Mathematics Revision & Exam Workbook - Blake Education

Get the Results You Want! Year 8 Mathematics Revision & Exam Workbook This book is suitable for students of all abilities studying Year 8 Mathematics. It has been specifically written to help students revise their work and succeed in all their class tests, half-yearly and yearly exams. 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 8 Australian Curriculum Mathematics course Over 170 pages of practice exercises Fourteen topic tests Four 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 Excel Essential Skills The Complete Fractions Workbook Year 7.

Your own checklist for Excel books for Year 8 students: Bookseller reference

Books

Level

3

English books:

978-1-74125-411-2

Excel Essential Skills Grammar and Punctuation Workbook

Years 7–8

978-1-74125-408-2

Excel Essential Skills Reading and Vocabulary Workbook

Years 7–8

978-1-74125-414-3

Excel Essential Skills Writing and Spelling Workbook

Years 7–8

978-1-74020-037-0

Excel Essential Skills English Workbook

Year 8

Mathematics books:

978-1-74020-040-3

Excel Essential Skills Step-by-Step Algebra 1 Workbook

Years 7– 8

978-1-74020-316-6

Excel Essential Skills Mathematics Extension Revision & Exam Workbook

Year 8

978-1-74125-435-8

Excel Essential Skills Problem Solving Workbook

Year 8

978-1-74125-474-7

Excel SmartStudy Mathematics

Year 8

978-1-74125-007-7

Excel Mathematics Study Guide

Year 8

978-1-74020-041-7


Years 8 –10

Science books:

978-1-74125-421-1

Excel SmartStudy Science

Year 8

978-1-74125-392-4

Excel Science Study Guide

Year 8

Year 8 Mathematics Revision & Exam Workbook AS Kalra

About the author

Excel E S S E N TI AL S KIL L S

Excel

YEAR

8

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

Get the Results You Want!

ISBN 978-1-74020-033-2

Visit our website for more information at www.pascalpress.com.au Our address is Pascal Press PO Box 250 Glebe NSW 2037 (02) 8585 4044

9781740200332_ESS Maths RandE WB Yr8 2015 spine 11mm.indd All Pages

9 781740 200332

AS Kalra 8/07/15 12:15 PM

YEAR

8

Mathematics Revision & Exam Workbook


AS Kalra

© 2000 AS Kalra and Pascal Press Reprinted 2001, 2002, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012 (twice) Updated in 2014 for the Australian Curriculum Reprinted 2015 (twice) ISBN 978 1 74020 033 2 Pascal Press PO Box 250 Glebe NSW 2037 (02) 8585 4044 www.pascalpress.com.au Publisher: Vivienne Joannou Project editor: Vivienne Joannou Edited by Science Desk International and May McCool Proofread by Diannah Johnston Answers checked by Chelsea Smithies and Peter Little Typeset by Science Desk International and lj Design (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: [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 son, who have helped me 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 033 2 Ch00_Prelim_2015 twice.indd 2

Excel Essential Skills Mathematics Revision & Exam Workbook Year 8 24/09/2015 2:06 pm

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi CHAPTER 1—Basic arithmetic and the calculator

CHAPTER 4—Indices Unit 1 Index notation . . . . . . . . . . . . . . . . . . . . . . . 33 Unit 2 Index laws: multiplication with indices . . . . . . . . . . . . . . . . . . . . . . . . . . 34

Unit 1

Approximations and rounding off . . . . . 1

Unit 2

Mixed operations . . . . . . . . . . . . . . . . . . . . . 2

Unit 3

Squares, cubes and powers . . . . . . . . . . . 3

Unit 4

Square roots and cube roots . . . . . . . . . . 4

Unit 5

Problem solving and the calculator . . . . 5

Unit 6 Index laws: miscellaneous questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

Topic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Topic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

CHAPTER 2—Percentages

CHAPTER 5—Rational numbers

Unit 1

Unit 1

Rounding off whole numbers . . . . . . . . . 41

Unit 2

Rounding off decimals . . . . . . . . . . . . . . . . 42

Unit 3

Changing fractions to terminating decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Unit 4

Recurring and terminating decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

The meaning of percentage . . . . . . . . . . . . 8

Unit 2 Changing percentages to fractions . . . . 9 Unit 3

Changing fractions to percentages . . . 10

Unit 4

Changing percentages to decimals . . . 11

Unit 5

Changing decimals to percentages . . . 12

Unit 3 Index laws: division with indices . . . . . 35 Unit 4 Index laws: powers of powers . . . . . . . . 36 Unit 5 Index laws: the zero index . . . . . . . . . . . 37

Unit 6 Finding a percentage of a quantity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Unit 5 Irrational numbers . . . . . . . . . . . . . . . . . . . 45

Unit 7

Increasing or decreasing by a given percentage . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Unit 6

Equivalent ratios . . . . . . . . . . . . . . . . . . . . . 46

Unit 8

Expressing quantities as percentages . . . . . . . . . . . . . . . . . . . . . . . . . 15

Unit 7

Using ratios . . . . . . . . . . . . . . . . . . . . . . . . . . 47

Unit 8

Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

Unit 9

Unitary method and percentages . . . . 16

Unit 10 Commission . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Unit 11 Discounts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Unit 12 Profit and loss . . . . . . . . . . . . . . . . . . . . . . . . 19 Unit 13 Problem solving and percentages . . . . 20 Topic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Unit 9 Conversion of rates . . . . . . . . . . . . . . . . . . . 49 Unit 10 Scale drawing . . . . . . . . . . . . . . . . . . . . . . . . 50 Unit 11 Problem solving . . . . . . . . . . . . . . . . . . . . . . 51 Topic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 CHAPTER 6—Basic algebra Unit 1

Algebraic expressions . . . . . . . . . . . . . . . . 54

Unit 2

Simplifying algebraic expressions . . . . . 55

Unit 3

Collecting like terms . . . . . . . . . . . . . . . . . . 56

Unit 4

Algebraic abbreviations . . . . . . . . . . . . . . . 57

Unit 5

Substitution (1) . . . . . . . . . . . . . . . . . . . . . . 58

Unit 6

Substitution (2) . . . . . . . . . . . . . . . . . . . . . . 59

Unit 7

Addition and subtraction of like terms (1) . . . . . . . . . . . . . . . . . . . . . . . . 60

Unit 8

Addition and subtraction of like terms (2) . . . . . . . . . . . . . . . . . . . . . . . . 61

Unit 8 Problem solving with integers . . . . . . . . 30

Unit 9

Multiplication of pronumerals . . . . . . . . . 62

Topic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Unit 10 Division of pronumerals . . . . . . . . . . . . . . 63

CHAPTER 3—Four operations with integers Unit 1 Addition of integers . . . . . . . . . . . . . . . . . . 23 Unit 2 Subtraction of integers . . . . . . . . . . . . . . . 24 Unit 3 Multiplication of integers . . . . . . . . . . . . . 25 Unit 4 Division of integers . . . . . . . . . . . . . . . . . . . 26 Unit 5 Mixed questions . . . . . . . . . . . . . . . . . . . . . . 27 Unit 6 Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Unit 7 Order of operations . . . . . . . . . . . . . . . . . . . 29

iii

Contents © Pascal Press ISBN 978 1 74020 033 2

Excel Essential Skills Mathematics Revision & Exam Workbook Year 8

Unit 11 Algebraic expressions and the order of operations . . . . . . . . . . . . . . . . . . . 64

CHAPTER 9—Circles

Unit 12 Applying the distributive law to expand algebraic expressions . . . . . . . . . 65

Unit 1 Parts of circles . . . . . . . . . . . . . . . . . . . . . . . 103

Unit 13 Common factors . . . . . . . . . . . . . . . . . . . . . . 66

Unit 2

Circumference of circles . . . . . . . . . . . . . 104

Unit 3

Applications of circumference . . . . . . . . 105

Unit 14 Problem solving and algebra . . . . . . . . . . 67 Topic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 CHAPTER 7—Length, mass and time Unit 1

Symbols and prefixes . . . . . . . . . . . . . . . . 70

Unit 2

Units of measurement . . . . . . . . . . . . . . . . 71

Unit 4 Area of circles . . . . . . . . . . . . . . . . . . . . . . . 106 Unit 5 Applications of area . . . . . . . . . . . . . . . . . 107 Unit 6

Miscellaneous questions . . . . . . . . . . . . 108

Unit 7

Problem solving with circles . . . . . . . . . 109

Topic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

Unit 3 Conversion of units of length . . . . . . . . 72

CHAPTER 10—Linear relationships

Unit 4 Pythagoras’ theorem (1) . . . . . . . . . . . . . .73

Unit 1

The number plane . . . . . . . . . . . . . . . . . . . 112

Unit 2

Tables of values . . . . . . . . . . . . . . . . . . . . . 113

Unit 3

Graphing straight lines . . . . . . . . . . . . . . 114

Unit 5 Pythagoras’ theorem (2) . . . . . . . . . . . . . .74 Unit 6

Perimeter of plane shapes . . . . . . . . . . . 75

Unit 7

Perimeter of irregular shapes . . . . . . . . 76

Unit 8

Conversion of units of mass . . . . . . . . . . 77

Unit 4 Using the intercept method to graph lines . . . . . . . . . . . . . . . . . . . . . . . . . . 115

Unit 9

Applications of mass . . . . . . . . . . . . . . . . . 78

Unit 5

Intersection of two lines . . . . . . . . . . . . . 116

Unit 10 Conversion of units of time . . . . . . . . . . 79

Unit 6

Determining whether or not a point lies on a line . . . . . . . . . . . . . . . . . . . 117

Unit 12 Clocks and times . . . . . . . . . . . . . . . . . . . . 81

Unit 7

Unit 13 Problem solving using 12- and 24-hour time . . . . . . . . . . . . . . . . . . . . . . . . . 82

Using graphs to solve linear equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

Topic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

Unit 14 Problem solving with length, mass and time . . . . . . . . . . . . . . . . . . . . . . . 83

CHAPTER 11—Equations

Topic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

Unit 1

CHAPTER 8—Area, volume and capacity

Unit 2 One-step equations (addition and subtraction) . . . . . . . . . . . . . . . . . . . . 122

Unit 1 Units of measurement . . . . . . . . . . . . . . . . 86

Unit 3

Unit 2 Formulae for plane shapes and solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

One-step equations (multiplication and division) . . . . . . . . . . . . . . . . . . . . . . . . 123

Unit 4

Two-step equations . . . . . . . . . . . . . . . . . 124

Unit 5

Three-step equations . . . . . . . . . . . . . . . 125

Unit 6

Equations with grouping symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

Unit 7

Formulae . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

Unit 8

Problem solving with equations . . . . . 128

Unit 9

Simple equations with one fraction . . . . . . . . . . . . . . . . . . . . . . . . . 129

Unit 11 Addition and subtraction of time . . . . . 80

Unit 3 Area of parallelograms . . . . . . . . . . . . . . . 88 Unit 4 Area of trapeziums . . . . . . . . . . . . . . . . . . . 89 Unit 5 Area of rhombuses . . . . . . . . . . . . . . . . . . . 90 Unit 6 Area of kites . . . . . . . . . . . . . . . . . . . . . . . . . 91 Unit 7 Area of plane shapes . . . . . . . . . . . . . . . . . 92 Unit 8 Problem solving with area . . . . . . . . . . . . 93 Unit 9 Volume of cubes . . . . . . . . . . . . . . . . . . . . . . 94 Unit 10 Volume of rectangular prisms . . . . . . . . . 95

Solving equations by inspection . . . . . 121

Topic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

Unit 11 Volume of triangular prisms . . . . . . . . . . 96 Unit 12 Volume of prisms—miscellaneous . . . . . 97 Unit 13 Problem solving with volume . . . . . . . . . 98 Unit 14 Capacity and volume . . . . . . . . . . . . . . . . . 99 Unit 15 Problem solving with area, volume and capacity . . . . . . . . . . . . . . . . . . . . . . . . . 100 Topic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

iv © Pascal Press ISBN 978 1 74020 033 2

Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook Excel Essential Skills Mathematics Revision & Exam Workbook Year 8

CHAPTER 12—Reasoning in geometry

EXAM PAPERS

Unit 1

Angles and the value of the pronumerals . . . . . . . . . . . . . . . . . . . . . . . . 132

Exam Paper 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

Unit 2

Parallel lines and angles . . . . . . . . . . . . 133

Exam Paper 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

Unit 3 The angle sum of a triangle . . . . . . . . . 134 Unit 4

Triangles and the value of the pronumerals . . . . . . . . . . . . . . . . . . . . . . . . 135

Unit 5 The angle sum of a quadrilateral . . . . 136

Exam Paper 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 Exam Paper 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 ANSWERS

Transformations . . . . . . . . . . . . . . . . . . . . . 137

Basic arithmetic and the calculator . . . . . . . . . . . 181

Unit 7 Congruence of plane shapes using transformation . . . . . . . . . . . . . . . . . . . . . . 138

Percentages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 Four operations with integers . . . . . . . . . . . . . . . 182

Unit 8

Recognising congruent figures . . . . . . 139

Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

Unit 9

Recognising congruent triangles . . . . 140

Rational numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

Unit 10 Naming congruent triangles . . . . . . . . . 141

Basic algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

Unit 11 Tests for congruent triangles . . . . . . . . 142

Length, mass and time . . . . . . . . . . . . . . . . . . . . . . 185

Unit 12 Applying properties to solve numerical problems . . . . . . . . . . . . . . . . . 143

Area, volume and capacity . . . . . . . . . . . . . . . . . . . 185

Unit 13 More numerical problems . . . . . . . . . . . . 144

Linear relationships . . . . . . . . . . . . . . . . . . . . . . . . . . 187

Unit 6

Topic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

Circles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 Reasoning in geometry . . . . . . . . . . . . . . . . . . . . . . 190

CHAPTER 13—Probability

Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

Unit 1 The language of probability . . . . . . . . . . 147

Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

Unit 2 Sample space . . . . . . . . . . . . . . . . . . . . . . . 148

Exam Papers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

Unit 3 Outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 Unit 4 Theoretical probability . . . . . . . . . . . . . . . 150 Unit 5 Complementary events . . . . . . . . . . . . . . 151 Unit 6 Venn diagrams . . . . . . . . . . . . . . . . . . . . . . 152 Unit 7 Language of ‘at least’, exclusive ‘or’, inclusive ‘or’ and ‘and’ . . . . . . . . . . . . . . . 153 Unit 8 Two-way tables . . . . . . . . . . . . . . . . . . . . . . 154 Topic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 CHAPTER 14—Statistics Unit 1 Review of basic statistics . . . . . . . . . . . . 157 Unit 2 Collecting data . . . . . . . . . . . . . . . . . . . . . . 158 Unit 3 Types of sampling . . . . . . . . . . . . . . . . . . . 159 Unit 4 Classification of data . . . . . . . . . . . . . . . . 160 Unit 5 Classificaton of data and sample types . . . . . . . . . . . . . . . . . . . . . . . . 161 Unit 6 Mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 Unit 7 Median and mode . . . . . . . . . . . . . . . . . . . 163 Unit 8

Using the mean, mode and median . . . . . . . . . . . . . . . . . . . . . . . . . 164

Unit 9 Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 Topic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

v

Contents © Pascal Press ISBN 978 1 74020 033 2


Introduction There are two workbooks in this series for the Year 8 Australian Curriculum Mathematics course: • Excel Essential Skills Year 8 Mathematics Revision & Exam Workbook (this book) and • Excel Essential Skills Year 8 Mathematics Extension Revision & Exam Workbook. This book should be completed before the Extension book. It is the core book, written specifically for the Year 8 Australian Curriculum Mathematics course and the third in 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 for students to master and consolidate the core skills and concepts of the course through extensive practice. This will ensure that students have a solid foundation on which to build towards both the Mathematics and 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 8 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 Four Exam Papers have been included to test students on the complete Year 8

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 record their scores in all tests and exams.

Ü Answers to all questions are provided at the back of the book. Ü There is a page reference to the Excel Mathematics Study Guide Year 8 in the top

right-hand corner of all pages, excluding the tests. If students need help with a specific section, they will find relevant explanations and worked examples on these pages of the study guide.

