Jacaranda Maths Quest Units 1&2 Specialist Mathematics 11 for Queensland

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Contents
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Chapter 1 Permutations and combinations
	1.1 Overview
		1.1.1 Introduction
	1.2 Counting techniques
		1.2.1 Review of set notation
		1.2.2 The inclusion–exclusion principle
		1.2.3 Types of counting techniques
		1.2.4 The addition and multiplication principles
	1.3 Factorials and permutations
		1.3.1 Factorials
		1.3.2 Permutations
		1.3.3 Arrangements in a circle
	1.4 Permutations with restrictions
		1.4.1 Like objects
		1.4.2 Restrictions
	1.5 Combinations
		1.5.1 When order does not matter
		1.5.2 Probability calculations
	1.6 Applications of permutations and combinations
		1.6.1 Permutations and combinations in the real world
		1.6.2 Lotto systems
	1.7 Pascal’s triangle and the pigeon-hole principle
		1.7.1 Pascal’s triangle
		1.7.2 Pigeon-hole principle
	1.8 Review: exam practice
	Answers
		Chapter 1 Permutations and combinations
REVISION UNIT 1 Combinatorics, vectors and proof
	TOPIC 1 Combinatorics
Chapter 2 Vectors in the plane
	2.1 Overview
		2.1.1 Introduction
	2.2 Vectors and scalars
		2.2.1 Introduction
		2.2.2 Vector notation
		2.2.3 Equality of vectors
		2.2.4 Addition of vectors — The triangle rule
		2.2.5 The negative of a vector
		2.2.6 Multiplying a vector by a scalar
	2.3 Position vectors in the plane
		2.3.1 Cartesian form of a vector
		2.3.2 Ordered pair notation and column vector notation
		2.3.3 The magnitude of a vector
		2.3.4 The polar form of a vector
		2.3.5 Unit vectors
		2.3.6 A vector between two points
	2.4 Scalar multiplication of vectors
		2.4.1 Equality of two vectors
		2.4.2 Solving vector problems
		2.4.3 Parallel vectors
	2.5 The scalar (dot) product
		2.5.1 Calculating the dot product
		2.5.2 The scalar product of vectors expressed in component form
		2.5.3 Finding the angle between two vectors
		2.5.4 Special results of the dot product
	2.6 The projection of vectors — scalar and vector resolutes
		2.6.1 Introduction
		2.6.2 The scalar resolute
		2.6.3 Vector resolutes
	2.7 Review: exam practice
	Answers
		Chapter 2 Vectors in the plane
Chapter 3 Applications of vectors in the plane
	3.1 Overview
		3.1.1 Introduction
	3.2 Displacement and velocity
		3.2.1 Applications of vector addition
		3.2.2 Applications using vector subtraction
	3.3 Force and the triangle of forces
		3.3.1 What is a force?
		3.3.2 What is a particle?
		3.3.3 What assumptions do we make in Newtonian dynamics?
		3.3.4 The resultant force, R~
	3.4 Force and the state of equilibrium
		3.4.1 Newton’s First Law of Motion
		3.4.2 Resolving a force into its components
		3.4.3 Friction
	3.5 Relative velocity
		3.5.1 Relationship between velocities
	3.6 Review: exam practice
	Answers
		Chapter 3 Applications of vectorsin the plane
REVISION UNIT 1 Combinatorics, vectors and proof
	TOPIC 2 Vectors in the plane
PRACTICE ASSESSMENT 1
	Specialist Mathematics: Problem solving and modelling task
		Conditions
		Context
		Task
Chapter 4 Introduction to proof
	4.1 Overview
		4.1.1 Introduction
	4.2 Number systems and writing propositions
		4.2.1 The real number system
		4.2.2 Converting between decimal fractions and common fractions
		4.2.3 Propositions
		4.2.4 Quantifiers
	4.3 Direct proofs using Euclidean geometry
		4.3.1 Axioms and postulates
		4.3.2 The fundamentals
		4.3.3 Two additional postulates
		4.3.4 Theorems of Euclidean geometry
	4.4 Indirect methods of proof
		4.4.1 Disproof by example/proof by counter example
		4.4.2 Contrapositive
		4.4.3 Proof by contradiction
	4.5 Proofs with rational and irrational numbers
		4.5.1 Proofs with consecutive numbers
		4.5.2 Prove that a number is irrational by contradiction
		4.5.3 Proofs with odd and even numbers
		4.5.4 Prove that a set of numbers is infinite
		4.5.5 Other proofs with real numbers
