Excel Essential Skills Year 7 Mathematics Pdf

Unformatted text preview: DiZign Pty Ltd Excel Excel Get the Results You Want! Year 9 Mathematics Extension Revision & Exam Workbook This is a revised and extended edition with over fifty extra pages of work for students to complete. In this book you will find: Topics covering the complete Year 9 Australian Curriculum Mathematics course Over 160 pages of practice exercises Eleven topic tests Three practice exams Answers to all questions AS Kalra is the author of many successful Mathematics books, including the Excel Essential Skills Mathematics Revision & Exam Workbook series for Years 7–10 (eight titles), and the Excel Mathematics General Revision & Exam Workbooks for Years 11–12. Your own checklist for Excel books for Year 9 students: Bookseller reference Books Level English books: 978-1-74020-038-7 Excel Essential Skills English Workbook Year 9 978-1-74125-412-9 Excel Essential Skills Grammar and Punctuation Workbook Years 9–10 978-1-74125-413-6 Excel Essential Skills Reading and Vocabulary Workbook Years 9–10 978-1-74125-415-0 Excel Essential Skills Writing and Spelling Workbook Years 9–10 Mathematics books: 978-1-74125-594-2 Excel Essential Skills Calculator Workbook Years 8–9 978-1-74125-593-5 Excel Essential Skills Non-Calculator Workbook Years 8–9 978-1-74125-271-2 Excel Essential Skills Mathematics Revision & Exam Workbook Year 9 978-1-74125-570-6 Excel Essential Skills Problem Solving Workbook Year 9 978-1-74125-475-4 Excel SmartStudy Mathematics Year 9 978-1-74125-479-2 Excel Mathematics Study Guide Years 9–10 Science books: 978-1-74125-393-1 Excel Science Study Guide Year 9 978-1-74125-422-8 Excel SmartStudy Science Year 9 ISBN 978-1-74020-034-9 Visit our website for more information at Our address is Pascal Press PO Box 250 Glebe NSW 2037 (02) 8585 4044 9781740200349_ESS Maths Ext RandE WB Yr9_2015.indd All Pages 9 781740 200349 Year 9 Mathematics Extension Revision & Exam Workbook AS Kalra About the author E S S E N TI AL S KIL L S This book will challenge and extend students studying Year 9 Mathematics. It has been specifically written to help students revise their work and succeed in all their class tests, half-yearly and yearly exams. YEAR 9 Mathematics Extension Revision & Exam Workbook Updated Edition for the Australian Curriculum Over 100 Units of Work Eleven Topic Tests and three Exams Get the Results You Want! AS Kalra 30/11/15 4:15 PM YEAR 9 Mathematics Extension Revision & Exam Workbook Get the Results You Want! AS Kalra 9781740200349_EES Mathematics Extension Revision & Exam Workbook Year 9_TP.indd 1 26/09/14 9:49 AM © 2000 AS Kalra and Pascal Press Reprinted 2001, 2003, 2004, 2006, 2008, 2010, 2011 Updated in 2014 for the Australian Curriculum Reprinted 2014, 2015 ISBN 978 1 74020 034 9 Pascal Press PO Box 250 Glebe NSW 2037 (02) 8585 4044 Publisher: Vivienne Joannou Project editor: Michael Cole-King Edited by Michael Cole-King Answers checked by Peter Little Typeset by Precision Typesetting (Barbara Nilsson) and lj Design (Julianne Billington) Cover and page design 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: [email protected] 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 my dear 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 74020 034 9 Ch00_PrelimExt_y9 2015.indd 2 Excel Essential Skills Mathematics Extension Revision & Exam Workbook Year 9 30/11/15 1:50 PM Contents INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi CHAPTER 1 – R ational numbers, rates and measurements Unit 1 Rounding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Unit 2 Positive and negative indices . . . . . . . . . . 2 Unit 3 Powers of 10 . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Unit 4 Scientific notation . . . . . . . . . . . . . . . . . . . . . 4 Unit 5 Scientific notation calculations . . . . . . . . . 5 CHAPTER 3 – Pythagoras' theorem Unit 1 Naming the hypotenuse of a right-angled triangle . . . . . . . . . . . . . . . . . . 31 Unit 2 Naming the sides of a right-angled triangle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Unit 3 Selecting the correct Pythagoras' rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Unit 4 Squares and square roots . . . . . . . . . . . . 34 Unit 5 Finding the length of the hypotenuse . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Unit 6 Comparing numbers in scientific notation . . . . . . . . . . . . . . . . . . . . . 