A note from the author

Mathematics is best learned if you have pen and paper with you and do every question in writing. Do not just read through the book—work through it and answer the questions, writing down all working. If this approach is coupled with a menu of motivation, realistic goal-setting and a positive attitude, it will lead to better marks in the examinations. My best wishes are with you; I believe this book will help you achieve the best possible results. Good luck in your studies! AS Kalra, MA, MEd, BSc, BEd vi © Pascal Press ISBN 978 1 74020 033 2


Chapter 1

Basic arithmetic and the calculator

Excel Mathematics Study Guide Year 8 Pages 2–5

UNIT 1: Approximations and rounding off Question 1 Round off the following numbers to the nearest ten. a 43

b 65

c 89

d 33

e 158

f 231

g 625

h 829

i 387

j 5672

k 9651

l 6382

Question 2 Round off the following numbers to the nearest hundred. a 763

b 530

c 248

d 2361

e 5389

f 6341

g 8935

h 6371

i 8537

j 483

k 935

l 621

Question 3 Write the following decimals correct to one decimal place. a 3.56

b 0.81

c 9.67

d 31.62

e 0.19

f 16.05

g 18.36

h 91.47

i 62.86

j 43.17

k 83.29

l 55.11

Question 4 Express the following decimals correct to two decimal places. a 5.674

b 8.937

c 9.616

d 33.258

e 41.673

f 83.189

g 52.367

h 81.289

i 63.136

j 59.325

k 129.638

l 538.632

Question 5 Express the following correct to one significant figure. a 52

b 3.456

c 89

d 9.362

e 0.006 83

f 0.0532

Question 6 Express the following correct to two significant figures. a 83.94

b 238

c 8.937

d 91.675

e 325.63

f 81.63

g 253.07

h 0.000 651

i 0.007 635

Chapter 1: Basic arithmetic and the calculator © Pascal Press ISBN 978 1 74020 033 2


1



UNIT 2: Mixed operations Question 1 Use your calculator to simplify the following. a 10 + 15 − 8 =

b 49 − 16 + 13 =

c 18 + 21 + 19 − 10 =

d 83 − 16 − 5 − 3 =

e 56 − (8 + 3) =

f (9 + 11) × 5 =

g 15 × 4 × 3 × 2 =

h 84 ÷ 3 × 2 × 2 =

i 1200 ÷ 6 ÷ 5 ÷ 2 =

j 3 + 4 × 5 =

k 9 + 16 ÷ 8 =

l 50 − 7 × 3 =

m 8 × 5 − 64 ÷ 8 =

n 9810 ÷ 9 ÷ 5 ÷ 2 =

o 7 − 15 ÷ 3 + 9 =

Question 2 Use your calculator to work out the following. a 235.62 + 8.9 =

b 565.67 × 1.2 =

c 35.8 + 89.5 − 3.6 =

d 3 × 6.9 + 2 × 8.7 =

e 5.6 × 8.9 × 2.3 =

f 56.7 + 83.2 × 2 =

g 5.9 × 6.8 − 12.5 =

h 6.7 × 2.5 + 1.6 × 3.5 =

i 0.2 × 1.8 + 8.2 × 1.3 =

j 67.5 − 3.6 × 2.1 =

k 5.8 × 2.3 × 1.9 =

l 100.5 + 6.1 × 2.3 =

c 3 5 + 4 3 – 2 5 =

Question 3 Calculate the following. 1

5

2

10

22

a 8 4 + 6 + 3 = 2

4

2

1

b 9 5 – 3 5 + 6 3 = 1

8

1

e 2 2 × 15 ÷ 3 4 =

d 5 × 11 × 34 =

2

2

4

2

1

1

f 8 7 ÷ 2 12 × 2 =

Question 4 Use your calculator to answer the following. a 92.7 − 8.9 + 16.35 =

b 6.9 + (3.4 × 1.2) =

c 80 ÷ 10 × 9 =

d 5673 ÷ (5.6 − 3.2) =

e 8.16 × 1.2 − 1.67 =

f − 3.7 + 8.9 =

g 613.5 × 8.1 − 214.7 =

h 9.3 × 8.5 × 6.3 =

i 86 + 134 − 62 =

Question 5 Use the fraction key on your calculator to work out the following. 5

8

1

a 6 + 9 – 3 = 1

2

1

d 3 4 × 4 5 ÷ 6 4 =

2 © Pascal Press ISBN 978 1 74020 033 2

b

3 7

1 7

+1 + 1

1

3 5

= 1

e 1 2 × 2 2 × 3 2 =

c

1 5

3

1

× 7 ÷ 2 = 1

2

7

f 1 2 ÷ 5 × 9 =




UNIT 3: Squares, cubes and powers Question 1 Use the x2 key to evaluate the following. a 52 =

b 62 =

c 152 =

d 392 =

e 652 =

f 892 =

g 3.52 =

h 2.12 =

i

6.72 =

j 15.252 =

k 16.32 =

l

121.32 =

Question 2 Use the x y key to find the answer. a 83 =

b 43 =

c 53 =

d 63 =

e 25 =

f 74 =

g 55 =

h 29 =

i

35 =

j 1.23 =

k 2.43 =

l

64 =

m 1.54 =

n 0.73 =

o

1.94 =

Question 3 Calculate the following correct to two decimal places. a 3.24 =

b 1.73 =

c 8.33 =

d 9.13 =

e 6.84 =

f 15.13 =

g 198.22 =

h 61.352 =

i

7.35 =

j 80.72 =

k 17.82 =

l

52.62 =

Question 4 Evaluate the following. (Leave your answers in fraction form.) 1

2

b 5 =

1

2

e 6 5 =

1

3

32 = h

1

4

15 = k

a 1 2 = d 5 3 = g 2 2 = j 1 3 =

3

3

1

2

1

2

1

4

1

2

c 1 4 =

2

2

f 8 2 =

1

3

i 4 2 =

2

3

l 2 3 =



3



UNIT 4: Square roots and cube roots

Question 1 Use the square root key on your calculator to simplify the following. a

9=

b

25 =

c

36 =

d

121 =

e

169 =

f

225 =

g

4 + 49 =

h

36 + 64 =

i

4 × 16 =

j

625 ÷ 25 =

k

256 ÷ 64 =

l

676 – 576 =

m

441 – 196 =

n

289 + 361 =

o

484 ÷

121 =

Question 2 Use the cube root key on your calculator to evaluate the following. a

3

8=

b

3

64 =

c

3

27 =

d

3

729 =

e

3

343 =

f

3

216 =

g

3

125 + 512 =

h

3

8 × 64 =

i

3

1000 ÷ 125 =

j

3

1331 × 27 =

k 8 × 125 =

l

3

1.728 =

3

3

3

3

3

Question 3 Use your calculator to simplify the following correct to one decimal place. a d

3

g

36 × 1.25 =

b

1.728 × 3 8 = 0.49 × 3 571.787 =

1.21 =

c

4×

e

10.24 × 3 2.197 =

f

0.04 × 0.64 =

h

49 ÷ 2.56 =

i

3

2.744 ×

3

3

0.343 =

125 ÷

5.76 =

Question 4 Use your calculator to simplify the following correct to two decimal places. 1

a

d

3

7 9

b

64 = 1

e

15 3 = 1

1

3

=

c

83 =

f

2

1

g

1 2 × 3 2 4 =

h

36 + 3 2 4 =

j

5 7

+ 3 10 =

7

k

93 +

5 6

=

n

m

3

6 ×

3


2

3

8 10

81 4

× 3 16 =

=

1

82 = 3

2

29 5 =

i

55 – 383 =

3

1

l

61 64

+ 25 =

o

3

31

1

72 ÷ 3=


Basic arithmetic and the calculator UNIT 5: Problem solving and the calculator


1 Find the perimeter of a square with side length 4.2 cm. 2 Calculate the volume of a cube with side length 5.3 cm. 3 A rectangular prism has sides 9 cm, 11.2 cm and 12.1 cm. Find its volume. 4 A cube has a volume of 4913 cm3. Find the length of each side of the cube. 5 Write 85 493 correct to the nearest thousand. 6 How many 20-mL bottles could be filled from a 1-litre container of fluid? 7 How much would 32 books cost if one book costs $25.95? 8 Find the cost of 25 pens at $5.95 each. 9 Find the cost of 12.5 kg of lamb at $8.95 a kilogram.

3 travel to school by bus. How many students travel by bus? 4

10 In a class of 32 students,

11 Find the sum of 15.09, 23.7, 18.5 and then subtract 8.75. 12 Divide $5673 equally among three people. 13 Find the average of 3.85, 8.67, 6.93 and 4.79. 1

14 Find the square root of 6 4 . 1

15 Find the cube root of 13 2 correct to two decimal places. 16 How many 25-cent stickers can we buy for $39.75? 17 If 1 litre of petrol costs 70.9 cents, what is the cost of 43 litres? 18 Find the value of

1 × 8.149 × 92 correct to two decimal places. 5

19 Use your calculator to evaluate 152 – 82 + (4.5)2 correct to three decimal places. 20 Cork tiles cost $55 per square metre and are sold only by the square metre. How much would I pay for

sufficient tiles to cover the floor of a square room of side 4.95 m? Chapter 1: Basic arithmetic and the calculator © Pascal Press ISBN 978 1 74020 033 2


5

Basic arithmetic and the calculator TOPIC TEST

PART A

Instructions • This part consists of 12 multiple-choice questions. • Fill in only ONE CIRCLE for each question. • Each question is worth 1 mark.

Time allowed: 15 minutes

Total marks: 12 Marks

1 Evaluate 6 × 9 + 8 × 7.

A 714

2 What is the value of

A 2 2324

A 17.21

4 9 × 5 × 2 × 20 equals:

A 1600

5 25 × 103 equals:

A 25 000

6 (0.5)2 − (0.2)2 equals:

7

132 – 122 equals: 5

A

C 110

D 390

1

B

C 1 121

D 2 121

1

B 27.12

C 27.21

D 17.12

1

B 2000

C 1800

D 2400

1

B 20 000

C 24 000

D 50 000

1

B 0.24

C 0.21

D 0.215

1

B 6

C 7

D 4

1

1 + 3 + 5 + 7 ? 2 4 6 8 23 1 24

3 8.21 + 6.1 × 3.1 equals:

A 0.25

B 434

8 Adrian’s pocket money is $25.75 each month. How much would he receive in 12 months?

A $309

9

1 × 1 = equals: 9 9 1 81

A

10 9.9 − 0.09 equals:

A 9.81

11 12

B $350 B

1 9

B 9.19

C $450 C

2 9

C 9.081

D $300 D

none of these

1 1

D 9.009

1

What is the number 6546 rounded to the nearest hundred?

A 7000

B 6600

C 6550

D 6500

1

A 50

B 500

C 5000

D none of these

1

Paper clips cost 40 cents per 100. How many paper clips would $20 buy?

Total marks achieved for PART A


12


Basic arithmetic and the calculator TOPIC TEST

PART B

Instructions • This part consists of 15 questions.

• Each question is worth 1 mark. • Answer each question in the space provided.



Simplify the following correct to two decimal places. 1 536.2 + 3.864 + 0.063 + 18

1

2 84.6 ÷ 0.018

1

7

3

5

1

3

3 1 8 ÷ 1 5 × 7

1 3

4 2 8 + 1 2 – 1 4 5

4 3

1

× 3.14 × 73

1

6 2.83

1

19

7 31

1

Simplify the following correct to one decimal place. 8 17.83 + (12.15 ÷ 3.9)

1

24 + 38

9

1

10 64 – 8

1

11 67.54 − 38.14 × 0.04

1

3

12

3

1 17.5 + 2.52

1

13

40.2 × 9.36 18.34

1

14

(8.15)2 9.6

1

15 5.92 – 3.22

1

Total marks achieved for PART B



15

7

Chapter 2

Percentages


UNIT 1: The meaning of percentage Question 1 Complete the following sentences. a 30% means 30 out of

.

c 7% means 7 out of

b 80% means 80 out of

.

.

d A percentage is actually a fraction with a denominator of e The symbol for per cent is

.

and it means out of

Question 2 Look at the diagram on the right. a What percentage is shaded?

b What percentage is unshaded?

.

Question 3

a If 65% of a diagram is shaded, how much is unshaded? b If 58% of a diagram is shaded, how much is unshaded? c If 3% of a diagram is shaded, how much is unshaded?

Question 4 I n grids of 100 squares, what percentage is unshaded when the following percentages are shaded? a 25%

b 20%

c 10%

d 67%

e 89%

f 51%

g 64%

h 78%

i

Question 5 Work out the following subtractions.

9%

a 100% – 32% =

b 100% – 47% =

c 100% – 91% =

d 100% – 69% =

e 100% – 37% =

f 100% – 77% =

Question 6 Add the following percentages. a 30% + 47% =

b 80% + 5% =

c 60% + 10% + 7% =

d 12% + 27% + 42% =

Questions 7

a If 12% of the students are away from the class, what percentage of students are present? b In a class spelling test if James got 86% of the words correct, what percentage of the words did he spell incorrectly?



Percentages


UNIT 2: Changing percentages to fractions

Question 1 Express the following percentages as fractions in simplest form. a 50% =

b 40% =

c 30% =

d 10% =

e 20% =

f 60% =

g 70% =

h 80% =

i 25% =

j 75% =

k 85% =

l 100% =

m 17% =

n 90% =

o 95% =

p 49% =

q 19% =

r 23% =

Question 2 Express the following percentages as fractions in simplest form. a 2.5% =

b 8.2% =

c 4.5% =

d 36.5% =

e 3.5% =

f 27.5% =

g 84.5% =

h 40.2% =

i 62.5% =

j 0.5% =

k 22.5% =

l 0.8% =

m 10.5% =

n 8.5% =

o 18.3% =

p 9.25% =

q 40.5% =

r 65.5% =

Question 3 Change the following percentages to fractions in simplest form. a 1 % = 2

b 1 % = 3

e 22 2 % =

1

c 1 % = 4

d 1 % = 8

g 5 12 % =

h 33 13 % =

i 66 23 % =

j 8 12 % =

k 5 12 % =

l 12 12 % =

m 10 12 % =

n 25 12 % =

o 35 12 % =

q 15 12 % =

r 20 14 % =

p 85 12 % =

Question 4 Convert the following to fractions in simplest form.

f 52 12 % =

a 38% =

b 56% =

c 62% =

d 25 13 % =

e 12 14 % =

f 3 14 % =

g 9.5% =

h 8.6% =

i 4.8% =

j 3.7% =

k 6.9% =

l 5.2% =

m 42% =

n 55% =

o 72% = 9

Chapter 2: Percentages © Pascal Press ISBN 978 1 74020 033 2


Percentages


UNIT 3: Changing fractions to percentages Question 1 Express the following fractions as percentages. a 30 =

b 50 =

d 40 =

e

g 62 =

h 39 =

25 = 100

k 16 =

100 100

100

j

100

43 = 100

100 100

c

80 = 100

f

84 = 100

i

56 = 100

l

72 = 100

c 7 =

f

9 = 50

i

7 = 50

c 13 =

f

7 = 40

i 14 =

c 5 =

f

1 = 3

Question 2 Express the following fractions as percentages. a 5 = 10

b 16 = 10

6 = 20

d 4 =

e

g 9 =

h 7 =

5

25

25

10

Question 3 Change the following fractions to percentages. a 3 = 4

b 5 = 80

d 7 =

e 2 =

g 9 =

h 3 =

60 60

8

5

20

80

Question 4 Express the following as percentages. a 3 =

b 5 =

d 7 =

e

8

11


9

5 = 12

8


Percentages


UNIT 4: Changing percentages to decimals Question 1 Express the following percentages as decimals. a 10% =

b 80% =

c 30% =

d 50% =

e 40% =

f 60% =

g 20% =

h 70% =

i 90% =

j 100% =

k 15% =

l 65% =

Question 2 Change the following percentages to decimals. a 16% =

b 19% =

c 39% =

d 12% =

e 61% =

f 56% =

g 14% =

h 73% =

i 67% =

j 98% =

k 81% =

l 78% =

m 62% =

n 43% =

o 49% =

Question 3 Convert the following percentages to decimals. a 5% =

b 2% =

c 8% =

d 9% =

e 6% =

f 7% =

g 3% =

h 1% =

i 4% =

j 1.5% =

k 2.5% =

l 3.3% =

m 2.1% =

n 1.7% =

o 4.9% =

Question 4 Change the following percentages to decimals. a 45.5% =

b 89.2% =

c 57.4% =

d 63.9% =

e 63.2% =

f 36.5% =

g 53.8% =

h 92.7% =

i 69.7% =

j 23.7% =

k 15.8% =

l 21.3% =

Question 5 Express the following percentages as decimals. a 33 13 % =

b 5 % = 6

c 3 % = 8

d 1 12 % =

e 66 23 % =

f 12 12 % =

g 9 14 % =

h 20 34 % =

i

7 = 9%

11



Percentages


UNIT 5: Changing decimals to percentages Question 1 Express the following decimals as percentages. a 0.15 =

d 0.95 =

g 0.18 = j 0.45 = m 0.91 =

b 0.25 =

e 0.14 = h 0.55 = k 0.67 = n 0.75 =

d 0.50 =

g 0.70 = j 0.01 =

m 0.04 =

b 0.60 =

e 0.90 = h 0.4 =

k 0.02 = n 0.06 =

d 0.189 =

g 0.835 = j 0.129 = m 0.687 =

b 0.625 =

e 0.427 = h 0.567 = k 0.816 = n 0.257 =

d 0.007 =

g 0.810 = j 0.004 = m 0.057 =

b 0.910 =

e 0.002 = h 0.037 = k 0.005 = n 0.089 =

c 0.1 =

d 2.56 =

g 8.25 = j 2.84 = m 5.27 = 12 © Pascal Press ISBN 978 1 74020 033 2

b 2.50 =

e 1.31 = h 3.41 = k 5.34 = n 8.03 =

f 0.2 = i 0.3 =

l 0.05 =

o 0.03 =

c 0.537 =

f 0.139 = i 0.683 = l 0.927 =

o 0.369 =

c 0.006 =

f 0.009 = i 0.021 = l 0.003 =

o 0.065 =

c 3.60 =

Question 5 Express the following decimals as percentages. a 1.20 =

l 0.65 =


i 0.17 =

o 0.72 =


f 0.85 =


c 0.35 =

f 3.57 = i 5.63 = l 8.13 =

o 2.06 =


Percentages

Excel Mathematics Study Guide Year 8

UNIT 6: Finding a percentage of a quantity Question 1 Evaluate the following. a 10% of 300 =

b 20% of 5000 =

c 30% of 900 =

d 40% of 630 =

e 50% of 580 =

f 75% of 840 =

g 25% of 370 =

h 35% of 144 =

i 5% of 210 =

j 60% of 225 =

k 70% of 890 =

l 100% of 79 =

m 45% of 125 =

n 80% of 830 =

o 85% of 369 =

p 65% of 1000 =

a 1% of 48 =

b 8.5% of 104 =

c 2.5% of 36 =

d 3.4% of 230 =

e 6.9% of 83 =

f 45.6% of 456 =

g 4.3% of 55 =

h 72.5% of 935 =

i 62.5% of 890 =

j 36.5% of 830 =

k 12.5% of 88 =

l 87.5% of 120 =

m 37.5% of 120 =

n 92.25% of 560 =

p 6.5% of 720 =

a 17% of 500 =

b 64% of $350 =

c 9% of 67 =

d 18.5% of 366 days =

e 5 2 % of 840 =

f 2.5% of $80 =

g 15% of $120 =

h 30% of 4 kg =

i 40% of $2 =

j 400% of 30 =

k 25% of 800 g =

l 25% of $812 =

m 5% of $1200 =

n 142% of $120 =

o 90% of 50 =

p 17% of 400 =

Question 2 Work out the following.

