Cambridge Senior Mathematics VCE: Specialist Mathematics VCE Units 1 & 2

Cover
Contents
Introduction and overview
Acknowledgements
1  Reviewing algebra
	1A Indices
	1B Standard form
	1C Solving linear equations and simultaneous linear equations
	1D Solving problems with linear equations
	1E Solving problems with simultaneous linear equations
	1F Substitution and transposition of formulas
	1G Algebraic fractions
	1H Literal equations
	1I Using a CAS calculator for algebra
	Review of Chapter 1
2  Number systems and sets
	2A Set notation
	2B Sets of numbers
	2C Surds
	2D Natural numbers
	2E Problems involving sets
	Review of Chapter 2
3 Sequences and series
	3A Introduction to sequences
	3B Arithmetic sequences
	3C Arithmetic series
	3D Geometric sequences
	3E Geometric series
	3F Applications of geometric sequences
	3G Recurrence relations of the form tn = rtn–1 + d
	3H Zeno’s paradox and infinite geometric series
	Review of Chapter 3
4 Additional algebra
	4A Polynomial identities
	4B Quadratic equations
	4C Applying quadratic equations to rate problems
	4D Partial fractions
	4E Simultaneous equations
	Review of Chapter 4
5 Revision of Chapters 1–4
	5A Technology-free questions
	5B Multiple-choice questions
	5C Extended-response questions
	5D Investigations
6 Proof
	6A Direct proof
	6B Proof by contrapositive
	6C Proof by contradiction
	6D Equivalent statements
	6E Disproving statements
	6F Mathematical induction
	Review of Chapter 6
7 Logic
	7A The algebra of sets
	7B Switching circuits
	7C Boolean algebra
	7D Logical connectives and truth tables
	7E Valid arguments
	7F Logic circuits
	7G Karnaugh maps
	Review of Chapter 7
8 Algorithms
	8A Introduction to algorithms
	8B Iteration and selection
	8C Introduction to pseudocode
	8D Further pseudocode
	Review of Chapter 8
9 Combinatorics
	9A Basic counting methods
	9B Factorial notation and permutations
	9C Permutations with restrictions
	9D Permutations of like objects
	9E Combinations
	9F Combinations with restrictions
	9G Pascal’s triangle
	9H The pigeonhole principle
	9I The inclusion–exclusion principle
	Review of Chapter 9
10 Revision of Chapters 6–9
	10A Technology-free questions
	10B Multiple-choice questions
	10C Extended-response questions
	10D Investigations
11 Matrices
	11A Matrix notation
	11B Addition, subtraction and multiplication by a real number
	11C Multiplication of matrices
	11D Identities, inverses and determinants for 2 x 2 matrices
	11E Solution of simultaneous equations using matrices
	11F Inverses and determinants for n x n matrices
	11G Simultaneous linear equations with more than two variables
	Review of Chapter 11
12 Graph theory
	12A Graphs and adjacency matrices
	12B Euler circuits
	12C Hamiltonian cycles
	12D Using matrix powers to count walks in graphs
	12E Regular, cycle, complete and bipartite graphs
	12F Trees
	12G Euler’s formula and the Platonic solids
	12H Appendix: When every vertex has even degree
	Review of Chapter 12
13 Revision of Chapters 11–12
	13A Technology-free questions
	13B Multiple-choice questions
	13C Extended-response questions
	13D Investigations
14 Simulation, sampling and sampling distributions
	14A Expected value and variance for discrete random variables
	14B Distribution of sums of random variables
	14C Populations and samples
	14D Investigating the distribution of the sample mean using simulation
	Review of Chapter 14
15 Trigonometric ratios and applications
	15A Reviewing trigonometry
	15B The sine rule
	15C The cosine rule
	15D The area of a triangle
	15E Circle mensuration
	15F Angles of elevation, angles of depression and bearings
	15G Problems in three dimensions
	15H Angles between planes and more difficult 3D problems
	Review of Chapter 15
16 Trigonometric identities
	16A Reciprocal circular functions and the Pythagorean identity
	16B Compound and double angle formulas
	16C Simplifying a cos x + b sin x
	16D Sums and products of sines and cosines
	Review of Chapter 16
17 Graphing functions and relations
	17A The inverse circular functions
	17B Reciprocal functions
	17C Graphing the reciprocal circular functions
	17D The modulus function
	17E Locus of points
	17F Parabolas
	17G Ellipses
	17H Hyperbolas
	17I Parametric equations
	17J Polar coordinates
	17K Graphing using polar coordinates
	Review of Chapter 17
18 Complex numbers
	18A Starting to build the complex numbers
	18B Multiplication and division of complex numbers
	18C Argand diagrams
	18D Solving quadratic equations over the complex numbers
	18E Solving polynomial equations over the complex numbers
	18F Polar form of a complex number
	18G Sketching subsets of the complex plane
	Review of Chapter 18
19 Revision of Chapters 15–18
	19A Technology-free questions
	19B Multiple-choice questions
	19C Extended-response questions
	19D Investigations
20 Transformations of the plane
	20A Linear transformations
	20B Geometric transformations
	20C Rotations and general reflections
	20D Composition of transformations
	20E Inverse transformations
	20F Transformations of straight lines and other graphs
	20G Area and determinant
	20H General transformations
	Review of Chapter 20
21 Vectors in the plane
	21A Introduction to vectors
	21B Components of vectors
	21C Scalar product of vectors
	21D Vector projections
	21E Geometric proofs
	21F Applications of vectors: displacement and velocity
	21G Applications of vectors: relative velocity
	21H Applications of vectors: forces and equilibrium
	21I Vectors in three dimensions
	Review of Chapter 21
22 Revision of Chapters 20–21
	22A Technology-free questions
	22B Multiple-choice questions
	22C Extended-response questions
Glossary
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