6 Unit 6 Finding the length of a side . . . . . . . . . . . 36 Unit 7 Problem solving and scientific notation . . . . . . . . . . . . . . . . . . . . . 7 Unit 8 Mixed questions on Pythagoras' theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Unit 8 Units of measurement . . . . . . . . . . . . . . . . . 8 Unit 9 Accuracy of measurements . . . . . . . . . . . . 9 Unit 7 Miscellaneous questions . . . . . . . . . . . . . . 37 Unit 9 Pythagorean triads . . . . . . . . . . . . . . . . . . . 39 Unit 10 Rates and proportions . . . . . . . . . . . . . . . . 10 Unit 10 Applications of Pythagoras' theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Unit 11 Rates and conversions . . . . . . . . . . . . . . . . 11 Unit 11 Problem solving . . . . . . . . . . . . . . . . . . . . . . 41 Unit 12 Graphs and rates of change . . . . . . . . . . 12 Topic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Topic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 CHAPTER 4 – Financial mathematics CHAPTER 2 – Algebraic techniques Unit 1 Wages and salaries . . . . . . . . . . . . . . . . . . . 44 Unit 1 Algebraic expressions . . . . . . . . . . . . . . . . 15 Unit 2 Overtime and holiday pay . . . . . . . . . . . . 45 Unit 2 Addition and subtraction in algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Unit 3 Commission and piecework . . . . . . . . . . . 46 Unit 3 Multiplication of pronumerals . . . . . . . . . 17 Unit 4 Deductions from income and taxation . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Unit 4 Division of pronumerals . . . . . . . . . . . . . . 18 Unit 5 Simple interest (1) . . . . . . . . . . . . . . . . . . . 48 Unit 5 Multiplication and division in algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Unit 6 Simple interest (2) . . . . . . . . . . . . . . . . . . . 49 Unit 6 The index laws (1) . . . . . . . . . . . . . . . . . . . 20 Unit 8 Borrowing money . . . . . . . . . . . . . . . . . . . . 51 Unit 7 The index laws (2) . . . . . . . . . . . . . . . . . . . 21 Unit 8 Combinations of the index laws . . . . . . . 22 Unit 9 Negative indices with variables . . . . . . . 23 Unit 7 Simple interest (3) . . . . . . . . . . . . . . . . . . . 50 Unit 9 Home loans . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Topic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Unit 10 Grouping symbols in algebra . . . . . . . . . 24 Unit 11 Expanding and simplifying algebraic expressions (1) . . . . . . . . . . . . . . . . . . . . . . . 25 Unit 12 Expanding and simplifying algebraic expressions (2) . . . . . . . . . . . . . . . . . . . . . . . 26 Unit 13 Substitution . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Unit 14 Factorisation using common factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Topic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 iii Contents © Pascal Press ISBN 978 1 74020 034 9 Excel Essential Skills Mathematics Extension Revision & Exam Workbook Year 9 CHAPTER 5 – L inear and non-linear relationships CHAPTER 6 – Equations Unit 1 Horizontal and vertical distances . . . . . 55 Unit 2 Two-step equations . . . . . . . . . . . . . . . . . . . 78 Unit 2 Using Pythagoras' theorem to find distances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 Unit 3 The distance formula . . . . . . . . . . . . . . . . . 57 Unit 4 The midpoint of an interval . . . . . . . . . . . 58 Unit 5 The midpoint formula . . . . . . . . . . . . . . . . . 59 Unit 6 Finding an endpoint . . . . . . . . . . . . . . . . . . 60 Unit 7 The gradient of a line . . . . . . . . . . . . . . . . . 61 Unit 8 The gradient formula . . . . . . . . . . . . . . . . . 62 Unit 9 Mixed questions on distance, midpoint and gradient. . . . . . . . . . . . . . . . 63 Unit 10 Graphing lines . . . . . . . . . . . . . . . . . . . . . . . . 64 Unit 11 Using the intercept method to graph lines . . . . . . . . . . . . . . . . . . . . . . . . 65 Unit 12 The gradient and y-intercept of a line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 Unit 13 The graph of y = mx + b . . . . . . . . . . . . . 67 Unit 14 General form of linear equations . . . . . . 68 Unit 15 Determining whether or not a point lies on a line . . . . . . . . . . . . . . . . . . 69 Unit 16 Finding the equation of a line . . . . . . . . . 70 Unit 17 Using graphs to solve linear equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Unit 18 Graphs of parabolas . . . . . . . . . . . . . . . . . . 