1

o 33 3 % of 180 = Question 3 Calculate the following.

1

Pages 26–41

13



Percentages


UNIT 7: I ncreasing or decreasing by a given percentage Question 1 Increase the following by the given percentage. a $45 by 30% =

b $8000 by 15% =

c $80 by 45% =

d $3000 by 60% =

e $350 by 20% =

f $750 by 35% =

g 900 g by 40% =

h 50 min by 20% =

i 400 kg by 60% =

j 240 L by 50% =

k 36 h by 100% =

l 80 t by 75% =

m $648 by 25% =

n $320.80 by 16% =

o $199.95 by 5% =

q 80 ha by 20% =

p $149.90 by 12 2 % =

1

r 600 cm by 70% =

Question 2 Decrease the following by the given percentage. a $63 by 19% =

b $84 by 32% =

c 4 m by 35% =

d 260 L by 24% =

e $930 by 10% =

f $6354 by 20% =

g $134 by 25% =

h $575 by 30% =

i $928.50 by 15% =

j $243.80 by 50% =

k 48 h by 25% =

l $840 by 70% =

m $365 by 15% =

n $960 by 45% =

o $96 by 40% =

p $60.50 by 80% =

q $940 by 28% =

r $620 by 35% =

Question 3

a B ill bought a block of land for $230 000. b Nathan earns $1500 a week. Calculate his new If the value of the land rose by 80%, find the weekly wage if he receives a pay rise of 20%. new value.

c T he price of a new car is $30 000 and after d A shirt priced at $130 was sold at a discount of 25%. 1 year it decreases in value by 20%. Find the Find the sale price. new value of the car.



Percentages


UNIT 8: Expressing quantities as percentages

Pages 26–41

Question 1

a Express 20 as a percentage of 200. b Express 12 as a percentage of 30. c Express 36 as a percentage of 63. d What percentage is 40 of 112? e What percentage is 28 of 77? Question 2 What percentage is: a 20 of 80?

b 60 of 240?

c 14 of 35?

d 15 of 60?

e 28 of 56?

f 14 of 42?

g 19 of 152?

h 81 of 90?

i 110 of 440?

j 10c of $2?

k 25c of $3?

l 63 cm of 1 m?

m 16 h of 1 day?

n 225 mL of 3 L?

Question 3 In the following, what percentage is the first quantity of the second? a 2 m, 16 m

b 8 s, 48 s

c 12 kg, 90 kg

d 6 L, 300 L

e 30 mL, 150 mL

f 125 g, 500 g

g 70 m, 210 m

h 80 min, 320 min

i 36 s, 2 min

j 30 cm, 3 m

k 18 h, 3 days

l $2, 500c

m 240 g, 6 kg

n 32 kg, 2 t

o 300 cm, 3.6 m

p 8 min, 2 h

Question 4 What percentage is: a 50c of $6?

b $2.50 of $10?

c 28 min of 3 h?

e 650 m of 4 km? g 70c of $3.50?

i 12 mm of 60 cm? k 45 cm of 81 cm? m 600 g of 8 kg

d 750 mL of 6 L? f $3.50 of $4?

h $5 of 150c?

j $7.50 of $30?

l 15 s of 50 s?

1

n 65 min of 4 3 h? 15



Percentages


UNIT 9: Unitary method and percentages Question 1

a If 50% of a number is 32, what is the number? c If 18% of a number is 9, what is the number?

Pages 26–41

b Find the total cost if 60% of it is $90.

d If 150% of a number is 60, what is the number?

Question 2 Use the unitary method to solve the following. a If 20% of a number is 32, what is the number?

c If 15% of a number is 360, what is the number?

b If 10% of a number is 63, what is the number?

d If 48% of a number is 336, what is the number?

Question 3 Find 100% of a number if a part of it is given. a 40% is 80; 100% = b 20% is 92; 100% = c 25% is 120; 100% =

e 50% is 70; 100% =

g 5% is 83; 100% =

i 2% is 94; 100% =

k 16% is 46; 100% =

d 15% is 60; 100% =

f 75% is 450; 100% = h 45% is 119; 100% = j 8% is 34; 100% = 1

l 12 2 % is 230; 100% =

Question 4 1

a If 33 3 % of a number is 9, find the number.

b J ohn’s income increased by 3%. If his income c Alku receives a 15% increase in her weekly wage. rose by $645, find his previous income. If the increase is $75, find her new weekly wage. d The price of a block of land increased by 20%. e Hari spends 40% of his weekly income on rent. If this increase was $28 000, what was the If his rent is $220, find his income. new price? f When an amount is increased by 20% it g The population of a small town decreases by 8% becomes $65. What is the original amount? every year. If this year’s population is 4600, what was the population last year?



Percentages


UNIT 10: Commission Question 1 Robert works for a company and gets a commission of 9% on all sales. How much commission will he receive in a week in which his sales total $27 000?

Question 2 Joshua is a car sales representative and is paid a retainer (basic wage) of $600 per week and a commission of 5% on all sales made. Find his weekly income in a week in which he sells a car to the value of: a $42 000

b $76 000

1

Question 3 Imogen is a salesperson and earns $350 a week plus 5 2 % commission on sales. Her weekly sales total is $75 000. What is her: a commission? b total earnings for the week?

Question 4

Max is a real estate agent and receives 2% commission on the first $400 000 and 1.5% on the value thereafter. Find his commission for selling a property worth $920 000.

Question 5 Katie sells cosmetics and is paid 12.5% on all sales.

a W hat is her income if she sells $5870 worth b How much would she need to sell of cosmetics in a week? to have an income of $1050?

17



Percentages


UNIT 11: Discounts Question 1 Complete the following table. Name of the item bought

chair

calculator

textbook

e-reader

computer

study lamp

Marked price

Percentage discount

$560

10%

$45

Discount in dollars

Sale price

20%

$64

8%

$130

5%

$950

15%

$140

25%

Question 2 A study desk with a marked price of $680 is discounted by 12%. What is the: a discount?

b sale price?

Question 3 Christina spent $235 after getting a discount of $65 on a new watch. a What was the price of the watch before b What percentage discount was given?

the discount?

1

Question 4 A tracksuit that usually costs $248 is reduced by 12 2 %. What is the: a discount? b sale price?

Question 5 Steph paid $178 after receiving a discount of 15% on a pair of shoes. a How much did the shoes cost before the discount? b How much money did she save?

Question 6 A dinner set was discounted by 45% and sold for $836. a How much did the set cost before the discount? b How much was the discount?



Percentages


UNIT 12: Profit and loss

Question 1 James bought some shares for $2540 and sold them for $3200. Find: a his profit on the sale

b his profit as a percentage of the cost price

c his profit as a percentage of the selling price

Question 2 N ancy bought a car for $20 600 and sold it to David at a loss of 40% after it was involved in an accident. David repaired it and then sold it, making a profit of 50% on his purchase price. a How much did David pay for the car?

b For how much did David sell the car?

Question 3 A book is sold for $56.80 including 10% GST. a How much GST is charged?

b What is the selling price of the book without GST?

Question 4 A bicycle is on sale for $450. This is 75% of the regular price. What is the regular price?

19



Percentages


UNIT 13: Problem solving and percentages 1 38% of some marbles are red and 18% are blue.

2 Of 80 cars, 45% are white. How many of

The rest are green. What percentage of the marbles are green?

3 Out of 1060 students, 30% were absent. How

4 102 out of 120 cows have calves. What percentage

many of the students were absent?

6 $500 is increased by 10% and this result is then

of the cows have calves?

5 If 16% of a mass is 80 kg, find the total mass.

the cars are white?

decreased by 10%. What is the final result?

7 A car bought for $2500 is sold for $2000. What

8 A salesman sold goods worth $35 000. Find the is the loss as a percentage of the cost price? commission he gained on the sale if the first $10 000 sales earned 7% and the amount sold above $10 000 earned 9%.

9 Find the simple interest on $2000 for 1 year

10 Find the simple interest on $3560 for

at 9.5% per annum.

4

11 Find 55% of $1640 and add it to 45% of $150.

3 years at 8 1 % p.a.

12 In an examination, 90% of a class of 30 students

passed. How many students failed?

13 A discount of 35% will be allowed on a coat priced at $170. What price will be paid for the coat?

14 Of the 960 students at a school, 15% are in Year 8.

a How many students are in Year 8? b There are 81 boys in Year 8. What percentage of Year 8 students are boys?



Percentages TOPIC TEST

PART A

Instructions • This part consists of 12 multiple-choice questions.

• Fill in only ONE CIRCLE for each question. • Each question is worth 1 mark.



1 0.7 expressed as a percentage is:

A 0.007%

B 0.7%

C 7%

D 70%

2 An item is bought for $80 and sold for $120. What is the percentage profit on the cost price?

A 40%

B 30%

3 18% of a number is 27. What is the number?

A 150

1

B 200

4 Which decimal does 4 2 % equal?

A 0.42

B 0.45

C 60%

D 50%

1

C 250

D 300

1

C 0.042

D 0.045

1

D $80

1

3 D 1000

1

D 84%

1

5 Ted pays $60 after receiving a discount of 20%. What is the normal price?

A $63

6 0.3% equals:

B $72

C $75

A 13

B 103

class was absent? 16%

B 19%

C 1003

1

7 At a roll call, there were 4 students absent and 21 present. What percentage of the roll

A

C 25%

8 A car was bought for $6000 and sold at a profit of 30%. What was its selling price?

A $1800

B $4200

C $6200

D $7800

9 The price of a tyre is reduced from $80 to $72. What is the percentage discount?

A 8%

B 10%

10 What percentage is $3 of $20?

A 10%

B 12%

11 If 120 is 20% of a number, what is the number?

A 24

12 p% of $q is:

A

$pq

B 96 B

p+q

$ 100

C 11%

D 90%

1

C 15%

D 18%

1

C 480

D 600

1

C

$100pq

D

pq

$ 100


1

12

21


1


Percentages TOPIC TEST

PART B





1 Find 37% of $300.

1

2 Increase 260 kg by 10% and then decrease the result by 10%.

1

7

3 Write 12 as a percentage correct to two decimal places.

1

4 If 15% of an amount is $140, what is the total amount?

1

5 After 25% of a bill has been paid, $80 still remains to be paid.

How much was the bill?

6 A concrete mixture contains one part cement, two parts sand

and three parts gravel. What percentage of the mixture is sand?

1

1

7 Express 700% as a fraction.

1

8 Find the simple interest on $800 at 9% p.a. for 1 year.

1

9 Express 52 as a percentage of 416.

1

10 Find 100%, given that 40% is 98.

1

11 David pays 28% of his income in tax. If he pays $14 200

income tax, what is his income?

12 A game is bought for $69.50 and sold for $89.50. What is the

gain as a percentage?

13 Ed earns 8% commission on all his sales. Find his commission

when his sales total $25 000.

14 $4800 is invested in a fund giving 12% interest per year. How

much interest is received for 5 years?

15 The price of a television is reduced by 18% to $1722.

What was the original price?



1

1

1

1

1

15


Chapter 3

Four operations with integers


UNIT 1: Addition of integers Question 1 Find the sum of the following (use a number line if necessary). a 8 + 3 =

b 7 + −2 =

c 6 + 5 =

d 12 + −3 =

e 5 + 8 =

f 3 + −4 =

g 12 + 2 =

h 10 + −2 =

i

a 7 + 6 =

b 9 + −5 =

c 23 + 8 =

d 7 + −3 =

e 3 + 21 =

f 15 + −2 =

g 3 + 9 =

h 5 + −7 =

i

Question 2 Find each sum.

Question 3 Add the following.

12 + 14 =

52 + 2 =

a 2 + 3 =

b 8 + −5 =

c 13 + 6 =

d −2 + −3 =

e 9 + 21 =

f 7 + −5 =

g 9 + 18 =

h 2 + −4 =

i

Question 4 Find the answers to these additions.

−9 + 18 =

a 10 + 14 =

b −3 + −2 =

c −7 + 22 =

d 9 + −2 =

e −6 + 42 =

f −9 + −5 =

g 4 + 8 =

h −8 + −3 =

i

Question 5 Find the values of the following.

−6 + 14 =

a −3 + 6 + 8 =

b 12 + −4 =

c −16 + 31 =

d −15 + 10 =

e −8 + 16 =

f −7 + −6 =

g −11 + 9 + 2 =

h −10 + −5 + −2 =

i

Question 6 Find the missing number. a 12 +

= 21

d 6 +

= −9

g 15 +

= 29

b

e −6 + 10 = h (−8) + −4 =

+ −3 = 12

−12 + 15 =

c −8 + 14 =

f 8 + i 9 + 11 =

Chapter 3: Four operations with integers © Pascal Press ISBN 978 1 74020 033 2

= −7


23



UNIT 2: Subtraction of integers Question 1 a 6 − 2 =

Find the answers for the following questions.

b 8 − −3 =

c 9 − 6 =

d 9 − −1 =

e 17 − 5 =

f 18 − −10 =

g 8 − 15 =

h 16 − −6 =

i

25 − 8 =

Question 2 Complete these subtractions (use a number line if necessary). a 13 − 2 =

b 28 − −3 =

c 9 − 4 =

d 15 − −3 =

e 18 − 4 =

f 82 − −5 =

g 19 − 4 =

h 56 − −2 =

i

Question 3 Find each difference.

15 − 6 =

a −17 − 4 =

b −8 − −2 =

c −10 − 3 =

d −15 − −3 =

e −6 − 4 =

f −9 − −3 =

g −10 − 7 =

h −12 − −8 =

i

Question 4 Find the answers for the following subtractions.

−7 − 21 =

a −4 − 13 =

b −5 − −3 =

c −5 − 12 =

d −6 − −2 =

e −7 − 16 =

f −8 − −3 =

g −8 − 24 =

h −6 − −4 =

i

Question 5 Find the values of the following.

−10 − 15 =

a −8 − 18 =

b −18 − −4 =

c 56 − 13 =

d −17 − −9 =

e −23 − 23 =

f −15 − −12 =

g −7 − 17 =

h −16 − −6 =

i

Question 6 Simplify the following.

−19 − 21 =

a 8 − 12 =

b −5 − 2 =

c −5 − 7 =

d 8 − −6 =

e −5 − 9 =

f −5 − −3 =

g −9 − 9 =

h −7 − 10 =

i


6 − 15 =




UNIT 3: Multiplication of integers Question 1 Multiply the following. a 5 × 2 =

b 12 × −7 =

c 15 × 10 =

d 8 × −3 =

e 2 × 6 =

f 12 × −8 =

g 6 × 9 =

h 6 × −15 =

i


13 × 4 =

a 3 × 2 =

b 5 × −3 =

c 21 × 9 =

d 15 × −8 =

e 11 × 4 =

f 6 × −7 =

g 9 × 3 =

h 9 × −7 =

i

Question 3 Find the answers to the following.

40 × 9 =

a −3 × 12 =

b −4 × −3 =

c −5 × 11 =

d −5 × −9 =

e −6 × 1 =

f −7 × −20 =

g −3 × 8 =

h −3 × −9 =

i

a −3 × 7 =

b −4 × −6 =

c −8 × 4 =

d −2 × −12 =

e −3 × 15 =

f −5 × −12 =

g −6 × 10 =

h −4 × −8 =

i

Question 4 Simplify.

Question 5 Find each product.

−4 × 5 =

−6 × 8 =

a 4 × 8 × 2 =

b –6 × –3 × 1 =

c –7 × 5 × 10 =

d 9 × –2 × –2 =

e –4 × 5 × –3 =

f 2 × –3 × 4 =

g 6 × 8 × –1 =

h –3 × –10 × –7 =

i

–1 × –2 × –5 × –3 =

Question 6 Complete the following tables. a ×

7

11

b ×

–4

–5

–9

8

c

×

3

7

–4

–7

–10

12

12



–25

–100

25



UNIT 4: Division of integers Question 1 Divide the following. a 24 ÷ 4 =

b 42 ÷ −6 =

c 54 ÷ 9 =

d 36 ÷ −9 =

e 28 ÷ 7 =

f 21 ÷ −3 =

g 16 ÷ 8 =

h 55 ÷ −5 =

i

Question 2 Work out the following divisions.