	4.6 Review: exam practice
	Answers
		Chapter 4 Introduction to proof
Chapter 5 Circle geometry
	5.1 Overview
		5.1.1 Introduction
	5.2 Review of congruent triangle tests
		5.2.1 Congruent triangle tests
	5.3 Circle properties 1 — angles in a circleand chords
		5.3.1 Useful definitions
		5.3.2 Useful theorems for angles
		5.3.3 Useful theorems for chords
	5.4 Circle properties 2 — tangents, secants and segments
		5.4.1 Useful definitions
		5.4.2 Useful theorems and an axiom
	5.5 Circle properties 3 — cyclic quadrilaterals
		5.5.1 Useful definitions
		5.5.2 Useful theorems
	5.6 Geometric proofs using vectors
		5.6.1 Review of vectors
	5.7 Review: exam practice
	Answers
		Chapter 5 Circle geometry
REVISION UNIT 1 Combinatorics, vectors and proof
	TOPIC 3 Introduction to proof
PRACTICE ASSESSMENT 2
	Specialist Mathematics: Unit 1 examination
	Conditions
Chapter 6 Complex numbers
	6.1 Overview
		6.1.1 Introduction
	6.2 Introduction to complex numbers
		6.2.1 Square root of a negative number
		6.2.2 Definition of a complex number
	6.3 Basic operations using complex numbers
		6.3.1 Complex number arithmetic
		6.3.2 Equality of two complex numbers
	6.4 Complex conjugates and division of complex numbers
		6.4.1 The conjugate of a complex number
		6.4.2 Division of complex numbers
		6.4.3 Multiplicative inverse of a complex number
	6.5 The complex plane (the Argand plane)
		6.5.1 Plotting numbers in the complex plane
		6.5.2 Geometrically multiplying a complex number by a scalar
		6.5.3 Addition of complex numbers in the complex plane
		6.5.4 Subtraction of complex numbers in the complex plane
		6.5.5 Geometrical representation of a conjugate of a complex number
		6.5.6 Multiplication by i
	6.6 Complex numbers in polar form
		6.6.1 The modulus of z
		6.6.2 The argument of z
		6.6.3 Expressing complex numbers in polar form
		6.6.4 Converting from polar form to Cartesian form
	6.7 Basic operations on complex numbers in polar form
		6.7.1 Addition and subtraction in polar form
		6.7.2 Multiplication, division and powers in polar form
		6.7.3 Powers of complex numbers
		6.7.4 Trigonometric proofs with complex numbers
	6.8 Roots of equations
		6.8.1 Linear factors of real quadratic polynomials
		6.8.2 The general solution of real quadratic equations
		6.8.3 The relationship between roots and coefficients
		6.8.4 Complex equations reducible to quadratics
	6.9 Review: exam practice
	Answers
		Chapter 6 Complex numbers
REVISION UNIT 2 Complex numbers, trigonometry, functions and matrices
	TOPIC 1 Complex numbers 1
Chapter 7 Sketching graphs
	7.1 Overview
		7.1.1 Introduction
	7.2 Sketching graphs of y = |f (x)| and y = f (|x|) from y = f (x)
		7.2.1 Review of relations and function
		7.2.2 An introduction to the modulus function
		7.2.3 Sketching y = |x|
		7.2.4 Graphing y = |f (x)| from y = f (x)
		7.2.5 Graphing y = f (|x|) from y = f (x)
		7.2.6 Sketching graphs of y = |f (x)| and y = f (|x|) from y = f (x)
	7.3 Sketching graphs of reciprocal functions
		7.3.1 Graphing reciprocal functions of linear equations
		7.3.2 Graphing reciprocal functions for quadratic and cubic functions
	7.4 Sketching graphs of rational functions
		7.4.1 Rational functions
		7.4.2 Graphing improper fractions
		7.4.3 Graphs that cross the horizontal asymptote
		7.4.4 Graphs without vertical asymptotes
		7.4.5 Oblique asymptotes
	7.5 Review: exam practice
	Answers
		Chapter 7 Sketching graphs
Chapter 8 Trigonometric functions
	8.1 Overview
		8.1.1 Introduction
	8.2 Review of trigonometry
		8.2.1 Periodic functions
		8.2.2 Radian measure
		8.2.3 Exact values and angles of any magnitude
		8.2.4 The unit circle
		8.2.5 Graphs of the sine and cosine function
		8.2.6 Finding the equation of a given trigonometric graph
		Exercise 8.2 Review of trigonometry
	8.3 Solving trigonometric equations
		8.3.1 Simple trigonometric equations
		8.3.2 Changing the domain
