MA TH S OXFORD STAGE 5 SERIES CONSULTANT: K AREN BELL AMY ALEX ANDER BL ANKSBY MORGAN LE VICK DANIEL MANSFIELD ELIZ ABETH BUSCH JENNIFER NOL AN MEL ANIE KOETSVELD JOE MARSIGLIO LYN ELMS DINA ANTONIOU MATHEMATICS NSW CURRICULUM 10 DRAFT
CONTENTS
Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship and education by publishing worldwide. Oxford is a registered trademark of Oxford University Press in the UK and in certain other countries.
Published in Australia by Oxford University Press
Level 8, 737 Bourke Street, Docklands, Victoria 3008, Australia.
© Karen Bellamy, Alexander Blanksby, Morgan Levick, Daniel Mansfield, Elizabeth Busch, Echo Gu, Jennifer Nolan, Melanie Koetsveld, Joe Marsiglio, Lyn Elms, Dina Antoniou © Oxford University Press 2024
The moral rights of the authors have been asserted.
First published 2024
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by licence, or under terms agreed with the reprographics rights organisation. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above. You must not circulate this work in any other form and you must impose this same condition on any acquirer.
ISBN 9780190342739
Reproduction and communication for educational purposes
The Australian Copyright Act 1968 (the Act) allows educational institutions that are covered by remuneration arrangements with Copyright Agency to reproduce and communicate certain material for educational purposes. For more information, see copyright.com.au.
Edited
by
Karen Jayne
Typeset by Newgen KnowledgeWorks Pvt. Ltd., Chennai, India
Proofread by XXX
Indexed by Max McMaster
Printed in Singapore by Markono Print Media Pte Ltd
Oxford University Press Australia & New Zealand is committed to sourcing paper responsibly.
Disclaimer
Links to third party websites are provided by Oxford in good faith and for information only. Oxford disclaims any responsibility for the materials contained in any third party website referenced in this work.
Acknowledgement of Country
Oxford University Press acknowledges the Traditional Owners of the many lands on which we create and share our learning resources. We acknowledge the Traditional Owners as the original storytellers, teachers and students of this land we call Australia. We pay our respects to Elders, past and present, for the ways in which they have enabled the teachings of their rich cultures and knowledge systems to be shared for millennia.
Warning to First Nations Australians
Aboriginal and Torres Strait Islander peoples are advised that this publication may include images or names of people now deceased.
DRAFT
Introducing Oxford Maths 7–10 ................................................................ XX Chapter 1 Financial mathematics ......................................................................... XX 1A Earning money ................................................................................................................ XX 1B Simple interest .................................................................................................................. XX 1C Compound interest ......................................................................................................... XX Checkpoint XX 1D Compound interest calculations XX 1E Depreciation XX Chapter review XX Chapter 2 Algebra XX 2A Indices XX 2B Negative indices XX 2C Simplifying XX 2D Expanding XX 2E Algebraic fractions....................................... XX Checkpoint 2F Factorising............................................................................................................................ XX 2G Factorising quadratic expressions ................................................................................... XX 2H Completing the square ..................................................................................................... XX 2I Factorising non-monic quadratic expressions .................... ................................. XX Chapter review XX Chapter 3 Real numbers ......................................................................................... XX 3A Rational and irrational numbers ...................................................................................... XX 3B Simplifying surds ................................................ .................................................... XX 3C Multiplying and dividing surds ....................... XX 3D Adding and subtracting surds XX 3E Rationalising the denominator XX Checkpoint XX 3F Fractional indices .......................... XX 3G Logarithms ............ XX 3H Logarithm laws .................................... ........................ XX 3I Logarithmic scales ............................................................................................................. XX Chapter review ...................................................................................................................... XX Chapter 4 Equations ............................................................................................... XX 4A Solving linear equations ....................................... XX 4B Solving linear inequalities ................................................................................................. XX 4C Simultaneous linear equations ........................................................................................ XX Checkpoint ............................................................................................................................ XX 4D Solving quadratic equations ...................... .......................................................... XX 4E The quadratic formula .................................. XX 4F Solving cubic equations XX Chapter review XX CONTENTS — iii OXFORD UNIVERSITY PRESS ADV ADV ADV ADV ADV DRAFT