48 ÷ 8 =

a 12 ÷ 2 =

b 24 ÷ –8 =

c 15 ÷ 5 =

d –20 ÷ 4 =

e –45 ÷ –5 =

f 28 ÷ –7 =

g 18 ÷ 9 =

h –120 ÷ 10 =

i


21 ÷ 3 =

a –27 ÷ 3 =

b −24 ÷ −6 =

c 36 ÷ 12 =

d −27 ÷ −9 =

e –63 ÷ 7 =

f 5 ÷ −5 =

g 33 ÷ –11 =

h −36 ÷ −3 =

i

Question 4 If a = 2, b = –4, c = 8 and d = –24, find the value of:

27 ÷ 3 =

a d ÷ b

b b ÷ a

c d ÷ c

d ab ÷ c

e bc ÷ a

f d ÷ ab

g a2 ÷ b

h b2 ÷ c

i

Question 5 Fill in each missing number. a –48 ÷ d

= –8

÷ –5 = –7

g –300 ÷ –50 =

b –50 ÷

= 10

e –49 ÷ 7 = h

ad ÷ b2

c 36 ÷

f ÷ –6 = 4


i

= –4 ÷ 10 = –8

–96 ÷

a –45 ÷ –9 ÷ –1

b –60 ÷ 3 ÷ –5

c –20 ÷ –2 ÷ –2

d 36 ÷ –4 ÷ –3

e 120 ÷ –12 ÷ 2

f –60 ÷ –20 ÷ –3

g 48 ÷ 4 ÷ –6

h 40 ÷ –4 ÷ –2

i


= 96

–12 ÷ –6 ÷ –2




UNIT 5: Mixed questions Question 1 Find answers to the following. a –2 – 4 =

b –6 + 5 =

c –2 + 9 =

d 3 – 7 =

e 2 – –8 =

f 3 + –5 =

g –4 – –3 =

h –2 + –10 =

i

Question 2 Find the value of the following.

–5 – –12 =

a –4 × –8 =

b –16 ÷ –8 =

c 54 ÷ –6 =

d –3 × 7 =

e 11 × –7 =

f –56 ÷ 7 =

h –100 ÷ –4 =

i

g –2 × 5 × –9 =


–3 × –4 × –6 =

a –3 + –5 =

b –3 × –5 =

c 10 ÷ –2 =

d 10 – –2 =

e –15 – 13 =

f –12 ÷ –4 =

g –6 + 17 =

h –8 + 8 =

i


–8 × 8 =

a (3 + 4) × –2 =

b 5 × (4 – 5) =

c (–6 + 4) × 8 =

d –20 ÷ –5 ÷ –2 =

e 12 × 3 ÷ –9 =

f –3 – 7 – 8 =

g (5 + –5) × –38 =

h (–2 – 5) × –7 =

i

Question 5 Fill in each missing number. a 9 + d g –81 ÷

(–4 + 12) ÷ –2 =

= 7

b

÷ 7 = –6

c –2 –

× –2 = –100

e

+ 8 = 3

f

– 9 = –1

= 5

i

+ 6 = –2

= 9

h –4 –

= –3

Question 6 Complete the following tables. a +

3

–7

–9

12

–15

b

×

–1

–5

6

11

–8

–6

–4

5

–10



8

–9

27



UNIT 6: Indices Question 1 Evaluate the following. a 23 =

b 52 =

c –33 =

d 32 =

e 42 =

f (–1)2 =

g 53 =

h 82 =

i

(–1)3 =

j 43 =

k (–2)3 =

l

(–1)4 =

m 25 =

n (–3)4 =

o (–2)4 =

p (–3)4 =

q –52 =

r (–5)3 =

Question 2 Evaluate the following. a (–1)10 =

b (–5)4 =

c (–5)3 =

d (–1)15 =

e (–2)5 =

f 2 × (–4)2 =

g (–1)99 =

h (–10)3 =

i

(–8)2 =

j (–6)3 =

k (–2)6 =

l

–4 × (–3)3 =

m (9)2 =

n (7)3 =

o (–2)2 × (–5)2 =

p (–4)3 =

q (3)4 =

r –6 × (–3)3 =

c (–4)3 + (–1)2 =

Question 3 Calculate the following. a (–2)3 × (–3)2 =

b (–9)2 – (–4) =

d 42 + (–5)2 =

g (–1)5 + (–3)3 =

h (–7)2 × (–1)3 =

j 82 ÷ (–2)4 =

k (–3)4 – (–5)2 =

l (–6)2 × (–2)3 =

m 72 × (–3)2 =

n 63 + (–2)3 =

o (–10)4 ÷ 102 =

p (–2)2 + (–2)3 =

q (–2)4 + (–3)3 =

r 83 ÷ (–2)5 =

e (–5)2 + (–10)2 =

Question 4 Evaluate the following.

f (–8)2 ÷ (2)5 =

i (–5)3 + –52 =

a 92 ÷ 3 – 42 × 2 =

b (–4)3 ÷ –43 =

c (–3)2 ÷ –32 =

d 4 × (–2)2 + 5 × (–1)4 =

e (–10)2 × 52 =

f 25 ÷ 22 =

g 2 × 103 + (–10)2 =

h (–5)2 + 4 × –10 =

i

(–10)2 × (–10)3 =

j –6 × (–10)3 × (–1)5 =

k (–8)2 + 2 × –20 =

l

(–5)3 + (–3)2 =

m (–9)2 + 3 × –6 =

n 3 × (–4)2 + 8 × (–2)4 =

o (–6)3 – (–5)2 =

p (–3)2 + 32 + (–1)2 =

q (–10)3 + (–10)2 – (–2)6 =

r –5 × (–10)2 × –10 =





UNIT 7: Order of operations

Question 1 Follow the correct order of operations when finding answers to these. a 2 + 3 × 5

b 12 – 5 × 3

c –3 + 21 ÷ 3

d 3 × 4 – 6 × 2

e –3 × 7 + 4 × 8

f –9 – 2 × –6

g 16 ÷ 8 – 3

h 5 – 12 ÷ 3

i

j –24 ÷ 6 + 7

k 28 ÷ 7 – 18 ÷ 2

l

Question 2 Remove the grouping symbols and simplify.

–5 × 20 ÷ 4 3 × –5 – 2 × –7

a (–5 + 8) × 2

b (3 – 7) × (2 – 5)

c –8 + (7 – 3) ÷ –2

d 12 × (–7 + 2)

e 56 – 2 × (5 – 9)

f (–6 + 14) ÷ (–5 + 1)

g (–3 + 9) ÷ (–2 × 3)

h 36 ÷ (1 – 4 – 6)

i

Question 3 Find answers to the following.

–11 – (2 + 3 × 4)

a [(12 – 5) – (3 – 4)] × –3

b 9 × [6 – (5 – 8)]

c [4 + (2 – 7) × 3] × (–2 + 7)

d 12 – (–9 + 4) × 3 × –2

e [(5 + 8) × (3 – 4) + 6] × –1

f 72 ÷ (–3 + 9) – 56 ÷ (–2 – 6)

g [3 + 12 ÷ (–2 + 8)] – 5

h [–1 – (2 + 3) – 7] × –2

i

3 × [6 × (4 – 7) ÷ (–2 + 11)]

Question 4 Insert grouping symbols to make these statements correct. a 5 + 7 ÷ 6 = 2

b –3 + 5 × –1 = –2

c 5 × 4 – 6 × 3 = –30

d 6 + 3 × 5 ÷ –7 = –3

e

f 54 ÷ –9 – 2 + 7 = –15

g –4 × 7 – 5 × –2 = 66

h 7 – 10 × 3 – 8 = 15

–4 + 7 – 9 × 2 = –12

i

10 – 7 + 4 × –3 ÷ 12 = 4



29

Four operations with integers UNIT 8: Problem solving with integers


1 The temperature was –3°. It rose 7° in an hour.

2 Daisy travelled 8 km east and then 5 km west. What was the temperature at the end of Where did Daisy end up relative to her the hour? starting point?

4 What negative number is both greater than –6 is 35° north of the equator. How many degrees and divisible by 4? are between Adelaide and Tokyo?

3 Adelaide is 35° south of the equator and Tokyo

5 After it was born, a baby gained 2.5 kg. Then

6 3 × 3 = 9. Which other number multiplied by itself it lost 3.5 kg. What was the baby’s weight then, gives 9? compared to its birth weight?

7 Charlie owes $3250 on his credit card.

a He pays $1500 off the bill. How much does b Then Charlie buys a laptop for $795 using his Charlie owe now? credit card. How much does Charlie now owe?

8 What is the combined effect of a profit of

9 Find the two numbers whose sum is –8 and $17 000 followed by a loss of $20 000? product is 15.

10 A spider is climbing a wall. It climbs up 5 cm,

11 Jake had $864 in the bank. He put another $56 in the falls back 3 cm, climbs up another 4 cm, falls bank and then withdrew $345. How much money back 6 cm and climbs up another 5 cm. How does Jake now have in the bank? far up the wall is the spider from its starting point?

12 The temperature fell 5 degrees during the day

13 Two numbers add to 4 but multiply to –12. and another 8 degrees during the night. What What are the numbers? was the total change in temperature?

14 Which of the integers, –5, 7, –9, 6, is closest

15 Start with –2, subtract 5 and multiply the result by 6. to zero on the number line? What is the answer?



Four operations with integers TOPIC TEST

PART A





1 3 – –5 equals:

A 2

2 –4 + –7 equals:

A 3

3 Which is equal to 4?

A –16 ÷ 4

B –2

C 8

D –8

1

B –3

C 11

D –11

1

B –20 ÷ –5

C 32 ÷ –8

D –24 ÷ –3

1

B –1

C 9

D –9

1

B –7

C 5

D –5

1

B 60

C –12

D 12

1

B –50

C 28

D –32

1

B 5

C –6

D 6

1

B –8

C 16

D –16

1

B –2

C 2

D 12

1

B –20

C –60

D 60

1

B 32

C 40

D 80

1

4 What is the sum of 4 and –5?

A 1

5 –3 + 2 × 5 equals:

A 7

6 –5 × –4 × –3 equals:

A –60

7 –2 – 3 × –10 equals:

A 50

8 What is the product of –2 and –3?

A –5

9 (–4)2 equals:

A 8

10 –3 – 4 – 5 equals:

A –12

11 –5 × –8 – 10 × –2 equals:

A 20

12 (–7 + 3) × (2 – 6) equals:

A 16




12

31

Four operations with integers TOPIC TEST

PART B





1 –6 – 5 =

1

2 9 – (–4) =

1

3 –7 + (–11) =

1

4 3 × –5 =

1

5 –24 ÷ –3 =

1

6 5 – 3 × –2 =

1

7 8 + 12 ÷ –4 =

1

8 (–10)3 =

1

9 –5 × –8 ÷ –4 =

1

10 7 × –2 – 3 × 5 =

1

11 (11 × –8) + (–4 × –3) =

1

12 –2 × –1 × 5 × –6 =

1

13 (6 – 10) × (–4 – 3) =

1

14 –3 × [–36 ÷ (–3 – 6)] =

1

15 At 6 am the temperature was –3°C. By 9 am it had risen 15°C.

What was the temperature at 9 am?



1

15


Chapter 4

Indices

Excel Mathematics Study Guide Year 8 Page 15

UNIT 1: Index notation Question 1 Write the following in expanded form. a 24 =

b 52 =

c 73 =

d 65 =

e 106 =

f 39 =

g 27 =

h 78 =

a 2 × 2 × 2 × 2 × 2 × 2 =

b 7 × 7 × 7 × 7 × 7 =

c 5 × 5 × 5 × 5 × 5 × 5 × 5 =

d 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 =

e 10 × 10 × 10 × 10 =

f 6 × 6 × 6 × 6 × 6 =

g 12 × 12 × 12 =

h 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 =

Question 2 Write in index form.

Question 3 Evaluate the following. a 24 =

b 33 =

c 112 =

d 53 =

e 132 =

f 105 =

g 63 =

h 26 =

i

Question 4 Write the following in index form.

34 =

a 25 =

b 8 =

c 10 000 =

d 36 =

e 32 =

f 49 =

g 10 000 000 =

h 9 =

i

Question 5 Write in expanded form. a 23 × 32 =

b 62 × 74 =

c 53 × 24 =

d 35 × 5 =

e 73 × 22 =

f 34 × 23 × 52 =

216 =

Question 6 Write each number as the product of its prime factors, giving the answer in index form. a 40 = b 48 = c 72 = d 225 = e 324 = f 486 = g 1568 = h 300 =

33

Chapter 4: Indices © Pascal Press ISBN 978 1 74020 033 2


Indices


UNIT 2: Index laws: multiplication with indices Question 1 Simplify the following, writing your answers in index form. a 23 × 25 =

b 37 × 32 =

c 56 × 54 =

d 78 × 73 =

e 29 × 22 =

f 104 × 105 =

g 66 × 63 =

h 112 × 112 =

i

57 × 55 =

j 310 × 36 =

k 212 × 210 =

l

78 × 79 =

Question 2 Simplify the following, writing your answers in index form. a 64 × 6 =

b 58 × 5 =

c 37 × 3 =

d 7 × 75 =

e 2 × 27 =

f 5 × 510 =

g 223 × 214 =

h 109 × 109 =

i

15 × 152 =

j 3 × 39 =

k 1212 × 1212 =

l

5 × 5 × 53 =

Question 3 Simplify the following. a 43 × 42 =

b 55 × 57 =

c 52 × 59 =

d 28 × 26 =

e 43 × 46 =

f 89 × 83 =

g 37 × 35 =

h 74 × 78 =

i

33 × 34 × 37 =

j 25 × 22 × 23 =

k 39 × 312 =

l

215 × 217 =


b 95 × 94 =

c 48 × 43 =

d 89 × 82 =

e 27 × 24 =

f 53 × 57 =

g 33 × 45 × 32 × 42 =

h 35 × 35 =

i

63 × 62 =

j 62 × 63 =

k 75 × 73 =

l

84 × 86 =


b 3 × 37 =

c 62 × 63 =

d 7 × 75 =

e 53 × 52 =

f 74 × 78 =

g 45 × 49 =

h 87 × 88 =

i

45 × 43 × 42 =

j 6 × 63 =

k 24 × 23 × 22 =

l

39 × 36 =

Question 6 Find the missing term in each of the following. a 57 ×

= 510

b

d 83 ×

= 85

e 45 ×

g 32 ×

= 39

h

j 62 ×

= 68 k × 74 = 77 l × 72 = 74


× 56 = 59 c 74 × = 711 = 48 f 84 × = 85 × 32 = 33 i × 92 = 96


Indices


UNIT 3: Index laws: division with indices Question 1 Simplify the following, writing your answers in index form. a 75 ÷ 72 =

b 28 ÷ 26 =

c 39 ÷ 33 =

g 1010 ÷ 102 =

h 74 ÷ 72 =

i

d 510 ÷ 57 =

j 212 ÷ 23 =

e 29 ÷ 24 =

k 117 ÷ 11 =

f 68 ÷ 64 = l

315 ÷ 35 = 52 ÷ 5 =

Question 2 Simplify the following, writing your answers as basic numerals. a 58 ÷ 57 =

b 39 ÷ 37 =

c 23 ÷ 22 =

g 613 ÷ 611 =

h 25 ÷ 2 =

i 56 ÷ 55 =

d 710 ÷ 78 =

j 1010 ÷ 104 =

e 514 ÷ 511 =

k 34 ÷ 3 =

f 37 ÷ 36 = l

212 ÷ 29 =

Question 3 Simplify the following, writing your answers in index form. a

215 23 =

e

28 24 =

i

216 2 =

5 20

b 5 5 =

7 49 77 =

c

f

59 53 =

67 g 6 6 =

j

1010 10 2 =

k 7 5 =

7 35

318

d 36 =

321 h 37 =

l

12 36 12 24 =

Question 4 Simplify the following. a 310 ÷ 32 =

b 911 ÷ 95 =

c 521 ÷ 516 =

g 715 ÷ 77 =

h 423 ÷ 48 =

i

d 58 ÷ 52 =

j 821 ÷ 814 =

e 212 ÷ 23 = k 632 ÷ 618 =

f 79 ÷ 73 =

l

918 ÷ 96 =

1054 ÷ 1028 =

Question 5 Simplify the following. a 37 ÷ 34 =

b 59 ÷ 52 =

c 87 ÷ 86 =

g 27 ÷ 24 =

h 79 ÷ 74 =

i

d 98 ÷ 93 =

j 810 × 37 ÷ (88 × 34) =

e 125 ÷ 122 = k 25 × 39 ÷ (23 × 34) =

f 98 ÷ 97 = l

510 × 48 ÷ (57 × 42) = 29 × 36 ÷ (24 × 35) =

Question 6 Find the missing term in each of the following. a 59 ÷

= 54 b 514 ÷ = 58 c 812 ÷ = 87

d

÷ 3 = 36 e 79 ÷ 76 = f 38 ÷ 35 = 48 6 2 7 g 8 ÷ = 8 h = 6 i = 46 2 6 j 24 × 34 ÷

= 23 × 32 k

28 × 312 ÷ 52 = 56 l = 25 × 36

35



Indices


UNIT 4: Index laws: powers of powers Question 1 Simplify, leaving your answers in index form. a (25)2 =

b (36)3 =

c (54)4 =

g (510)5 =

h (38)2 =

i

d (73)5 =

j (103)6 =

e (27)4 =

k (512)5 =

Question 2 Use a calculator to find the value of the following.

f (69)2 =

l

(112)2 = (36)6 =

a (32)4 =

b (25)2 =

c (73)3 =

g (37)2 =

h (26)3 =

i

d (24)5 =

j (23)4 =

e (52)6 =

k (112)3 =

Question 3 Simplify, leaving your answers in index form.

f (64)2 =

l

(72)2 = (35)3 =

a (37)3 =

b (25)4 =

c (67)2 =

g (210)10 =

h (102)5 =

i

d (59)4 =

j (122)4 =

e (72)3 =

k (77)7 =


f (113)7 =

l

(64)3 = (26)5 =

a (45)3 =

b (37)5 =

c (810)4 =

d (518)8 =

e (215)6 =

f (512)7 =

g (79)2 =

h (410)8 =

i

(211)6 =

j (916)3 =

k (79)7 =

l

(314)9 =

Question 5 Complete the following to express each in simplest index form. a 362 = (62)2 b 83 =

c 812 =

812 =

362 =

83 =

d 1252 =

e 494 =

f 323 =

494 =

323 =

1252 =

Question 6 Simplify the following, leaving your answers in simplest index form. a (42)3 =

b (83)4 =

c (94)5 =

d (816)4 =

e (1214)2 =

f (272)5 =

g (253)2 =

h (10005)3 =

i

j (274)6 =

(162)5 =



Indices


UNIT 5: Index laws: the zero index Question 1 Complete the following. a 32 ÷ 32 = 9 ÷ 9

32 ÷ 32 =

b 23 ÷ 23 =

÷

b 23 ÷ 23 =

d 53 ÷ 53 =

÷

d 53 ÷ 53 =

e 72 ÷ 72 = e 72 ÷ 72 =

÷

c 104 ÷ 104 =

÷

c 104 ÷ 104 =

f 25 ÷ 25 =

÷

f 25 ÷ 25 =

Question 2 Use the index laws to simplify, leaving the answer in index form. a 32 ÷ 32 =

b 23 ÷ 23 =

c 104 ÷ 104 =

d 53 ÷ 53 =

e 72 ÷ 72 =

f 25 ÷ 25 =

Question 3 Fill in the blank.

