PDF Revision & Exam Workbook Mathematics Revision Exam

YEAR Mathematics

9 Revision & Exam Workbook Updated Edition for the Australian Curriculum Over 100 Units of Work Fifteen Topic Tests and four Exams

Get the Results You Want!

AS Kalra

YEAR Mathematics

9 Revision & Exam Workbook

Get the Results You Want!

AS Kalra

? 2006 AS Kalra and Pascal Press Reprinted 2008, 2009, 2010, 2011, 2012

Updated in 2013 for the Australian Curriculum

Reprinted 2014, 2015, 2016

ISBN 978 1 74125 271 2

Pascal Press PO Box 250 Glebe NSW 2037 (02) 8585 4044 .au

Publisher: Vivienne Joannou Project editor: Vivienne Joannou Edited by May McCool, Valerie McCool and Peter McCool Proofread by Diannah Johnston Answers checked by Valerie McCool and Peter Little Typeset by Typecellars Pty Ltd, Grizzly Graphics and Julianne Billington Cover by DiZign Pty Ltd Printed by Green Giant Press

Reproduction and communication for educational purposes The Australian Copyright Act 1968 (the Act) allows a maximum of one chapter or 10% of this book, whichever is the greater, to be copied by any educational institution for its educational purposes provided that the educational institution (or the body that administers it) has given a remuneration notice to Copyright Agency Limited (CAL) under the Act.

For details of the CAL licence for educational institutions contact:

Copyright Agency Limited Level 15, 233 Castlereagh Street Sydney NSW 2000 Telephone: (02) 9394 7600 Facsimile: (02) 9394 7601 Email: enquiry@.au

Reproduction and communication for other purposes Except as permitted under the Act (for example, any fair dealing for the purposes of study, research, criticism or review) no part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means without prior written permission. All inquiries should be made to the publisher at the address above.

Dedication This book is dedicated to the new generation of young Australians in whose hands lies the future of our nation and who by their hard work, acquired knowledge and intelligence will take Australia successfully through the 21st century.

This book is also in the loving, living and lasting memory of my dear mum, dad and uncle, who will remain a great source of inspiration and encouragement to me for times to come.

Acknowledgements I would especially like to express my thanks and appreciation to my dear wife and son, who have helped me to find the time to write this book. Without their help and support, achievement of all this work would not have been possible.

? Pascal Press ISBN 978 1 74125 271 2

Excel Essential Skills Mathematics Revision & Exam Workbook Year 9

Contents

INTRODUCTION

CHAPTER 1 ? Rates and proportion

Unit 1 Equivalent ratios . . . . . . . . . . . . . . . . . . . . . . . 1 Unit 2 Using ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Unit 3 Rates (1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Unit 4 Rates (2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Unit 5 Conversion of rates . . . . . . . . . . . . . . . . . . . . 5 Unit 6 Conversion graphs . . . . . . . . . . . . . . . . . . . . . 6 Unit 7 Direct variation (1) . . . . . . . . . . . . . . . . . . . . 7 Unit 8 Direct variation (2) . . . . . . . . . . . . . . . . . . . . 8 Topic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9

CHAPTER 2 ? Algebra

Unit 1 Algebraic expressions . . . . . . . . . . . . . . . . .11 Unit 2 Substitution . . . . . . . . . . . . . . . . . . . . . . . . . . .12 Unit 3 Addition and subtraction of

pronumerals . . . . . . . . . . . . . . . . . . . . . . . . . .13 Unit 4 Multiplication of pronumerals . . . . . . . . . .14 Unit 5 Division of pronumerals . . . . . . . . . . . . . . .15 Unit 6 Algebraic expressions with grouping

symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16 Unit 7 Substitution into formulae . . . . . . . . . . . .17 Topic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

CHAPTER 3 ? Indices

Unit 1 Index notation (1) . . . . . . . . . . . . . . . . . . . .20 Unit 2 Index notation (2) . . . . . . . . . . . . . . . . . . . .21 Unit 3 Index laws--multiplication

with indices . . . . . . . . . . . . . . . . . . . . . . . . . . .22 Unit 4 Index laws--division with indices . . . . . .23 Unit 5 Index laws--powers of powers . . . . . . . .24 Unit 6 Index laws--the zero index . . . . . . . . . . .25 Unit 7 Index laws . . . . . . . . . . . . . . . . . . . . . . . . . . .26 Topic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

CHAPTER 4 ? Pythagoras' theorem

Unit 1 Hypotenuse of a right-angled triangle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29

Unit 2 Naming the sides of a right-angled triangle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30

Unit 3 Selecting the correct Pythagorean rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31

Unit 4 Squares, square roots and Pythagorean triads . . . . . . . . . . . . . . . . . . . .32

Unit 5 Finding the length of the hypotenuse . . . . . . . . . . . . . . . . . . . . . . . . . . .33

Unit 6 Finding the length of one of the other sides . . . . . . . . . . . . . . . . . . . . . . . . . . .34

Unit 7 Mixed questions . . . . . . . . . . . . . . . . . . . . . . .35 Unit 8 Miscellaneous questions on

Pythagoras' theorem . . . . . . . . . . . . . . . . . .36 Unit 9 Problem solving and Pythagoras'

theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37 Topic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

CHAPTER 5 ? Financial mathematics

Unit 1 Simple interest (1) . . . . . . . . . . . . . . . . . . . .40 Unit 2 Simple interest (2) . . . . . . . . . . . . . . . . . . . .41 Unit 3 Applying the simple interest

formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .42 Unit 4 Hire purchase . . . . . . . . . . . . . . . . . . . . . . . . .43 Unit 5 Problem solving and percentages . . . . .44 Topic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

CHAPTER 6 ? Scientific notation

Unit 1 Negative indices . . . . . . . . . . . . . . . . . . . . . .47 Unit 2 Powers of 10 . . . . . . . . . . . . . . . . . . . . . . . . . .48 Unit 3 Scientific notation (1) . . . . . . . . . . . . . . . . .49 Unit 4 Numbers greater than one . . . . . . . . . . . .50 Unit 5 Numbers less than one . . . . . . . . . . . . . . . .51 Unit 6 Scientific notation calculations . . . . . . . .52 Unit 7 Comparing numbers in scientific

notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .53 Unit 8 Significant figures . . . . . . . . . . . . . . . . . . . . .54 Unit 9 Scientific notation (2) . . . . . . . . . . . . . . . . .55 Topic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

Contents

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? Pascal Press ISBN 978 1 74125 271 2

Excel Essential Skills Mathematics Revision & Exam Workbook Year 9

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