Chapter 5 Linear and non-linear relationships ...................................................... XX 5A Linear relationships ......................................................................................................... XX 5B Gradient, midpoint and distance between two points ................................................ XX 5C Graphing parabolas using intercepts ........................................................................... XX 5D Graphing parabolas using transformations .................................................................. XX 5E Cubic and other non-linear relationships XX Checkpoint XX 5F Graphing circles XX 5G Graphing exponential and logarithmic relationships ..... XX 5H Graphing hyperbolas XX 5I Direct and inverse variation XX 5J Rates of change XX Chapter review ...................................................................................................................... XX Chapter 6 Polynomials ............................................................................................ XX 6A Functions and relations XX 6B Polynomials XX 6C Dividing polynomials ...................................................................................................... XX 6D Remainder and factor theorems..................................................................................... XX Checkpoint ............................................................................................................................ XX 6E Solving polynomial equations ........................................................................................ XX 6F Sketching graphs of polynomials using intercepts .............. XX 6G Sketching graphs of polynomials using transformations ........ XX Chapter review XX Semester 1 review XX AMT explorations 1 .................................................................................................. XX Chapter 7 Geometry ............................................................................................... XX 7A Geometrical properties XX 7B Congruence and similarity ............................................................................................. XX 7C Geometric proofs ............................................................................................................. XX Checkpoint ............................................................................................................................ XX 7D Circle geometry: angles .................................................................................................. XX 7E Circle geometry: chords XX 7F Circle geometry: tangents and secants XX Chapter review XX Chapter 8 Measurement XX 8A Area review XX 8B Surface area review XX 8C Volume review XX Checkpoint XX 8D Surface area of pyramids and cones XX 8E Volume of pyramids and cones XX 8F Surface area and volume of spheres XX Chapter review ...................................................................................................................... XX iv — OXFORD MATHS 10 NSW CURRICULUM OXFORD UNIVERSITY PRESS ADV ADV ADV STN STN X T EXT EXT DRAFT
Chapter 9 Pythagoras’ theorem and trigonometry............................................... XX 9A Pythagoras’ theorem ....................................................................................................... XX 9B Trigonometry .................................................................................................................... XX 9C Applications of trigonometry .......................................................................................... XX 9D Three-dimensional problems XX 9E The sine and area rules XX Checkpoint XX 9F The cosine rule XX 9G The unit circle XX 9H Exact values XX 9I Trigonometric graphs XX 9J Solving trigonometric equations ...................................................................................... XX Chapter review ...................................................................................................................... XX Chapter 10 Networks .............................................................................................. XX 10A Introduction to networks XX 10B Planar graphs ............................................................................................................... XX 10C Platonic solids ................................................................................................................ XX Checkpoint ............................................................................................................................ XX 10D Special types of walks ................................................................................................... XX 10E Applications of networks ................................................................................................ XX Chapter review XX Chapter 11 Statistics and probability..................................................................... XX 11A Bivariate data and scatter plots ................................................................................... XX 11B Sampling methods ............................ XX 11C Analysing reports XX 11D Theoretical probability...................................................................................................XX 11E Experiments with and without replacement XX Checkpoint XX 11F Two-way tables XX 11G Venn diagrams XX 11H Conditional probability .................................................................................................. XX Chapter review ...................................................................................................................... XX Semester 2 review .................................................................................................... XX AMT explorations 2 .................................................................................................. XX STEAM projects .......................................................................................... XX Answers ......................................................................................................... XX Glossary ......................................................................................................... XX Index XX Acknowledgements ...................................................................................... XX CONTENTS — v OXFORD UNIVERSITY PRESS ADV ADV ADV STN STN STN DRAFT