		8.3.3 Further trigonometric equations
		8.3.4 General solutions of the cosine and sin functions
		Exercise 8.3 Solving trigonometric equations
	8.4 The tangent function
		8.4.1 Features of the tangent function
		8.4.2 Sketching the tangent function
		8.4.3 Solving the tangent function
		8.4.4 General solutions of the tangent function
		Ex ercise 8.4 The tangent function
	8.5 The reciprocal functions
		8.5.1 Naming the reciprocal functions
		8.5.2 Exact values
		8.5.3 Sketching the reciprocal functions
		Exercise 8.5 The reciprocal functions
	8.6 Modelling periodic functions
		8.6.1 Periodic phenomena in the real-world
		Exercise 8.6 Modelling periodic functions
	8.7 Review: exam practice
	Answers
		Chapter 8 Trigonometric functions
Chapter 9 Trigonometric identities
	9.1 Overview
		9.1.1 Introduction
	9.2 Pythagorean identities
		9.2.1 Using the Pythagorean identity to solve simple trigonometric unknowns
		9.2.2 Other Pythagorean identities
		9.2.3 Quadratic trigonometric equations
	9.3 Compound angle formulas
		9.3.1 Angle sum and angle difference formulas
		9.3.2 Finding exact values
		9.3.3 Using compound angle formulas and Pythagorean identities
		9.3.4 Proofs using the compound angle formulas
	9.4 Multiple angle formulas
		9.4.1 Double angle formulas
		9.4.2 Using the double angle formulas to solve trigonometric equations
		9.4.3 Proofs using the double angle formulas
		9.4.4 Half-angle formulas
		9.4.5 Multiple angle formulas
	9.5 Product–sum identities
		9.5.1 Expressing sums as products and products as sums
		9.5.2 Using exact values
		9.5.3 Trigonometric proofs
		9.5.4 Solving trigonometric equations
	9.6 Convert a cos (x) + b sin(x) to R cos (x ± α) o
r  R sin (x ± α)
		9.6.1 Express a cos (x) + b sin (x) in the form R cos (x ± α) or R sin (x ± α)
		9.6.2 General transformations and applications
	9.7 Review: exam practice
	Answers
		Chapter 9 Trigonometric identities
REVISION UNIT 2 Complex numbers, trigonometry, functions and matrices
	TOPIC 2 Trigonometry and functions
CHAPTER 10 Matrix arithmetic
	10.1 Overview
		10.1.1 Introduction
	10.2 Addition, subtraction and scalar multiplication of matrices
		10.2.1 Introduction to matrices
		10.2.2 Operations on matrices
		10.2.3 Special matrices
	10.3 Matrix multiplication
		10.3.1 Multiplication of matrices
	10.4 Determinants and inverses
		10.4.1 Determinant of a 2 × 2 matrix
		10.4.2 Determinant of a 3 × 3 matrix
		10.4.3 Inverse of a 2 × 2 matrix
		10.4.4 Inverse of a 3 x 3 matrix
	10.5 Matrix equations and solving 2 × 2 linearequations
		10.5.1 Matrix equations
		10.5.2 Solving 2 × 2 linear equations
		10.5.3 Geometrical interpretation of solutions
	10.6 Review: exam practice
	Answers
		Chapter 10 Matrix arithmetic
Chapter 11 Matrix transformations
	11.1 Overview
		11.1.1 Introduction
	11.2 Translations
		11.2.1 Matrix transformations
		11.2.2 Translations
		11.2.3 Translations of an object
		11.2.4 Translations of a curve
	11.3 Reflections and rotations
		11.3.1 Reflections
		11.3.2 Reflection in the x-axis (y = 0)
		11.3.3 Reflection in the y-axis (x = 0)
		11.3.4 Reflection in a line that passes through the origin (0,0)
		11.3.5 Reflection in the line y = x tan ɵ
		11.3.6 Rotations
		11.3.7 Special rotations in an anticlockwise direction
	11.4 Dilations
		11.4.1 Dilations from the x- and y-axes
		11.4.2 Dilation from both x- and y-axes
	11.5 Combinations of transformations
		11.5.1 Double transformation matrices
		11.5.2 Inverse transformation matrices
		11.5.3 Interpreting the determinant of the transformation matrix
	11.6 Review: exam practice
	Answers
		Chapter 11 Matrix transformations
REVISION UNIT 2 Complex numbers, trigonometry, functions and matrices
	TOPIC 3 Matrices
		PRACTICE ASSESSMENT 3
			Specialist Mathematics: Unit 2 examination
			Conditions
		PRACTICE ASSESSMENT 4
			Specialist Mathematics: Units 1& 2 examination
			Conditions
GLOSSARY
INDEX