72 Unit 19 Graphs of exponentials . . . . . . . . . . . . . . . 73 Unit 20 Circles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 Topic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Unit 1 Simple equations . . . . . . . . . . . . . . . . . . . . . 77 Unit 3 Two- and three-step equations . . . . . . . 79 Unit 4 Equations with pronumerals on both sides . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Unit 5 Equations involving grouping symbols (1) . . . . . . . . . . . . . . . . . . . . . . . . . . 81 Unit 6 Equations involving grouping symbols (2) . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Unit 7 Equations with one fraction (1) . . . . . . . 83 Unit 8 Equations with one fraction (2) . . . . . . . 84 Unit 9 Harder equations . . . . . . . . . . . . . . . . . . . . . 85 Unit 10 Solving problems using equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Topic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 CHAPTER 7 – Area and volume Unit 1 Areas of triangles and quadrilaterals . . . . . . . . . . . . . . . . . . . . . . . . 89 Unit 2 Areas of plane shapes . . . . . . . . . . . . . . . . 90 Unit 3 The area of parts of a circle . . . . . . . . . . 91 Unit 4 Area of an annulus . . . . . . . . . . . . . . . . . . . 92 Unit 5 Composite areas (1) . . . . . . . . . . . . . . . . . . 93 Unit 6 Composite areas (2) . . . . . . . . . . . . . . . . . . 94 Unit 7 Shaded areas (1) . . . . . . . . . . . . . . . . . . . . . 95 Unit 8 Shaded areas (2) . . . . . . . . . . . . . . . . . . . . . 96 Unit 9 Surface area of rectangular prisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Unit 10 Surface area of triangular prisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 Unit 11 Surface area of cylinders . . . . . . . . . . . . . 99 Unit 12 Further surface area . . . . . . . . . . . . . . . . . 100 Unit 13 Volume of right prisms (1) . . . . . . . . . . . 101 Unit 14 Volume of right prisms (2) . . . . . . . . . . . 102 Unit 15 Volume of cylinders (1) . . . . . . . . . . . . . . 103 Unit 16 Volume of cylinders (2) . . . . . . . . . . . . . . 104 Unit 17 Problem solving (1) . . . . . . . . . . . . . . . . . 105 Unit 18 Problem solving (2) . . . . . . . . . . . . . . . . . 106 Topic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 iv © Pascal Press ISBN 978 1 74020 034 9 Excel ESSENTIAL SKILLS Year 9 Mathematics Extension Revision & Exam Workbook Excel Essential Skills Mathematics Extension Revision & Exam Workbook Year 9 CHAPTER 8 – Similarity Unit 1 The enlargement factor . . . . . . . . . . . . . . 109 Unit 2 Further enlargement factors . . . . . . . . . 110 Unit 3 Properties of similar figures (1) . . . . . . 111 Unit 4 Properties of similar figures (2) . . . . . . 112 Unit 5 Similar figures . . . . . . . . . . . . . . . . . . . . . . . 113 Unit 6 Similar triangles (1) . . . . . . . . . . . . . . . . . 114 Unit 7 Similar triangles (2) . . . . . . . . . . . . . . . . . 115 Unit 8 Further similar figures . . . . . . . . . . . . . . . 116 Unit 9 Using similar triangles to find lengths and angles . . . . . . . . . . . . . . . . . . 117 Unit 10 Miscellaneous questions . . . . . . . . . . . . . 118 Unit 11 Areas of similar figures . . . . . . . . . . . . . . 119 Unit 12 Volumes of similar solids . . . . . . . . . . . . 120 Topic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 CHAPTER 9 – Trigonometry Unit 1 Naming the sides of a right-angled triangle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 Unit 2 The trigonometric ratios . . . . . . . . . . . . . 124 Unit 3 Trigonometric ratios and the calculator . . . . . . . . . . . . . . . . . . . . . . . 125 CHAPTER 11 – D ata representation and analysis Unit 1 Review of statistics . . . . . . . . . . . . . . . . . . 146 Unit 2 Mean, mode, median and range . . . . . 147 Unit 3 Using the mean, mode and median . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 Unit 4 Measures of location and spread . . . . . 149 Unit 5 Skewed displays . . . . . . . . . . . . . . . . . . . . . 150 Unit 6 Description of data . . . . . . . . . . . . . . . . . . 151 Unit 7 The shape of a display . . . . . . . . . . . . . . . 152 Unit 8 Back-to-back stem-and-leaf plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 Unit 9 Dot plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 Topic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 EXAM PAPERS Exam Paper 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 Exam Paper 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 Exam Paper 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 ANSWERS Unit 4 Finding the length of a side (1) . . . . . . 