Any (non-zero) number raised to the zero power is equal to

Question 4 Find the value.

.

a 70 =

b 90 =

c 60 =

d 230 =

e 370 =

f (–2)0 =

g 190 =

h ( 2 )0 =

1

i

a 20 + 30 =

b 50 – 80 =

c 110 + 40 – 30 =

d 6 + 60 =

e 9 – 70 =

f 100 – 2 =

g 120 – 90 – 60 =

h 15 + 150 – 20 =

i

70 + 50 + 4 =

j 2 × 30 =

k (5 + 9)0 =

l

4 × 60 + 6 × 80 =

a x0 =

b y0 =

c a0 =

d 2x0 =

e 3b0 =

f 5m0 =

g (4k)0 =

h (3t)0 =

i

(7n)0 =

j (2a2)0 =

k (pq)0 =

l

pq0 =

m 7x0 + 3y0 =

n 9a0 – 80 =

o 5a0 + (5a)0 =

Question 5 Find the value.

Question 6 Simplify.

2580 =

37



Indices


UNIT 6: Index laws: miscellaneous questions Question 1 Simplify the following, leaving the answers in index form. a 74 × 75 =

b 22 × 25 =

c 76 × 72 =

d 46 × 46 =

e 32 × 37 =

f 82 × 8 × 83 =

g 82 × 83 =

h 53 × 52 =

i

6 × 62 =

Question 2 Simplify, giving answers in index form. a 49 ÷ 46 =

b 28 ÷ 25 =

c 67 ÷ 65 =

d 55 ÷ 53 =

e 47 ÷ 44 =

f 38 ÷ 36 =

g 36 ÷ 32 =

h 56 ÷ 54 =

i

46 ÷ 43 =

Question 3 Give the answers in simplest index form. a (32) =

b (23)2 =

c (73)2 =

d (43) =

e (63) × 64 =

f (87) ÷ 86 =

h (35) =

i

c 8n0 =

f (x2) =

i

3

4

g (54) × (55) = 3

2

2

6

2

(53)4 =

Question 4 Simplify the following. a 4m0 =

d 5m0 × (8m)0 = g (5y3) = 0

b (6m)0 = e 26 b0 =

h 57 ÷ 57 =

0

96 ÷ 94 =

Question 5 Simplify the following, giving the answers in index form. a 87 ÷ 82 =

b 69 × 62 =

c (25) =

d (53) =

e 53 ÷ 5 =

f 52 × 52 =

g 22 × 63 × (24 × 63) =

h 43 × 36 ÷ (42 × 34) =

i

32 × 3 =

j 92 ÷ 9 =

k 77 × 49 ÷ (75 × 47) =

l

(42)2 =

2


4


Indices TOPIC TEST

PART A





1 3 equals: 4

A 3 + 3 + 3 + 3

2 38 ÷ 34 equals:

A 3 4

3 72 × 74 equals:

A 49 6

5 8 × 31 4 5 4 × 34 equals: 52 33

A

5 44 × (410 ÷ 42) equals:

A 4

20

6 (102)4 equals:

A 100 000

7 (43) equals:

B 4 + 4 + 4

C 3 × 3 × 3 × 3

D 4 × 4 × 4

1

B 3

C 1

D 1

1

B 49

C 7

D 7

1

2

4

8

B

6

54 33

B 4

2

8

C 5 × 3

D 5 × 3

1

C 4

D 4

1

2

12

3

10

4

3

6

B 1 000 000

C 10 000 000

D 100 000 000

1

B 4

C 4 6

D 4

1

C 4

D 7

1

2

A 16 4

8 3 + 40 equals:

32

A 1

B 2

A 3

B 3

34 × 38 9 32 equals: 6

10 (710 ÷ 72)2 equals:

A 7

25

11 53 × 56 equals:

A 5

18

12 (23 × 34)2 equals:

A 2 × 3 5

6

5

10

C 3

D 3

1

B 7

C 7

D 7

1

B 5

C 25

14

8

64

9

B 2 × 3 6

8

8

C 6

16

18

D 25

1

D 6

1

24

9

9


39


12


Indices TOPIC TEST

PART B





Simplify the following, giving your answer in index form. 1 60 × (62) = 3

3 (83) = 2

2 57 ÷ 55 =

1

1

4 4t0 + (7t)0 + (9t3)0 =

1

1

5 320 ÷ (34) = 2

1

Simplify the following, giving your answer in index form. 6 39 × 35 =

7 ×5 8 7 4 × 5 2 =

6

4

7 98 ÷ 94 =

1

1

1

9

5 ×3 33 = 0

9

1

10 (92) ÷ 93 = 2

1

Simplify the following, writing your answers in the simplest index form. 11 37 × 34 × 33 =

13 (1000a12b15)0 =

12 90 ÷ 9–2 =

1

1

1

14 50 + 20 + (34)0 =

1

15 252 × 252 × 643 × 643 =

1



15


Rational numbers

Chapter 5 Excel Mathematics Study Guide Year 8 Pages 2–5

UNIT 1: Rounding off whole numbers

Question 1 Round off the following numbers to the nearest whole number. a 8.3

b 11.6

c 14.5

g 6.499

h 34.501

i

d 9.16

e 7.45

Question 2 Round off the following numbers to the nearest ten.

f 7.913

23.148

a 68

b 52

c 93

g 145

h 377

i

d 397

e 74

f 82

568

Question 3 Round off the following numbers to the nearest hundred. a 169

b 578

c 435

g 281

h 332

i

d 671

e 814

f 950

2541

Question 4 Round off the following numbers to the nearest thousand. a 5632

b 8199

c 7650

d 4781

e 2369

f 3334

g 4961

h 5831

i

j 9325

6289

Question 5 Round off the following numbers to the nearest ten thousand. a 24 683

b 91 561

c 32 655

d 47 960

e 52 390

f 61 833

g 74 634

h 83 597

i

j 20 613

48 139

Question 6 Round off the following numbers to the nearest million. a 2 600 000

b 5 718 000

c 8 123 000

d 5 672 000

e 28 671 500

f 31 814 632

g 48 361 410

h 92 234 612

i

j 31 234 612

8 714 321

41

Chapter 5: Rational numbers © Pascal Press ISBN 978 1 74020 033 2


Rational numbers


UNIT 2: Rounding off decimals Question 1 Write the following decimals correct to one decimal place. a 2.34 =

b 8.915 =

c 30.612 =

g 89.47 =

h 32.143 =

i

d 81.14 = j 53.345 =

e 92.83 =

k 91.831 =

f 41.36 = l

54.156 = 39.418 =

Question 2 Write the following decimals correct to the nearest tenth. a 81.348 =

b 32.149 =

c 36.481 =

g 51.318 =

h 39.615 =

i

d 41.943 = j 28.471 =

e 62.458 = k 58.653 =

f 92.357 = l

42.835 = 73.852 =

Question 3 Write the following decimals correct to two decimal places. a 7.813 =

b 19.625 =

c 21.538 =

d 63.829 =

e 51.367 =

f 72.123 =

g 84.351 =

h 63.839 =

i

41.638 =

j 64.836 =

k 75.612 =

l

81.139 =

Question 4 Write the following decimals correct to the nearest hundredth. a 7.417 =

b 15.632 =

c 28.139 =

d 0.941 =

e 33.458 =

f 47.438 =

g 53.235 =

h 64.831 =

i

78.356 =

j 81.892 =

k 92.635 =

l

125.836 =

Question 5 Write the following decimals correct to three decimal places. a 5.6781 =

b 25.8314 =

c 19.7156 =

d 37.8395 =

e 42.8386 =

f 59.2347 =

g 63.6152 =

h 72.8192 =

i

81.3419 =

j 93.1453 =

k 120.6158 =

l

92.1835 =

Question 6 Write the following decimals correct to the nearest thousandth. a 88.6152 =

b 63.3412 =

c 230.3614 =

d 95.6487 =

e 94.8325 =

f 512.1581 =

g 120.1581 =

h 134.6429 =

i

832.3248 =

j 435.2345 =

k 437.1298 =

l

531.6413 =



Rational numbers


UNIT 3: Changing fractions to terminating decimals Question 1 Write the following as decimals. a

d g j

3 10

43 10

=

b

=

e

h

k

93 100

=

549 1000

=

9 10

c

=

f

=

i

l

=

7 100

239 100

6342 10 000

=

Question 2 Change the following to decimals. 3

9

7 10

=

12 100

=

783 1000

=

764 10 000

=

7

a 5 + 10 =

b 8 + 10 =

c 15 + 100 =

d 28 + 100 =

e 16 + 100 =

f 94 + 10 =

g 123 + 100 =

h 128 + 10 =

i

532 + 100 =

j 81 + 10 =

k 58 + 10 =

l

94 + 100 =

c

3 100

f

i

l

7 8

c

3 15

=

f

=

i

=

l

12 50

c

5 8

f

i

l

5

3

3

1

8

7

Question 3 Change each fraction to a decimal. a

d g j

1 10

b

e

=

h

=

k

=

17 100 3 5 1 4

=

6 10

=

63 1000 7 50

=

=

8 125

=

Question 4 Express the following as decimals. a

d g j

8 80

=

249 100 63 50

=

=

9 500

=

b

e

h

k

9 50

=

68 1000 304 100 11 250

Question 5 Write the following as decimals. a

d g j

3 1000 6 15

=

103 500 11 40

=

=

=

b

e

h

k

114 10 000 6 20

=

=

27 200

=

322 1000

=

7

37

19

=

415 10 000 3 8

=

= =

56 20

= =

935 1000

=

=

=

37 50 32 25

= =

28 500

=

43



Rational numbers


UNIT 4: Recurring and terminating decimals

Question 1 Which of the following are recurring decimals and which are terminating? a 0.125

b 0.333 ...

c 1.32

d 0.43

e 2.43

f 0.4545 ...

g 0.1111 ...

h 1.8345

i

0.8231

j 0.7

k 0.8835

l

9.8

Question 2 Write the following recurring decimals in the shorter way. a 0.3333 ... =

b 0.777 ... =

c 0.533 33 ... =

d 0.8888 ... =

e 0.272 727 ... =

f 0.266 666 ... =

g 0.434 343 ... =

h 0.121 212 12 ... =

i

0.818 181 ... =

j 0.6666 ... =

k 0.428 571 428 571 ... =

l

0.080 808 ... =

Question 3 Write the following recurring decimals in the expanded way. a 4.3 =

b 8.6 =

c 0.1 =

= d 0.31

e 0.7 =

f 2.2 =

= g 1.72

= h 0.227

i

= 1.24

j 0.7083 =

k 0.5 =

l

= 0.15

Question 4 Write the following as recurring decimals. a 0.083 33 ... =

b 0.2222 ... =

c 1.4444 ... =

d 1.689 292 92 ... =

e 1.6363 ... =

f 5.123 123 ... =

g 6.230 693 069 ... =

h 5.0666 ... =

i

3.255 55 ... =

j 0.456 456 ... =

k 2.1111 ... =

l

0.936 936 ... =

Question 5 Write the following as recurring decimals. a 0.253 53 ... =

b 0.3333 ... =

c 0.666 ... =

d 0.3888 ... =

e 0.2323 ... =

f 0.153 33 ... =

g 1.7272 ... =

h 0.444 ... =

i

1.7777 ... =

j 0.002 22 ... =

k 3.585 858 ... =

l

8.3737 ... =

=

c

2 9

=

f

=

i

=

l

Question 6 Write the following fractions as recurring decimals. a

d g j

1 3

3 9

=

b

=

e

h

k

3 11

=

5 110

=


2 3 5 9

4 11

1 90

=

2 11 5 11

2 90

= = =


Rational numbers


UNIT 5: Irrational numbers Question 1 Write rational, irrational or neither for each number. a

4 7

b 0.2

d

e π

f 5 2

g 17

h

49

i

j

16 + 25

l

c

2

9+ 3

k 0.6

5 1

3

7

Question 2 Write rational, irrational or neither for each number. a

81

b

52

8

d

−25

f

0.4

2.25

h

13

j

l

c

3

e

15 17

g i

8

k

22 7

3

1 −8

1 16

3 + 17

Question 3 Which of the following are irrational? a

11

b 12%

c

0.9

d

e

144

f 5π

33 7

Question 4 Between which two consecutive integers does each of the following lie? a

7

b

21

c

72

d

220

e

32

f

98

45



Rational numbers


UNIT 6: Equivalent ratios

Question 1 Express the following ratios in their simplest form without using the calculator. a 6 : 3 =

b 2 : 8 =

c 28 : 7 =

d 12 : 36 =

e 15 : 5 =

f 5 : 55 =

g 32 : 4 =

h 3 : 39 =

i

81 : 9 =

j 8 : 48 =

k 64 : 16 =

l

12 : 144 =

Question 2 Simplify the following ratios without using the calculator. a 35 : 75 =

b 72 : 36 =

c 51 : 17 =

d 20 : 115 =

e 56 : 7 =

f 88 : 12 =

g 63 : 18 =

h 8 : 72 =

i

32 : 6 =

j 8 : 76 =

k 9 : 45 =

l

20 : 45 =

c 1 2 : 5 =

Question 3 Express the following ratios in their simplest form. 1 1 : = 4 12 1 7 : = 8 8

1

a 3 : 9 : 15 =

b

d 1 4 : 6 =

e

h 0.7 : 0.9 =

i

1.2 : 4.8 =

j 1.2 : 5 =

l

3.5 : 4 =

m 2 : 4 : 8 =

k 3 : 8 =

o 14 : 28 : 42 =

1

g

2 5

3

: = 5

1

n 5 : 15 : 45 =

5

f 4 : 6 =

Question 4 Use a calculator to simplify the following ratios. a 10 cm : 80 cm =

b 30 kg : 75 kg =

c 6 h : 2 days =

d 900 g : 3 kg =

e 30c : 70c =

f 4 days : 4 weeks =

g 60 cm : 3.5 m =

h 80 s : 2 min =

i

5 kg : 1200 g =

j 600 mL : 1 L =

k 8 km : 500 m =

l

m 80 cm : 2 m =

n 40c : $2 =

20 cm : 160 mm =

Question 5 Use a calculator to express the following ratios in their simplest form. 1

a 40 cm : 3 2 m =

b 800 g : 10 kg =

c 30 min : 2 h =

d 25 min : 2 h =

e 3 h : 40 min =

g 3 3 : 6 =

j 3.45 : 4.45 =

h 1 : 6 =

f 5 4 : 3 =

2


5

k 8.2 : 10 =

1

i

3.5 : 6.5 =

l

9.6 : 3 =


Rational numbers


UNIT 7: Using ratios Question 1

a Divide $560 in the ratio 3 : 4.

b Divide 2 tonnes in the ratio 2 : 3.

c Divide $720 in the ratio 4 : 5.

d $800 is divided in the ratio 3 : 5. Find the larger part.

e $3600 is divided in the ratio 1 : 3. Find the smaller part.

Question 2

a The ratio of girls to boys is 5 : 4. If there are 35 girls, how many boys are there?

b The three angles of a triangle are in the ratio 2 : 3 : 4. Find the size of each angle.

c The ratio of adults to children on a train trip is 3 : 2. If the train is carrying 800 passengers, find the number

of adults and children on the train.

d The ratio of flour to sugar in a recipe is 4 : 1. If a recipe uses 320 g of flour, how much sugar should be used?

e Georgie and Isabel share $24 000 in the ratio 5 : 3. What is Georgie’s share?

Question 3

a Two sides of a rectangle are in the ratio 3 : 4. If the longer side is 20 cm, what is the perimeter of the rectangle?

b Find the ratio of the areas of two squares whose sides are 3 cm and 4 cm.

c The dimensions of a rectangle are 6 cm and 10 cm. What is the ratio of its length to its perimeter?

d Divide $96 000 in the ratio of 4 : 5 : 7.

e Divide $5400 between two girls in the ratio of their ages, 8 years and 10 years.

47



Rational numbers


UNIT 8: Rates Question 1 Complete the following sentences. a 960 km in 12 hours is a rate of

per hour.

b If 2400 litres of water flows through a tap in 8 hours, it flows at a rate of c 8 kg of peas cost $20, which equals

per minute.

per kg.

d Angus works for 15 hours and is paid $450, and so his rate of pay is e Maddy earns $1250 for a 40-hour week. Her hourly rate of pay is

per hour. dollars per hour.

Question 2

a Anna drives 360 km in 4 hours. Find her average speed. b A car travels at the speed of 25 m/s. How many kilometres does it travel in 1 hour? c A car uses petrol at the rate of 12.5 L/100 km. How many litres would be used to travel 850 km?

