New senior mathematics for years 11 & 12

Preliminary pages
	Introduction and dedication
	Features of the third edition
	Contents
Year 11
	Chapter 1 Algebraic techniques
		1.1 Simplifying algebraic expressions
		1.2 Substitution in formulae
		1.3 Basic polynomials
		1.4 Factorising by grouping in pairs
		1.5 Standard factorisations
		1.6 Factorising quadratic trinomials
		1.7 Factorising non-monic trinomials
		1.8 Mixed factorisations
		1.9 Algebraic fractions
		1.10 Adding and subtracting algebraic fractions
		1.11 Real numbers and surds
		1.12 Adding and subtracting surds
		1.13 The distributive law
		1.14 Rationalising denominators
		Chapter review 1
	Chapter 2 Trigonometry
		2.1 Review of right-angled triangles
		2.2 Angles of any magnitude
		2.3 Trigonometric graphs
		2.4 Exact values of the trigonometric ratios
		2.5 More trigonometric exact values
		2.6 Direction and bearing
		2.7 Angles of elevation and depression
		2.8 The sine rule
		2.9 The cosine rule
		2.10 Area of a triangle
		2.11 Applied trigonometry
		Chapter review 2
	Chapter 3 Further algebraic techniques
		3.1 Linear equations in one variable
		3.2 Linear equations involving fractions
		3.3 Simple linear inequalities
		3.4 Quadratic equations
		3.5 Quadratic equations without a linear term
		3.6 Quadratic equations without a constant term
		3.7 General quadratic equations
		3.8 Completing the square
		3.9 Solving quadratic equations by completing the square
		3.10 Quadratic equations with non-rational solutions
		3.11 Completing the square for non-monic equations
		3.12 The quadratic formula
		3.13 Problems involving quadratic equations
		Chapter review 3
	Chapter 4 Functions
		4.1 Functions and relations
		4.2 Sketching basic functions
		4.3 Square roots and absolute value
		4.4 Absolute value functions
		4.5 Circles
		4.6 Cubic polynomials
		4.7 The equation y = k/x and inverse variation
		4.8 Working with functions
		Chapter review 4
	Chapter 5 Equations and functions
		5.1 Gradient of a straight line
		5.2 Equation of a straight line
		5.3 Intersection of two lines
		5.4 Simultaneous equations
		5.5 Problem solving with simultaneous equations
		5.6 Solving simultaneous equations—linear and second degree
		5.7 Solving simultaneous equations—linear and second degree in the general form
		5.8 Quadratic functions
		5.9 Parabolas and discriminants
		5.10 Further examples involving discriminants
		5.11 Solution set of simultaneous equations
		Chapter review 5
	Chapter 6 Further trigonometry
		6.1 Radian measure of an angle
		6.2 Arc length and sector area of a circle
		6.3 Angles of any magnitude—radians
		6.4 Graphs of trigonometric functions using radians
		6.5 Trigonometric identities and proofs
		6.6 Solving trigonometric equations
		Chapter review 6
	Chapter 7 Introduction to differentiation
		7.1 Continuity and gradients of tangents
		7.2 Limit and continuity
		7.3 Gradient of a curve
		7.4 Finding the derivative from first principles
		7.5 Conditions for differentiability
		7.6 Standard derivatives
		7.7 The product rule
		7.8 The chain rule
		7.9 The quotient rule
		7.10 Tangents and normals to a curve
		7.11 The gradient as a rate of change
		7.12 Velocity and acceleration as a rate of change
		Chapter review 7
	Chapter 8 Exponential and logarithmic functions
		8.1 Index laws with integers as indices
		8.2 Index laws with fractional indices
		8.3 Solving equations with exponents
		8.4 Logarithms
		8.5 Solving equations with logarithms
		8.6 Exponential functions
		8.7 Some applications of exponential functions
		8.8 Natural logarithms
		8.9 Graphs of exponential and logarithmic functions
		8.10 Logarithms in the real world
		Chapter review 8
	Chapter 9 Probability
		9.1 Introduction to probability
		9.2 Venn diagrams
		9.3 Finite sample spaces
		9.4 Successive outcomes
		9.5 Independent events
		9.6 Dependent events
		Chapter review 9
	Chapter 10 Discrete probability distributions
		10.1 Discrete random variables
		10.2 Expected value, variance and standard deviation of discrete probability distributions
		10.3 The uniform distribution
		10.4 Discrete distributions in practical situations
		Chapter review 10
Year 12
	Chapter 11 Descriptive statistics