126 Rational numbers, rates and measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 Unit 5 Finding the length of a side (2) . . . . . . 127 Algebraic techniques . . . . . . . . . . . . . . . . . . . . . . . . . 172 Unit 6 Finding the length of a side (3) . . . . . . 128 Pythagoras' theorem . . . . . . . . . . . . . . . . . . . . . . . . . 173 Unit 7 Finding the unknown angle (1) . . . . . . 129 Financial mathematics . . . . . . . . . . . . . . . . . . . . . . . 174 Unit 8 Finding the unknown angle (2) . . . . . . 130 Linear and non-linear relationships . . . . . . . . . . 174 Unit 9 Mixed exercises . . . . . . . . . . . . . . . . . . . . . 131 Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 Unit 10 Problem solving . . . . . . . . . . . . . . . . . . . . . 132 Area and volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 Topic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 Similarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 Trigonometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 CHAPTER 10 – Probability Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 Unit 1 Review of basic probability . . . . . . . . . . 135 Data representation and analysis . . . . . . . . . . . . 182 Unit 2 Relative frequency . . . . . . . . . . . . . . . . . . . 136 Exam Papers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 Unit 3 Experimental and theoretical probability . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 Unit 4 Expected results . . . . . . . . . . . . . . . . . . . . . 138 Unit 5 Venn diagrams . . . . . . . . . . . . . . . . . . . . . . 139 Unit 6 Two-way tables . . . . . . . . . . . . . . . . . . . . . . 140 Unit 7 Tree diagrams . . . . . . . . . . . . . . . . . . . . . . . 141 Unit 8 Two-step chance experiments . . . . . . . 142 Unit 9 Miscellaneous questions . . . . . . . . . . . . . 143 Topic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 v Contents © Pascal Press ISBN 978 1 74020 034 9 Excel Essential Skills Mathematics Extension Revision & Exam Workbook Year 9 Introduction There are two workbooks in this series for the Year 9 Australian Curriculum Mathematics course: • Excel Essential Skills Year 9 Mathematics Revision & Exam Workbook and • Excel Essential Skills Year 9 Mathematics Extension Revision & Exam Workbook (this book). This book should be completed after the first book. It has been written specifically for the Year 9 Australian Curriculum Mathematics course and forms part of a series of eight Revision & Exam Workbooks for Years 7 to 10. Each book in the series has been specifically designed to help students revise their work so that they can prepare for success in their tests during the school year and in their half-yearly and yearly exams. The emphasis in this book is to challenge and extend students through extensive practice. This will ensure that students are fully prepared for the Advanced Mathematics courses in senior years. The following features will help students achieve this goal: Ü This book is a workbook. Students write in the book, ensuring that they have all their questions and working in the same place. This is invaluable when revising for exams—no lost notes or missing pages! Ü Each page is a self-contained, carefully graded unit of work; this means students can plan their revision effectively by completing set pages of work for each section. Ü Every topic from the Year 9 Mathematics syllabus is covered in this book, so if students have a particular area of weakness they can concentrate on that topic. Ü A Topic Test is provided at the end of each chapter. These tests are designed to help students test their knowledge of each syllabus topic. Practising tests similar to those they will sit at school will build students' confidence and help them perform well in their actual tests. Ü Three Exam Papers have been included to test students on the complete Year 9 Mathematics course, helping students prepare for their half-yearly and yearly exams. Ü A marking scheme is included in both the Topic Tests and Exam Papers to give students an idea of their progress. Ü A Topic Test and Exam Paper Feedback Chart, found on the inside back cover, enables students to reco...
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