Question 3

1

a A tree grows to a height of 13.75 m over a period of 5 2 years. What is the average annual growth rate

in metres per year?

b In a cricket match, runs were scored at a rate of 5.4 runs per over. How many overs did it take to score

270 runs?

c Change 120 km/h to km/min.



Rational numbers


UNIT 9: Conversion of rates Question 1 Complete the equivalent rates. a 90 km/h =

km/min

b 60 L/h =

L/day

c 30 m/min =

m/h

d $2/min =

$/h

f 30°/min =

°/s

e 40 mL/min =

mL/h

g 500 mm/s =

cm/s

i

kg/week

12.5 t/week =

k 315 L/min =

kL/min

h 8.5 ha/day =

m2/day

j 0.85 m/s = l

cm/h

100 km/h =

km/day

Question 2 A speed of 46 metres per second is how many: a metres per minute? b metres per hour? c kilometres per hour?

Question 3 A car is travelling at 120 km/h. How many metres does it travel in one second?

Question 4 A flow rate of 25 millilitres per second is how many: a millilitres per minute?

b millilitres per hour?

c litres per hour?

Question 5 Change the following.

a 82 km/h to m/s

b 20 m/s to km/h

49



Rational numbers


UNIT 10: Scale drawing Question 1 Write each of the following scales in the ratio form. a 1 mm to 1 m

b 1 cm to 1 m

c 1 cm to 100 m

d 10 cm to 1 km

e 4 mm to 1 m

f 5 cm to 1 m

g 1 mm to 20 m

h 20 cm to 1 m

i

1 mm to 6 m

Question 2 Using a scale of 1 : 100 what length is represented by each of the following? a 1 cm

b 3 cm

c 5 cm

d 8 mm

e 6 mm

f 12 m

Question 3 Using a scale of 1 : 1000 find the real length represented by the following. a 8 mm

b 5 cm

c 6 m

d 9.5 cm

e 8.3 m

f 63.25 m

Question 4 The distance between two points in real life is given. What will be the distance between these points on a scale drawing with a scale of 1 cm to 100 m? a 500 m

b 400 m

c 1260 m

d 80 m

e 3000 m

f 2835 m

Question 5 A drawing of a block of land along with the proposed building has been drawn using a scale of 1 : 500. Measure the plan and answer the questions using metres. a How wide is the block of land? N

b How deep is the block of land? c Find the area of the block of land in square metres. d How far is the proposed building from the southern boundary? e Find the area of the proposed building in square metres.


Proposed building

Area I

Area II Scale 1 : 500


Rational numbers


UNIT 11: Problem solving 1 In a class of 30 students, there are 18 boys. What is the ratio of:

a boys to girls? b girls to boys?

2 Michael delivered 480 bottles of milk every morning between 6:00 am and 9 : 00 am.

Find his hourly rate of delivery.

3 Tony buys a pen for $30 and sells it for $40. What is the ratio of the:

a cost price to the selling price?

4 John drives 240 km in 4 hours.

b selling price to the cost price?

Find his average speed.

5 Divide $300 in the ratio 2 : 3.

6 Two angles of a triangle are 40° and 60°. What is the ratio of the:

a third angle to the angle sum of the triangle?

b smallest angle to the largest angle?

7 A car travels at 450 km in 5 hours. What is the speed of the car per hour?

8 If a 20-kg box of oranges cost $15, calculate the price of 1 kg of oranges.

9 A man wishes to divide $120 000 in the ratio of 3 : 7 to give to his son and his wife respectively.

How much will each one get?

10 A concrete mixture is made up of five parts of metal, three parts of sand and two parts of cement. Find the

quantity of each needed to make 50 cubic metres of concrete.

51



Rational numbers TOPIC TEST

PART A





1 What is 218 625 396 rounded off to the nearest million?

A 218 000 000

B 218 600 000

C 218 700 000

D 219 000 000

1

D 0.785

1

C 17.99

D 18.00

1

B 1 : 8

C 1 : 3

D 3 : 1

1

B 0.85

C 0.72

D 0.625

1

2 Which of the following is irrational? 2

A 3

3

B

25

C

3 If 17.895 is rounded off to two decimal places the result is:

A 17.89

B 17.90

4 What is the ratio of 8 hours to 1 day?

A 8 : 1

5

5 8

as a decimal equals:

A 0.58

6 0.6 as a fraction in simplest form is: 3

A 5

2

B 3

5

C 6

7 Leo and Ben share $12 000 in the ratio 2 : 3. What is Ben’s share?

A $2400

B $4800

C $6000

8 What is the average speed if a car travels 245 km in 3½ hours?

A 60 km/h

B 65 km/h

C 70 km/h

6

D 7

1

D $7200

1

D 75 km/h

1

9 The ratio of cows to sheep on a farm is 3 : 8. If there are 240 cows on the farm, how

many sheep are there?

A 90

B 150

C 640

10 A rate of 7.2 litres per hour is how many millilitres per second?

A 0.2

B 2

C 20

D 880

1

D 200

1

11 Using a scale of 1:100 000 what is the real length represented by a distance on a map of 5 cm?

A 5 km

B 500 m

C 50 m

12 When expressed as a decimal, which of these is not a recurring decimal? 4

A 5

4

B 7

4

C 9

D 5 m 4

D 11



1

1

12


Rational numbers TOPIC TEST

PART B


• Answer each question in the space provided.



1 Write 13.238 correct to one decimal place. 2 Find

7 100

1

3

+ 10 as a decimal.

1

3 Write 0.3 as a fraction in simplest form.

1

4 Express these ratios in simplest form.

b 0.7 : 2

a 12 : 4

2

5 Divide 84 in the ratio 3 : 4.

1

6 On a journey of 300 km the average speed was 75 km/h. How long did the journey take?

1

7 Sally is paid $752.50 for working 35 hours. What is her hourly rate of pay?

1

8 A map will be drawn using a scale of 1 : 1000.

a What length on the map will represent a b A length on the map of 13 cm would real distance of 8 m? represent what actual distance?

2

9 Change 15 m/s to km/h.

1

10 The ratio of boys to girls in a class is 5 : 3. If there are 15 girls, how many boys are in the class?

1

11 Determine whether each number is rational or irrational.

a

7

b

3 5

. c 0. 7


15

53


3


Chapter 6

Basic algebra


UNIT 1: Algebraic expressions Question 1 Write an expression for each of the following. a The sum of 5x and 6y = b 15 less than m = c The double of 3a = d The difference between a and b = e Two-thirds of y =

Question 2 Write an algebraic expression for each of the following. a Six times the number n minus 5 = b The sum of 5a and 32 = c The sum of x, 2y and 5z = d The product of 4a and 3b = e The average of 5a and 7a =

Question 3 If x represents any number, write an algebraic expression for each of the following. a Three times the number plus 9 = b One-fifth of the number plus 8 = c The sum of the number and 20 = d The difference between the number and 8 = e Seven more than the number =

Question 4 Show the sum of each of the following. a 17 and a =

b 6m and 7n = c 3a, 4b and 5c = d 9x, 11y and 2z = e 8m, 10n and 7p =

Question 5 Write an algebraic expression for each of the following. a To the sum of 6a and 5b, add 7c =

b From the product of 4x and 5y, take away 10 = c Divide 3a by 4b and then add 15 = d Divide the sum of a and b by 10 = e 18 plus x, all divided by 6 =



Basic algebra


UNIT 2: Simplifying algebraic expressions Question 1 Write down the coefficient for each of the following terms. a 6x

b 19m

c 16t

d 24x

e 14y

f 54n

g 96q

h 35y

i

j 41p

k 15l

l

32a

Question 2 Circle the like terms.

31n

a 3a, 4b, 10a

b 5x, 6y, 9x

c 7m, 3n, 8x

d 5c, 8d, 9c

e 14y, 8a, 6y

f 5l, 4m, 6l

g 3a, 4c, 5c

i 18y, y, 3x

h 12, 5a, 6a

Question 3 Simplify the following. a 5a + 7a =

b y + y + y + y =

c m + m + m + m + m =

d x + x + x + x =

e a + a + a + a + a =

f d + d + d =

g 20d + 5d =

i 4a + 15a =

h 7k + 5k + k =

Question 4 Simplify the following expressions. a 16x – 3x =

b 28b – 17b =

c 35x – 12x =

d 20a – 3a =

e 49x – 6x =

f 18a – 5a =

g 12y – 5y =

h 14c – 8c =

i 21y – 2y =

Question 5 Simplify the following. a 9 × a =

b 5 × a × b =

c x × y × z =

d 6 × x × y =

e 42 × m × n × l =

f 8 × m × n =

g a × b × 10 =

h 4 × 5 × m × n =

i

14 × a × d × e =

Question 6 Write the following expressions in expanded form. a 28ab =

b 8abc =

c 7xy =

d 7mn =

e 9abc =

f 18m2 =

g 2xyz =

h 9a2b =

i

j 8a3 =

k 5ace =

l 17a2b2 =

m 16x =

n 28x2y3 =

14mnp =

55

Chapter 6: Basic algebra © Pascal Press ISBN 978 1 74020 033 2


Basic algebra


UNIT 3: Collecting like terms Question 1 Collect like terms to simplify the following. a a + a + a + a =

b x + x + x + y + y + y + y =

c x + x + x + x + y =

d l + l + l + l + l + m =

e m + m + m + n + n =

f k + k + k + m + m + m =

Question 2 Simplify the following by collecting like terms. a 5x + 7y + 9x =

b 14a + 17 + 5a + 12 =

c 2a + 5b + 3a + 7b =

d 7x + 3y + 8y =

e 6m + 4n + 8m + 3n =


f 3a + 4b + 8a + 11b =

a 16x – 9x – 3x + 2y =

b 10x + 9y – 8x + 7y =

c 9p + 3l + 8p – l =

d 9m – 4n + 12m + 6n =

e 15y + 31x + 4y =

f 18xyz – 14xyz =

g 20a – 9a + 6b + 10b + b =

h 9a + 8b + 5a – 5b – 2b =

Question 4 Simplify the following. a 10m – 2m – m =

b 8p – 5p + 3p =

c 9y2 + 7y2 – 8y2 =

d 12x – 7x – 3x =

e 9a – 7b + 3a – a =

f y + 5y – 2y =

g 10x + 5x + 2x =

h 11d – d – 5d – 3d =

Question 5 Simplify the following. a 9x – x – 4x =

b a2 – 7a – a + 15 =

c 7y – 3x – y =

d p3 + 3p2 – p2 – 10 =

e 15a + 2b – b – 7a =

f 5x + 10y + 9x – 2y =

g ab + 4b + 3ab =

h 2xy + 4x – xy + 2x =

Question 6 Collect like terms and simplify. a xy + yz – xy – yz + xy =

b 15m2n – 6mn2 + 7mn2 + 3m2n =

c 5a2 + 15a2 – 4a2 =

d 18xyz + 8x + 5xyz – 4x =

e 20xyz + 12xyz – 5xyz =

f 25x2 + 17y2 – 19x2 =

g 9x2y2 + 8x + 2x2y2 + 9x =

h 9a3 + 7a3 – 4b3 + 8b3 =



Basic algebra


UNIT 4: Algebraic abbreviations Question 1

a Write 8 × y in a shorter way. b Write 2 × 4 × a in a shorter way. c Write 5 × m × m × m in another way. d Write 7ab, showing multiplication signs. e What is the difference between 24y and 2 × 4 × y?

Question 2 Write the following expressions without multiplication or division signs. a 3 × 5 × a =

b 5 × n × 7 =

c a + 7 × b =

d 4 × (x + 16) =

e 3x ÷ 5 =

f a × b × c =

g 7 × a × 6 =

i

j 2 × m + 5 =

k 9+4×x=

l 3 × a + 4 × b =

m 23 ÷ x =

n 6a ÷ 11 =

o m ÷ 10 =

p (m + n) ÷ 5 =

r (8x + 3) ÷ 2a =

h 8a × b × b =

q 5x ÷ (3a + 2) =

4×m×5×n=

Question 3 Write the following expressions by showing all multiplication or division signs. a 9a =

b 3y =

c 12a =

d 4x – 5 =

e 8m + 3 =

f 60 – 3x =

g ab + 3 =

h 2x – 3y =

i

j 14xyz =

k 7m2 + 4 =

a3b2 =

l x2 – y2 =

Question 4 Write the following in a shortened form. a 6 × a × a × a × b =

b 12 × a × a × b × b =

c 5 × (x + 9) =

d 5 × (m – 5) =

e 7 × a × (c + 2) =

f 4 × 7 × (x – 2) =

g m × n × (p + 3) =

h 6 × (5 × a + 9) =

i

j 8 × (6 × a – 2 × b) =

k 3a + 4 × a + 5 =

l 4a + 5 × 2a – 5 =

m n × n × 7 × n =

n 6 × a × a × a × 3 =

o x × x × x × y × y =

p 3 × m – 6 + 5 × m – 3 =

q a + 3 × 5a + 7 =

r a – 3 + 4a – 7 =

8 + (4 × 5 + 4 × m) =

57



Basic algebra


UNIT 5: Substitution (1) Question 1 If a = 3, find the value of each expression. a 7a =

b 9a + 1 =

c 9a – 1 =

d a2 =

e 5a2 =

f a(a + 1) =

g a3 =

h a2 – 2a =

i (2a + 7) × 3a =

j 7a – 12 =

k 180 – 6a =

l (a – 2) ÷ 15 =

Question 2 If a = 1, b = 3, c = 5 and d = 10, find the value of each of the following expressions. a a + b =

b a+b+c+d=

c abc – d 2 =

d abc =

e 2a + 3b + 4c =

f 3b + 5c – d =

g 16bc =

h 8c – d =

i 8d ÷ b =

j 5a – a2 =

k (c + d) – a2 =

l b 2 + d 2 – abc =

Question 3 Complete each table of values. a b = 3a + 2 0

a b

b y = 4x – 2

1

2

3

4

0

1

1

2

3

4

e p = 2q + 3

d y = 6x – 1 x y

x y

c m = 5l – 2

2

3

4

5

6

q p

1

0

l m

1

2

3

3

4

4

f v = 9u – 7 2

3

4

u v

0

1

2

5

6

Question 4 Complete the following table. x

y

a

5

1

b

8

3

c

6

2

d

7

5

e

9

4

f

4

2

g

10

3

h

7

4

i

8

1

x+y


x–y

xy

x2

y2

4x + 5y


Basic algebra


UNIT 6: Substitution (2) Question 1 If a = 2, b = 3, c = 4 and d = 5, evaluate the following. a abc b a + b + c – d

e bc ÷ a

f abcd

i

3ab + 2cd

j 3a2c – d

c ab + bc

g b2 + c2 – ad

k 5c2 – 12

e 6x – x

f 2x (x – 3)

2

i

x

3

j (2x) 2

m (x – 3)

n (x + 2) (x – 2)

3

l

a3 + b3

Question 2 If x = 5, find the value of the following expressions. b 65 – 4x

h b2 + 10

a 3x + 2

d a2 + b2 + c2

c 4(x + 3)

d (2x – 7)2

g (x + 2) 2

h (x – 3)2

k

21 – x l 2x2

o x – 7

2

Question 3 I f x = 6.5, y = 2.4 and z = 5.8, find correct to one decimal place the value of the following expressions. a x + y

b x + y + z

e xyz

f x

i

yz

2

j (x – z) + 3

m (x + y)

n

2

x+y+z

c x + y – z

g x + z 2

2

k x ÷ y

l

(x + y) ÷ z

o

h y3

d xy

3

x+y+z

59



Basic algebra


UNIT 7: Addition and subtraction of like terms (1)

Pages 43–64

Question 1 Simplify the following expressions by collecting like terms. a 2x + 3x =

b 5x – 2x =

c 5a + 4a =

d 9y – 6y =

e 3y + 7y =

f 4q – 3q =

g 8m + 6m =

h 9a – a =

i

j 8t – 2t =

k 7n + 5n =

l

m 8p – 5p =

n 8xy + 7xy =

o 7p – 3p =

p 18x2 – 12x2 =

a 5p + 6p – 3p =

b 8m – 3m – 2m + 7m =

c 8x – 5x + 7x =

d 4xy + 6xy – 3xy – 2xy =

e 12y – 4y + 5y =

f 8k + 4k + 2k – 5k =

g 8xy + 2xy + 5xy =

h 9a + 2a + 3a – 7a =

i

6m – 3m + 10m =

j 11p + 5p – 7p =

k 5a + 7a + 3a + 6a =

l

m 8x2 + 7x2 – 6x2 – 3x2 =

n 6a2 + 7a2 + 8a2 – 10a2 =

o 4x – 2x + 9x – 6x =

p 11y – 6y – 3y – y =

2b + 15b =

5mn + 3mn =


6ab – 3ab – ab + 2ab =

Question 3 Simplify by collecting like terms. a 4x + 3x + 2y + 7y =

b 11a + 7b – 3a =

c 3m + 7m + 8n + 9m =

d 9c – 6c – 2c + 3d =

e 8a + 7a – 2m – 3m =

f 9x2 – x2 – 3x2 =

g 3x + 2y + 5x =

h 12mn – 6mn + 3mn =

i

j 5x + 7y – 4y – 2x =

k 8m + 2n + 9n + 2n =

l

m 7y + 6y – 3x + 7x =

n 6a + 9 – 3a =

o 12 – 3x – 2x =

p 9m + 7mn – 6m – 2mn =

q 10m + 5n + 3n + 4m =

r 5x + 3y – 2x – 2y =

8y + 7x – 3x – 2x =


5t + 17 – 2t – 8 =


Basic algebra


UNIT 8: Addition and subtraction of like terms (2)

Pages 43–64

Question 1 Simplify the following expressions by collecting like terms. a 3a – 7a =

b –2x + 3x =

c 6y – 9y =

d –2p – 3p =

e 8a + –3a =

f 9x – –2x =

g –2m2 + 5m2 =

h –8n – n =

i

j –6p – 2p =

k –y + y =

l

m 6a – 8a =

n –5t – t =

o x – 5x =

p 2k – 14k =

3x – 11x =

–10x + 4x =

Question 2 Simplify the following by collecting like terms. a 5n + –2n =

b –y – y – y =

c –4a – –6a =

d –k + 2k – 3k =

e 8y – –3y =

f –3p + 6p + 3p =

g 5x – 7x =

h –8n + 15 – 2n =

i

–6m – –10m =

j 3a – 2a2 + 7a2 =

k –x – 2x – 3x =

l

m 9 – 7t + 12 =

n –3k2 – 2k2 + 9k =

o x – 5x + 3y =

p 8xy – 25 – 10xy =

–3y + 4x – 7y =

Question 3 Simplify by collecting like terms. a 2x + 3x – y – 5y =

b 3n + 2p – 7n =

c 8a + 9b – 3a + 2b =

d 6n – 3p – 10n + p =

e 2a – 3b – 2a – 3b =

f a – b – a + a =

g –7x + 15 + 7x =

h 8m2 – 7m + 3a2 + m =

i

j 6a – 3b – 9a – b =

k 7k + 5 – 4k + 12 =

l

m 4m – 7 + 6m – 8 =

n 4a – 5b – 3a =

o a – 8t + 2a – t =

p 6ab – 3b + ab – 9ab =

q y – 5y + 7 – 18 =

r –6y2 – 3y – y + 2y2 =

9y – 3 – 2y – 2 =

7xy + 9x – 2x + xy =

61



Basic algebra


UNIT 9: Multiplication of pronumerals Question 1 Find the products of the following. a 7 × 3a =

b 4a × 9b =

c 4m × 5n =

d ab × a =

e –2x × 5 =

f –8m × –2m =

g 4a × –3a =

h –9m × –3 =

i

8 × 3b × b =

j –5x × –x =

k –2a × –3b =

l

m 4mn × 3m × 2n =

n –2p × 5 × –5p =

o 6ab × 5 =

p –6m × –5mn =

Question 2 Work out the following products.

