New Senior Mathematics, 3rd Edition offers a series of student books and worked solutions designed to help you prepare for your classes with ease and ensure students reach their potential. Its the new edition built for New South Wales on a solid foundation. Reader+ is the home of your eBooks. It gives you more options, more flexibility and more control when it comes to the classroom materials you use. It comes with features like in-text note taking, bookmarking, highlighting, interactive videos, audio tools, presentation tools and more.
Author(s): Bob Aus; John Bernard Fitzpatrick
Series: New senior mathematics
Edition: Third edition.
Year: 2019
Language: English
Pages: 309
Tags: HSC
Preliminary pages
Introduction and dedication
Features of the 3rd edition
Contents
Year 12
Chapter 1 Complex numbers
1.1 Arithmetic of complex numbers and the solution of quadratic equations
1.2 Geometrical representation of a complex number as a point
1.3 Other representations of complex numbers
1.4 De Moivre’s theorem and its applications
1.5 Complex numbers and polynomial equations
1.6 Zeros of a polynomial
1.7 Solving quadratic equations with complex coefficients
1.8 Geometrical representation of a complex number as a vector
1.9 Roots of complex numbers
1.10 Curves and regions on the Argand diagram
Chapter review 1
Chapter 2 The nature of proof
2.1 The language and logic of proof
2.2 Methods of proof
2.3 Inequalities
2.4 Mathematical induction, harder questions
2.5 Other induction questions
2.6 Using induction to prove first-order recursive formulae
Chapter review 2
Chapter 3 Further work with vectors
Overview of vectors in two-dimensional space
3.1 Vectors in three dimensions
3.2 Scalar product of vectors in three dimensions
3.3 Using vectors in geometric proofs
3.4 Cartesian coordinates in three-dimensional space
3.5 Parametric and Cartesian equations
3.6 Vector equation of a line
3.7 Parallel and perpendicular lines in three dimensions
Chapter review 3
Chapter 4 Integration by substitution
4.1 Integration of trigonometric functions
4.2 Integrals involving inverse trigonometric functions
4.3 Integrals involving logarithmic functions
4.4 The substitution t = tan A/2
Chapter review 4
Chapter 5 Further integration
5.1 Partial fractions, linear factors
5.2 Partial fractions, quadratic factors
5.3 Using partial fractions to find integrals
5.4 Integration by parts
5.5 Recurrence relations
5.6 Other useful techniques
5.7 Uses of integration
Chapter review 5
Chapter 6 Mechanics
6.1 Velocity and acceleration as functions of x
6.2 Simple harmonic motion (SHM)
6.3 Other examples of motion
6.4 Mathematical representation of motion in physical terms
6.5 Resisted motion
6.6 Projectiles and resisted motion
6.7 Resistance proportional to the square of the velocity
Chapter review 6
Summary
Mathematics Extension 2 Course Outcomes
Answers
Answers for Chapter 1 Complex numbers
Answers for Chapter 2 The nature of proof
Answers for Chapter 3 Further work with vectors
Answers for Chapter 4 Integration by substitution
Answers for Chapter 5 Further integration
Answers for Chapter 6 Mechanics
Glossary