		11.1 Statistical investigations
		11.2 Types of data
		11.3 Displaying data
		11.4 Measures of central tendency
		11.5 Standard deviation
		11.6 Analysis of data
		Chapter review 11
	Chapter 12 Trigonometric functions and graphs
		12.1 Transformation of graphs of the trigonometric functions
		12.2 Further solution of trigonometric equations
		12.3 Graphical solution of equations
		12.4 Applications involving trigonometric functions and graphs
		Chapter review 12
	Chapter 13 Differential calculus
		13.1 Approximations of trigonometric functions when x is small
		13.2 Derivatives of trigonometric functions
		13.3 Derivative of the logarithm function
		13.4 Derivative of e^f(x)
		Chapter review 13
	Chapter 14 The first and second derivative
		14.1 The sign of the derivative
		14.2 The first derivative and turning points
		14.3 The second derivative and concavity
		14.4 The second derivative and turning points
		14.5 Problem solving with derivatives
		14.6 Applications of the exponential and logarithmic functions
		14.7 Further applications of trigonometric functions
		14.8 Using derivatives in motion in a straight line
		Chapter review 14
	Chapter 15 Graphing techniques
		15.1 Transformation of graphs using y = f(x + b) and y = f(x) + c
		15.2 Transformation of graphs using y = kf(x) and y = kf(x + b)
		15.3 Transformation of graphs using y = f(ax) and y = f(a(x + b))
		15.4 Graphing rational algebraic functions
		15.5 Applications involving graphing functions
		15.6 Graphical solution of equations
		15.7 Regions and inequalities
		15.8 Simultaneous linear inequalities
		Chapter review 15
	Chapter 16 The anti-derivative
		16.1 Primitive functions
		16.2 Indefinite integrals
		16.3 Primitives of trigonometric functions
		16.4 Integrating the exponential function
		16.5 Integrals resulting in logarithmic functions
		Chapter review 16
	Chapter 17 Integral calculus
		17.1 Area under a curve
		17.2 The definite integral and the area under a curve
		17.3 The definite integral and the primitive function
		17.4 More areas
		17.5 Area between two curves
		17.6 Area bounded by the y-axis
		17.7 Definite integrals involving trigonometric functions
		17.8 Definite integrals involving exponential and logarithmic functions
		17.9 Applications involving integrals
		17.10 Approximate methods of integration—trapezoidal rule
		17.11 Average value of a function—an application of integration
		Chapter review 17
	Chapter 18 Financial mathematics
		18.1 Investments and loans
		18.2 Arithmetic sequences
		18.3 Series and sigma notation (Σ)
		18.4 Arithmetic series
		18.5 Geometric sequences
		18.6 Finite geometric series
		18.7 Infinite geometric series
		18.8 Compound interest applications
		18.9 Further applications of series
		Chapter review 18
	Chapter 19 Bivariate data analysis
		19.1 Types of data and their interpretation
		19.2 Scatterplots and association
		19.3 Calculating the correlation coefficient
		19.4 Modelling by finding the equation of the line of best fit
		19.5 The statistical process
		Chapter review 19
	Chapter 20 Random variables
		20.1 Continuous probability distributions
		20.2 The normal distribution
		20.3 The standard normal distribution
		Chapter review 20
Summary
Mathematics course outcomes
Answers
	Answers for Chapter 1 Algebraic techniques
	Answers for Chapter 2 Trigonometry
	Answers for Chapter 3 Further algebraic techniques
	Answers for Chapter 4 Functions
	Answers for Chapter 5 Equations and functions
	Answers for Chapter 6 Further trigonometry
	Answers for Chapter 7 Introduction to differentiation
	Answers for Chapter 8 Exponential and logarithmic functions
	Answers for Chapter 9 Probability
	Answers for Chapter 10 Discrete probability distributions
	Answers for Chapter 11 Descriptive statistics
	Answers for Chapter 12 Trigonometric functions and graphs
	Answers for Chapter 13 Differential calculus
	Answers for Chapter 14 The first and second derivative
	Answers for Chapter 15 Graphing techniques
	Answers for Chapter 16 The anti-derivative
	Answers for Chapter 17 Integral calculus
	Answers for Chapter 18 Financial mathematics
	Answers for Chapter 19 Bivariate data analysis
	Answers for Chapter 20 Random variables
Glossary