3a × 4am =

a 3 × 2 × 5a × b =

b 7a × 2a =

c 8b × –3b =

d –6a × 3 =

e 2m × 3mn =

f 8x × –5 =

g ab × bc =

h –9t × 5t =

i

j –3k × –2k =

k xy × yz =

l

m 2mn × np × 3n =

n –a × 5b =

o 4ab × –3bc =

p –2a × –2b =

q –7a × 2ab × c =

r –6y × –7y =

a –2x × 4 × –5x =

b –2x × –5 × –8y =

c 3a × 5 × –4y =

d 6m × –5m =

e –6 × –4a =

f 4n × –15m =

g –9x × –2y =

h –3n × –2n × –5n =

i

–8p × 5p =

j xy × 3xy × –5xy =

k 5 × –2x × 3y =

l

m –a × 7ab =

n –4a × –5b =

o –m × –2m × –3n =

p –2m × 10 × –5m =

q –5a × –a =

r –2ab × –5bc × –3cd =

7mn × 8np =



Pages 43–64

–6 × –5x =

–x × –y × –z =


Basic algebra


UNIT 10: Division of pronumerals Question 1 Simplify the following. 10 x = 2x 27 mn c = 9m

a

30 ab = 5a

b

d 36xy ÷ 9xy =

e 15abc ÷ 5ab =

f 12m2 ÷ 4m =

g 9y ÷ y =

h abc ÷ ac =

i

j mk ÷ k =

k 32xy ÷ 8y =

l

m 9y2 ÷ 9y =

n 60abc ÷ 10ac =

o 25m2 ÷ 5m =

p 72x2 ÷ 12x =

28a ÷ 7a =

Question 2 Work out the following divisions. 12 a = 4 2 10 a b c = 5a2

a

8n2 ÷ 4n =

16 m = 2m

b

d 25m ÷ 5m =

e 12a ÷ –6 =

f –10pq ÷ 5p =

g –32a ÷ –8a =

h –48xy ÷ –16x =

i

j –9xy ÷ xy =

k 5x ÷ –5 =

l

m 18xy ÷ xy =

n –18a ÷ 6a =

o abc ÷ ab =

p 9ab ÷ 3a =

q 5m ÷ 4m =

r –36mn ÷ –9m =

b

d

e –20t ÷ –t =

f –30ab ÷ –10a =

g –50ab ÷ –5b =

h a2bc ÷ abc =

i

x2y ÷ xy =

j m2n ÷ mn2 =

k 27ab2 ÷ 9a2b =

l

m 48x2 ÷ –8x =

n 49ab ÷ –7a =

o –16pqr ÷ 8pr =

p –42a2 ÷ 6a =

q –9y2 ÷ –9y =

r –27mn ÷ –9m =

50ab ÷ 25ab =

Question 3 Simplify the following. a c

−18 a = 6 − xyz = − xy

60m ÷ –10m =

90 abc = −10 a −33y = −11y

–24a2 ÷ 8a =

63



Basic algebra


UNIT 11: A lgebraic expressions and the order of operations Question 1 Simplify the following. a 2x × 5x × 4 =

b 6a × 12ab ÷ a2b =

c 7mn × 5m ÷ n =

d 3a × 2a × 5b =

e –4a × 8a × –3 =

f 20xyz ÷ 5xy ÷ z =

g 12x × 7 ÷ 4x =

h 20 × 3m ÷ 5 =

i

j 15a ÷ 3a × 5 =

a (9x)2 ÷ 3x × 2 =

b –5 × –3x × 8 =

c 81ab ÷ 9a ÷ 3b =

d 21ab ÷ –21ab =

e (4ab)2 ÷ 16a2b =

f 9m × –5 × –2m =

g –5a × 3b × –4ab =

h 28xy ÷ 7x ÷ 4y =

12 × 8mn ÷ 4n =

Question 2 Find answers to the following.

Question 3 Simplify the following. a (18y ÷ 6) – 2y

b 8x + (6 × 3x)

c (5 × 8p) – (35p ÷ 7)

d (–5x × 8) – 4x – 3x e 85t – (8 × 4t) – 2t

f (16a ÷ 2) – (42a ÷ 7)

g 9a ÷ (8a – 5a) h 5x + 8 × 3x – 4x

i


64 a ÷ 16 = 18 a 2 ÷ 9 a

26 x + 16 x = 2x × 3

8y × 6y 8n × 5n d = e = 12 y 2 ÷ 2 y ( 2 n )2

a


b

c

20a – (15a ÷ 3) – 7a

35 x 2 ÷ 7 x = 2 x + 3x

8 a − 24 a f = 3a + 5 a


Basic algebra


UNIT 12: A pplying the distributive law to expand algebraic expressions Question 1 Expand the following expressions.

a 5(a + 3) =

b 6(x – 7) =

c –2(6 + a) =

d –5(x + 7) =

e 9(2a + 5) =

f 3(5x – 9) =

g 2a(6 + 3a) =

h x(2x – 5) =

i m(6m + 3) =

j 5x(x – 3) =

k 7n(2n – 3) =

l –3a(a – 2) =

m –2(a + 5) =

n –7(3p – 4) =

o 5a(a – 1) =

p –3x(2x – 2) =

q –(x + 9) =

r –(4y – 7) =

Question 2 Expand and simplify by collecting like terms. a 3(x + 5) + 6x = b 6(a – 5) – 5a =

c 4(m – 3) + 2m =

d 2(x – 3) + 3x + 7 =

e 6y(y + 4) – 2y2 =

f 6(m – 2) – 3m =

g 5x + 3(10 – x) =

h 9x + 3(x – 2) =

i 6m – 2(m + 1) =

Question 3 Expand and simplify. a 3(x + 2) + 4(x – 2) =

b 8(m – 3) + 3(m – 2) =

c 5(p – 7) + 3(p + 2) =

d 8(x + 3) + 2(x – 1) =

e 4(x + 3) – 2(x + 1) =

f x(x + 1) – (x – 3) =

g 5(p – 6) – 2(p – 1) =

h p(5p + 6) – 3(2p – 3) =

i 2m + 3(m – 3) + 7 =

65



Basic algebra


UNIT 13: Common factors

Question 1 Factorise the following by taking out the highest common factor. a 5a + 5 =

b 8x – 8 =

c 3y – 3 =

d 2x + 2 =

e 6m + 6 =

f 7m + 7 =

g 3p + 6 =

h 4q + 8 =

i

6x – 9y =

j 4x – 16 =

k 9b – 18 =

l

5a + 20 =

m 2a + 6 =

n 3m + 12 =

o 6n – 24 =

p 8x – 32 =

q 3a + 15 =

r 2a + 14 =

Question 2 Factorise by taking the common factor out. b 5m + 5n = a 3a + 3b =

c 6p – 6q =

d 7a + 14b =

e 3l – 9m =

f m2 + 7m =

g y2 + 6y =

h 9x – 18y =

i 3a – 24b =

j 4x + 4y =

k mp – 3p =

l 8x – 32y =

m 6x – 36 =

n 3m + 12m2 =

o 5y – y2 =

p 9x – 6 =

q 8m – 8n =

r 6x – 3x2 =

s 2x2 – 4x =

t 6pq – 12p2 =

u 10x – 10y =

Question 3 Factorise the following. b –5x + 10 = a –3x + 6 =

c –4x + 8 =

d –6x + 18 =

e –2x + x2 =

f –6a + 24 =

g –3a + 12 =

h –4a + 16 =

i –6a – 12 =

j –4y – 8 =

k –2x – 10 =

l –8y – 4x =

m –3p – 9q =

n –5x – 25 =

o –x – 5 =

Question 4 Factorise. a 7a + 7b =

b 4a – 20 =

c 9x – 9y =

d 3m + 15 =

e 6 – 6t =

f m2 – 4m =

g 5ab – a2 =

h 7m – 14n =

i 8ab – 6a2b =

j –4 – 12a =

k –3 – 15p =

l –3m – 6n =

m 9m – 36 =

n –4a – 20a2 =

o –x – 7 =



Basic algebra


UNIT 14: Problem solving and algebra 1 Write the sum of 2x and 3y.

2 Write the product of m and n.

3 Write the average of 2x, y and 3z.

4 Find the expression 3 more than 2x.

5 If the first number is x, write the next

6 Find the area of a square with side length x metres.

consecutive integer.

7 Increase 5x by 2.

8 Find the perimeter of a square with side length a cm.

9 Find the volume of a cube with side length y cm. 10 Find the number x less than 3x + 4y.

11 Write the perimeter of a rectangle of length

12 Your pocket money is $x per week. How much do

15 cm and width x cm.

you earn in 7 weeks?

13 Write the perimeter of the following shapes.

a b c 3x

x

x

5x

2x

2x + 3

2x + 5

x

8x

14 Find the area of the following shapes.

a b c x 2x

x 8x + 4

2x – 3

15 If I bought p pens and 3q pencils and my sister

16 Three different types of sweets cost 5y, 3y and 2y

bought 5p pens and 2q pencils, how many pens and pencils do we have altogether?

cents each. If I buy 4 of each type, what would be the total cost?

67



Basic algebra TOPIC TEST

PART A





1 8x – 3x – x equals:

A 4x

2 a3 + a3 equals:

A a 6

3 5xy2 equals:

A 3 × x × y × 2

4 –4x + 5x equals:

A x

5 2(x – 7) + x equals:

A 3x – 7

6 –7a × 4 equals:

A 28a

7 –9x × –4y equals:

A –36y

B 6x

C 8x – 3

D 5

B a

C 2a

D 2a

6

1

B 5 × xy × xy

C 5xy × 5xy

D 5 × x × y × y

1

B 9x

C –45x

D –20x

1

B 3x – 14

C x – 7

D x – 14

1

B 74a

C –74a

D –28a

1

B –94xy

C 36xy

D 94xy

1

B a + bc

C ac

D a + c

1

B 3b

C –3a b

D 3a b

1

B x – 5x

C –4x

D –5x

1

B 6n

C 600n

D 150n

1

C 1200

D 3600

1

9

3

2

8 b is a factor of ab + bc. What is the other factor?

A a

9 –30ab ÷ 10a equals:

A –3b

10 x(x – 5) equals:

A x – 5 2

11 30 × 2n ÷ 10 equals:

A 60n

2

12 If a = 4 and b = 5 then 3ab2 equals:

A 120

B 300

2

1

2

2

2



12


Basic algebra TOPIC TEST

PART B





1 Simplify – 5a + 6a + 3a

1

2 Simplify (3ab)2

1

3 Simplify ab × 32b2

1 2

1

4 Simplify 5ab + 3a × 2b

1

5 Expand and simplify 5a + 3(2 – a)

1

6 Simplify –9x × –2x

1

7 Expand and simplify x(2x – 1) – 2(x2 – x)

1

8 Factorise 2p2q + 4pq2

1

9 Expand and simplify 3(x + 5) + 4(x + 3) – 6(3x – 2)

1

10 Expand and simplify y – 2 + 7(2y + 5)

1

11 Simplify 5a – 7b – 8b + b

1

12 If x = 5 and y = –7, what is the value of 2x – y?

1

13 Simplify 64ab ÷ 8b

1

14 Expand and simplify 4(x + 5) – 2(3x – 1)

1

15 Factorise –7x – 21

1


69


15


Chapter 7

Length, mass and time


UNIT 1: Symbols and prefixes

Question 1 Complete the following table by writing the symbol for the name of the unit.

a

Quantity

Name of unit

Length

metre

m

b

millimetre

c

centimetre

d

kilometre

e

Mass

gram

f

milligram

g

kilogram

h

tonne

i

Time

second

j

minute

k

hour

l

day

Question 2 Complete the following table by writing the symbol of the prefix. Prefix

Symbol

Symbol

Meaning

Question 3 State the most appropriate unit (kilometres, metres or centimetres) for the following. a Length of a basketball court

a

mega

b

kilo

c

hecto

100

d

deca

10

c Distance between Sydney and Brisbane

e

deci

1 10

d Length of a pen

f

centi

1 100

g

milli

1 1000

h

micro


1 000 000 1 000

b Height of a door

_

1 1000 000




UNIT 2: Units of measurement Question 1 Complete the following. a 1 cm =

mm

b 1 m =

cm

c 1 m =

mm

d 1 km =

m

e 1 g =

mg

f 1 kg =

g 1 t =

kg

h 1 min =

s

i

min

j 1 day =

h

1h=

g

Question 2 Complete the following. a 1 normal year =

days

b 1 leap year =

c 1 year =

months

d 1 year =

e 1 year =

weeks

f 1 fortnight =

g 1 decade = i

1 millennium =

j 1 year =

years

k noon = 12 o’clock in the

m am = from midnight to

fortnights

h 1 century =

years

days weeks years seasons

l midnight = 12 o’clock in the n pm = from midday to

Question 3 Complete the table for the number of days in each month. (Assume it is not a leap year.) Month

Days

Month

a January

g July

b February

h August

c March

i

September

d April

j

October

e May

k November

f

l

June

December

71

Chapter 7: Length, mass and time © Pascal Press ISBN 978 1 74020 033 2

Days




UNIT 3: Conversion of units of length Question 1 Convert the following to centimetres (cm). a 1 m =

b 4 m =

c 2 m =

d 4.1 m =

e 3 m =

f 6 m =

g 3.5 m =

h 8 m =

i

5 m =

j 7 m =

k 2.25 m =

l

m 10 mm =

n 80 mm =

o 700 mm =

p 167 mm =

Question 2 Convert the following to metres (m).

5.34 m =

a 200 cm =

b 1200 cm =

c 90 cm =

d 60 cm =

e 500 cm =

f 2500 cm =

g 150 cm =

h 20 cm =

i

j 4000 cm =

k 560 cm =

l

n 15 km =

o 4.75 km =

p 20.07 km =

8000 cm =

m 1 km =

Question 3 Convert each of the following lengths to millimetres (mm).

1570 cm =

a 1 m =

b 3.5 m =

c 2.25 m =

d 10 m =

e 6 m =

f 12 m =

g 6.5 m =

h 7.9 m =

i

j 5 m =

k 9.52 m =

l

n 80 cm =

o 25.5 cm =

p 50.1 cm =

m

d 640 mm =

8 m =

m 20 cm =

Question 4 Convert the following measurements to the units shown. a 5 m =

cm

b 4000 mm =

m

c 4.5 km =

e 7 m =

mm

f 463 mm =

cm

g 6.35 cm =

i

cm

j 800 cm =

mm

9m=

m 6 km =

m

n 5.3 m =

cm

e 0.006 km = i

0.009 m =

m 0.02 m =

h 2.3 km =

k 60 cm =

mm

l

o 8560 mm =

m

p 2.31 m =

Question 5 Complete the following conversions. a 0.8 m =

mm

5.5 m =

18 m =

b 4 km =

cm

c 0.3 m =

mm

d 3.7 m =

f 0.04 m =

cm

g 0.002 m =

mm

h 12.69 m =

mm

j 0.007 m =

cm

k 85 m =

mm

n 9 mm =

km

o 0.05 km =

cm m


cm m

l

58 cm =

p 365 mm =

cm m cm cm

cm mm mm cm




UNIT 4: Pythagoras’ theorem (1) Question 1 If c > 0, find c when: a c2 = 16

b c2 = 225

c c2 = 81

d c2 = 16 + 9

e c2 = 25 + 144

f c2 = 225 + 64

Question 2 Find the length of the hypotenuse in these right-angled triangles. a 7 cm

40 m

b c 9m

24 cm

77 mm

36 mm

Question 3 Find the length of the missing side correct to 1 decimal place. a 5 cm

b c 19 mm

22 mm

7.5 cm 6.8 cm

8 cm

Question 4 Use Pythagoras’ theorem to test if the following triangles are right-angled. a 8 7

8 15

4.1

b c 10

6

0.9

73


4




UNIT 5: Pythagoras’ theorem (2) Question 1 If a > 0, find a when: a 25 = a2 + 16

b 289 = a2 + 225

c 625 = 576 + a2

Question 2 Find the length of the unknown side in these right-angled triangles. 3 mm

a x

a

b c 12 m

5 mm

y

17 cm 8 cm

13 m

Question 3 Find the value of x correct to 1 decimal place. 16 cm a 6 cm

b c x

x

10 m

5 mm

x

2 mm

Question 4 A tree 6 m tall casts a shadow 1.1 m long. What is the distance from the tip of the shadow to the top of the tree?

d

Question 5 A right-angled triangle is drawn inside a circle, using the diameter as the hypotenuse. If the diameter of the circle is 15 cm long and the shortest side of the triangle is 9 cm, what is the perimeter of the triangle?





