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Author(s): Bob Aus; John Bernard Fitzpatrick
Edition: Third edition.
Publisher: Pearson Australia Group
Year: 2019
Language: English
Pages: 445
City: Melbourne, Victoria.
Tags: HSC
Preliminary pages
Introduction and dedication
Features of the third edition
Contents
Year 11
Chapter 1 Further work with functions
1.1 Quadratic inequalities
1.2 Rational function inequalities (x in denominator)
1.3 Inequalities involving absolute value and square roots
1.4 Circular and simultaneous inequalities
Chapter review 1
Chapter 2 Polynomials
2.1 Polynomials
2.2 Division of polynomials and the remainder theorem
2.3 The factor theorem
2.4 Relationship between roots and coefficients
2.5 Multiple roots of a polynomial equation
2.6 Polynomial functions
Chapter review 2
Chapter 3 Graphing functions
3.1 Reciprocal functions
3.2 Square root functions
3.3 Absolute value functions
3.4 Graphing polynomials by adding ordinates
3.5 Graphing polynomials by multiplying ordinates
3.6 Parametric form of a function or relation
Chapter review 3
Chapter 4 Further trigonometric identities
4.1 Sum and difference of two angles
4.2 Double angle formulae
4.3 Half-angle formulae—the t formulae
4.4 Using identities to simplify expressions and prove results
4.5 Trigonometric products as sums or differences
4.6 Overview of trigonometric equations
4.7 Simple trigonometric equations
4.8 Trigonometric equations involving angle formulae
Chapter review 4
Chapter 5 Inverse functions
5.1 Inverse functions
5.2 Inverse trigonometric functions
Chapter review 5
Chapter 6 Permutations and combinations
6.1 Fundamental counting principle
6.2 Pigeonhole principle
6.3 Permutations
6.4 Arrangement of n objects when some are identical
6.5 Combinations
6.6 Counting techniques in probability
6.7 Expansion of (1 + x)ⁿ, Pascal’s triangle
6.8 More Pascal’s triangle expansions
6.9 Pascal’s triangle relations and the binomial theorem
Chapter review 6
Chapter 7 Rates of change and their application
7.1 Rates of change with respect to time
7.2 Velocity and acceleration as rates of change
7.3 Exponential growth and decay
7.4 Harder exponential growth and decay
7.5 Related rates of change
Chapter review 7
Year 12
Chapter 8 Trigonometric equations
8.1 Solving trigonometric equations using the auxiliary angle method
8.2 Solving quadratic trigonometric equations
8.3 Solving equations using angle formulae, including the t formulae
Chapter review 8
Chapter 9 Proof by mathematical induction
9.1 Mathematical induction involving series
9.2 Proving divisibility by induction
9.3 When induction doesn’t work
Chapter review 9
Chapter 10 Vectors in two dimensions
10.1 Introduction to vectors
10.2 Vectors in two dimensions
10.3 Vectors in component form
10.4 Scalar product of vectors
10.5 Projections of vectors
10.6 Vectors in geometric proofs
Chapter review 10
Chapter 11 Applications of calculus
11.1 Volumes of solids of revolution
11.2 Indefinite integrals and substitution
11.3 Definite integrals and substitution
11.4 Integration of sin² x and cos² x
11.5 Integrals of the type ∫ f’(x) (f(x))ⁿ dx
11.6 Integrals involving trigonometric substitution
11.7 Differentiation of inverse trigonometric functions
11.8 Integration involving inverse trigonometric functions
Chapter review 11
Chapter 12 Differential equations
12.1 Introduction to differential equations
12.2 Direction fields
12.3 Solving differential equations of the form dy/dx = f(x)
12.4 Solving differential equations of the form dy/dx = g(y)
12.5 Solving differential equations of the form dy/dx = f(x) g(y) using separation of variables
12.6 Modelling with first order differential equations
Chapter review 12
Chapter 13 Motion, forces and projectiles
13.1 Problems involving displacement and velocity
13.2 Problems involving forces
13.3 Projectile motion
Chapter review 13
Chapter 14 The binomial distribution
14.1 Bernoulli trials
14.2 Binomial distribution
14.3 Mean and variance of the binomial distribution
14.4 Normal approximation for the sample proportion
Chapter review 14
Summary
Mathematics Extension 1 course outcomes
Answers
Answers for Chapter 1 Further work with functions
Answers for Chapter 2 Polynomials
Answers for Chapter 3 Graphing functions
Answers for Chapter 4 Further trigonometric identities
Answers for Chapter 5 Inverse functions
Answers for Chapter 6 Permutations and combinations
Answers for Chapter 7 Rates of change and their application
Answers for Chapter 8 Trigonometric equations
Answers for Chapter 9 Proof by mathematical induction
Answers for Chapter 10 Vectors in two dimensions
Answers for Chapter 11 Applications of calculus
Answers for Chapter 12 Differential equations
Answers for Chapter 13 Motion, forces and projectiles
Answers for Chapter 14 The binomial distribution
Glossary
