C
			Answers
	D - Cyclic quadrilaterals
		Investigation 2 - Cyclic quadrilaterals
		Exercise 21D
			Answers
		Investigation 3 - Circles and triangles
	Review set 21A
		Answers
	Review set 21B
		Answers
22. Introduction to calculus
	Opening problem
	A - Estimating gradients of tangents to curves
		Exercise 22A
			Answers
	B - Gradients using quadratic theory
		Exercise 22B
			Answers
	C - Gradients using limit theory
		Exercise 22C
			Answers
	D - Differentiation
		Investigation 1 - Derived functions
		Exercise 22D.1
			Answers
		Exercise 22D.2
			Answers
	E - Optimisation
		Exercise 22E
			Answers
	F - Areas under curves
		Investigation 2 - The area under y=x² from x=0 to x=1
		Exercise 22F
			Answers
	G - Integration
		Exercise 22G.1
			Answers
		Exercise 22G.2
			Answers
	H - The definite integral
		Exercise 22H
			Answers
	Review set 22A
		Answers
	Review set 22B
		Answers
23. Counting and probability
24. Locus
25. Networks
Answers
Index