UNIT 6: Perimeter of plane shapes Question 1 Find the perimeter of each of the following triangles.

a b c

d

7cm cm 7 cm 8 cm 7 cm8 cm 8 cm 7 cm cm 7 cm 787cm 8 cm 13 cm 8cm cm8 cm 1213 cm 7 cm7 cm 777cm 7 cm 13 cm cm 8 cm8 cm 813 12 cm cm cm 8 cm 8 cm8 7cm cm 77cm 13cm cm 13 12 13 cm 8 cm 8 cm 12cm cm 1212cm 12 cm 13 cm cm 12 cm cm 7 cm 7 cm 7 cm 7 7cm 8 cm 8 cm cm 7 cm 8 cm 7 cm 7 cm 8 cm 8 13 cm 13 cm 8 cm 7 cm 7 cm 8 cm 8 cm8 cm 13 cm 12 cm1213cm 12 cm 7 cm 8 cm 8 cm 13cm cm 12 cm 7 cm 7 cm 7 cm 8 cm cm 8 cm 13 cm 1312 8 cm cmcm 1212 cm 7 cm 7 7cm 7 cm 7 cm 8 cm 8 cm 8 cm 8 cm 6 cm 5 cm 5 cm 6 cm 13 13 cm cm 7 cm 6 cm 5 cm 6 cm 5 cm 8 12 cm13 5cm 8 cm 6 cm 5 cm5 cm 512cm 7 cm 6 cm6 cm 6 cm 7 cm cmcm 12 cm cm 7 7cm 7 cm7 cm 77cm cm 6 cm 5 cm 6 cm 5 cm 6 cm 5 cm 6 cm 5 cm 7 cm 7 cm 7 cm 6 cm 5 cm 76cm cm 5 cm 7 cm 6 cm 5 cm 7 cm 7 cm 6 cm 5 cm 53cm 6 cm 53 cm cm cm 3 cm 7 cm 7 cm cm cm 3 3cm 36cm 7 cm cm 7 cm 7 cm 3cm cm 737cm 7 cm 7 cm cm 7 cm 7 7 cm 7 cm 9 cm 9 cm 7 cm 7 cm 9 cm 9 cm 11 cm 11 cm 3 cm cm 7 cm 11 cm 3 cm7 cm 3 cm3 cm 9 cm9 cm 6 9cmcm 9 cm611 7 cm 3 cm7 cm 116 cm 11e cm f cm cm 6 cm 11 cm 11 cm 3 cm 7 cm 7 cm cm6 cm 6 cm 6 cm 7 cm 7 cm cm 7 cm 3 cm7 cm 7 cm7 cm 9 6cm 9 cm 11 cm11 cm 7 cm7 11 11 cm 9 cm cm 711cm 7.5 cm 7.5 cmcm 73 cm cm 96cm cm 3 7.5 cm 77.5 cmcm 7.5 cm cm 6 cm1169 cm cm 7 cm 9 cm 7.5 cm 3 cm 6 cm 6 cm 6 cm 7.5 cm 9 cm 7.5 cm 7 cm 6 cm 6 cm 7 cm 7 cm 6 cm 67 cm 6 11 cm6cm 4 cm cm 7 cm cm 4 cm49 cm 6cm cm 4 cm11 cm cm 9cm cm4 4cm cm 446cm 7.5 cm cmcm 11 cm 11 cm6 cm 77.5 7.5 cm 7.5 cm 9cm 7.5 cm 6 cm 6 cm 6 cm 6 cm 7.5 cm 6 cm 7.5 cm 4 cm 4 cm 4 cm 66cm 6 cm6 cm 4 cm cm 4 cm 4 cm 6 cm 7.5 cm 7.5 cm 7.5 cm 4 cm 6 cm 6 cm 6 cm 4 cm 4 cm 4 cm

Question 2 Find the perimeter of the following squares and rectangles. 12 m

12 m

12 m

12 m

30 cm 30 cm 30 cm 12 c m12 m 12 m 12 m 30 30 cmcm a 30 cm 30 cm 30 cm b

d

12 m 12 m 12 m 12 m 30 cm30 cm 30 cm 12 m 30 cm 9m 12 9 6m9cm cm 77mm 7 m 6cm cm 712 m7mm 30 cm 3030 m 9 m 99mm 9 9mm cm 6 6cm 6 cm6 cm 66cm cm 7m 7 m 12 m 12 12 m 30 cm 30 cm 30 cm 9m 9m 9m 6 cm 6 cm 7m 7m 6 cm 7m 9 m 9 m 6 cm 6 cm 7 m 9m 6 cm 7m 9m 6 cm 7m 9m 9m 6 cm 6 cm 7m 6 cm 7m 9m 7m

7m 7m

20 m 20 m 20 m 20 20 m m 20 m 20 m 20 m 20 m 20 m 20 m 20 m 20 m 2012 m m 820 m 8 m 8m8m 12 m m 12 12 m m 8 m 12 m m 8 m 8 m 88mm 8 8mm 8m 12 m 20 m 8 m20 8 m 208 m 12 m 12 m e f 8 m 12 m 12 m 8m 8m 8m 8m 12 m 88m 8m 8m 12 m12 m 8m m 12 m 8m 8m 12 m 8m 8m 8m 12 m 12 m 12 m 8m 8 m 8m 8m

8m 8m

33cm 3 cm 6 cm 6 cm cm 3 3cm cm 6 6cm 6 cm6 cm 66cm cm cm 9 cm9 cm 9 cm 9 cm 3 cm 3 cm 6 cm 6 cm 3 cm66 cm cm b ccm 64cm 3 cm3 cm 6 cm 6 cm 4 cm 46 cm 9 cm 9 cm 9 cm 6 cm 3 cm 66cm cm 4 cm 9 cm cm 6 cm6 cm 3 cm 6 cm 9 cm 4 cm4 cm 4 cm 4 cm 6 cm 7 cm 7 cm 7 cm 7 cm 9 cm 5 cm 5 cm 5 cm 7 cm 7 cm 3 cm 3 cm 59 cm5 cm 5 cm 5 5cm 6 cm 6 cm 736cm 7 cm 6 cm cm cm cm 6 cm 6 cm 4 cm 6 cm4 cm 4 cm 9 cm 9 cm 9 cm 6 cm 4 cm 7 cm 7 cm 6 cm 7 6cm 7 cm 4 cm 5 cm 5 cm 5 cm 4 cm cm cm 7 cm 5 cm 5 cm 4 cm 10 cm 7 cm 10 10 10 cm 10 cm 5 cm 7 cm 10 cm cm 6 cm 6 cm 5 cm 10 cm 4 cm 4 cm 10 cm 6 cm 4 cm 7 cm 7 cm 7 cm 5 cm 5 cm 5 cm 10 cm10 cm 10 cm 10 cm 10 cm 10 cm 10 cm 10 10 cm 10 cm 7m 7m m cm7 7mm 7 m 7 m 77m 6 m 6 m 6 m6 m 6m 7m 7m 7 m 6m 7m 7m 6m 6m 7m 55mm 5 m 5m 5 m5 m 7m 6m 6m 6m 6m 5m 5m 7m 7m 6m 6m e f 7m 6m 5m 5m 5m 5 m 5 m 6m 6m 5 m 5m 6m 5m 5m 5m

3 cm Question 3 perimeter of the following. 3 cm3 cm 9 cm 9 cm 9 cm Find the 9 cm

a

d

75





UNIT 7: Perimeter of irregular shapes 9

9

10

10

14

Question 1 Find the perimeter of the following. (All10measurements are in centimetres.) 9 2

14

14 2 3 3 14 101010 141414 9 9 99 39 10 103 14 4 2 14 2 10 9 4 2 3 a b c 3 33 1010 3 2 2 22 214 4 10 3 23 3 3 3 3 33 3 42 3 33 339 3 2 12 2 33 3 4 4 4442 42 2 12 3 10 3 3 3 6 6 2 2 2 2 4 4 6 3 3 36 3 3 3 3 2 10 12 101010 10 8 4 48 4 73 272 22 2 10 33 3 6 33 3 6 4 12 12 2 4 4 12 2 1212 4 8 12 7 6 6366 6 6 6 66 6 3 10 8 2 6 8 8 12 4 7 7 77 7 8 8 3 6 8 8 8 6 7 6 36 6 8 3 8 7 6 8 8 88 8 3 3 33 3 6 6 66 6 8 3 6 12 15 12 8 3 15 6 12 4 15 4 4 3 4 3 12 121212 151515 12 3 15 15 4 6 3 12 4 3 15 9 9 6 9 d 9 4 4 e f 4 3 3 4 3 4 4 312 15 9 6 44 4 444 4 9 63 333 3 3 4 4 6 6 6 5 4 9 9 99 9 5 33 3 9 9 99 9 44 6 66 4 3 4 6 9 9 3 363 4 44 4 3 6 5 4 4 442 4 6 63 2 4 4 3 6 4 9 6 6 4 2 2 5 4 4 5 5 5 5 6 44 4 5 12 3 3 333 3 2 2 4 4 54454554444 4 12 4 6 33 3 3 5 5 4 4 4 2 2 224 2 4 2 2 22 2 33 5 12 3 5 5 5 5 3 2 2 5 4 55 455 121212 12 12 55 5 4 12 3 2 24 5 5 4 4 12 44 4 4

3 3

9

3

Question 2 Find 28 the missing lengths of the following shapes and then find the perimeter of each. 8 8 28 (All measurements are in centimetres.) 8 28 12 a 12 12

12 121212 12 12 12

16

282828 28 28 28

28

4

20

4 20 4 c 4 4 44 4 4 4 16 16 16 161616 16 16 16

4

12

4

12

4

20

20 202020 20 20 20

b

4 4 4 44 4 4

12

d

4

12 121212 12 12 Question 3 12 4 12

4 4 4 44 4

4 4

12

6

6

12 8

8 8 88 8

8

8

8

8 8 8 88 8 8 8 88 8 8 88 8 24 8 24 24 242424 24 24 24 24 12 12 12 6 121212 12 12 12 6 6 6 6612 6 6 6 6 6 6 6 6 6 6 66 6 6 6 6 6 6 66 6 6 6 6 6 6 66 6 6 6 6 12 121212 12 12 12

8

8

a If the perimeter of a square is 72 metres, b A room is measured 8.64 metres long and 5.36 metres find the length of each side. wide. Find the difference between the length and width in metres.

76

Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook

© Pascal Press ISBN 978 1 74020 033 2




UNIT 8: Conversion of units of mass Question 1 Convert the following to kilograms. a 3 t =

b 3.5 t =

c 9.35 t =

d 8 t =

e 8.32 t =

f 4.9 t =

g 12 t =

h 1.25 t =

i

5.1 t =

j 4 t =

k 7.5 t =

l

8.392 t =

m 5000 g =

n 500 g =

o 3600 g =

p 8000 g =

q 750 g =

r 5675 g =

Question 2 Change the following to grams. a 5 kg =

b 1 t =

c 8000 mg =

d 7 kg =

e 12 kg =

f 6.357 kg =

g 3.25 kg =

h 15.35 kg =

i

2 t =

j 9 mg =

k 3.875 kg =

l

2.508 kg =

m 8 kg =

n 50 mg =

o 6.07 kg =

p 300 mg =

q 6.5 kg =

r 9.008 kg =

Question 3 Convert the following to the units shown. a 7000 g =

kg

d 15 000 kg =

t

b 38.3 t =

kg

e 3500 g =

kg

c 6.5 g =

mg

f 25 000 mg =

g

g 890 g =

kg

h 635 g =

kg

i

8.9 t =

j 2000 g =

kg

k 9000 kg

t

l

8605 kg =

m 1.75 g =

mg

n 2.25 t =

kg

o 3.205 t =

kg

p 450 g =

kg

q 4368 mg =

r 8900 kg =

t

Question 4 Complete the following. a 1 000 000 mg =

kg

b 11 000 kg =

g

t

d 2.1 g =

mg

e 1000 g =

t

g 600 g =

kg

h 9500 kg =

t

t

c 5.1 t =

kg

f 3 t =

g

i

mg

9 t =

77


kg




UNIT 9: Applications of mass Question 1

a A ship has a mass of 36 500 000 kg. What b A packet of sugar weighs 800 g. How many is this in tonnes? of these packets would weigh 1 tonne?

c There are five members in a family and the d A truck and its load have a mass of 33 t 600 kg. average mass is 42.5 kg. What is the total mass? The mass of the truck is one-third of this. What is the mass of the load?

e Find the mass of the container of a product if f Find the net mass (mass of contents) if the gross its gross mass is 4.5 kg and net mass is 2540 g. mass of a package is 980 g and the container’s mass is 160 g.

Question 2

a Arrange the following masses in ascending b A truck weighing 2.5 t is carrying a load of order (from smallest to largest). 1635 kg. What is the total weight of the truck 380 g, 23.5 t, 18.8 kg, 3600 g, 1.9 kg, 4.2 t and the load? Give your answer in tonnes.

c Clare buys 3.5 kg of flour and she uses 360 g d Penny’s cat weighed 2.5 kg in March and by for baking. How many grams of flour are left? August had put on 300 g. What was the cat’s weight in kilograms in August?





UNIT 10: Conversion of units of time Question 1 Complete the following table. a 1 minute (min) =

b 1 hour (h) =

seconds (s)

c 1 day =

d 1 week =

hours (h)

e 1 fortnight = g 1 year =

weeks

h 1 year =

i

days

j 1 leap year =

k 1 decade =

l

years

m 1 millennium =

days

f 1 month =

weeks

1 year =

minutes (min)

weeks months days years

1 century =

years

Question 2 Which unit would be the best to use to measure the time: a to travel from home to school?

b to travel from India to Australia by plane? c to swim a distance of 100 metres? d to play a hockey match? e to drive from Sydney to Canberra?

Question 3 Complete the following. a 4 decades =

years

c 3 centuries =

years

e 9 minutes =

seconds

g 7 weeks = i

days

b 480 minutes = d 2 years = f 5 minutes =

hours days seconds

h 2 hours =

minutes days

72 months =

years

j 96 hours =

k 156 weeks =

years

l

10 minutes =

seconds

79





UNIT 11: Addition and subtraction of time

Pages 152–154

Question 1 a

h min b h min c h min 6 20 12 46 9 28 + 5 18 + 9 12 + 6 18

d

h min e h min f h min 5 34 9 41 15 40 + 3 37 + 3 52 – 7 16

g

h min h h min i h min 19 47 10 53 6 23 – 6 38 – 8 48 – 4 41

Question 2

a Add 4 days, 6 hours and 32 minutes to 7 days, 9 hours and 45 minutes. b From 19 h 36 min take away 7 h 23 min. c How many hours are there from Friday noon to 10 pm (the same day)? d How many hours are there from 9.00 am to 3 pm the same day?

Question 3 What will be the time: a 20 minutes after 10:20 am?

b 15 minutes after 5:40 am?

c 50 minutes after 2:15 pm?

d 25 minutes after 6:30 am?

e 15 minutes after 4:51 pm?

f 32 minutes after 5:43 pm?

g 10 minutes after 8:57 am?

h 17 minutes after 6:30 am?

i

j 3 hours after 9:10 pm?

35 minutes after 6:09 pm?

Question 4 What is the length of time between: a 10 am and 11 am?

b 3:30 am and 5:40 am?

c 5 pm and 9 pm?

d 3:25 am and 7:45 am?

e 6 am and 11 am?

f 5:10 am and 10:30 am?





UNIT 12: Clocks and times

Question 1 Write in two different ways the time shown on the clocks below. Write your answers in words. 12 12 1 12 11 1 11 1 12 11 12 12 a c 1 1 11 11 11 1 1 11 b 1 11 11 1 12

12

2

10

2

10

4

8 7

6

4

8

5

7

6

2

9

39

39

9

10

10

7

2

4 7

6

5

6

7

6

5

8

4 7

3

4 6 7

5 6

2

10

2 3

39 8

84 5

6

2

10

2

9

3

9

4

8 5 7

10

10 2 3

39 8

8

5

10

12

3

9

4

4

8

5

7

6

5

d e f

Question 2 Change the following to digital times. a half past four

b 8 o’clock

c a quarter past ten

d midnight

e midday

f twenty past ten

Question 3 Write the following times using am or pm. a 7 in the morning

b 10:20 at night

c 6:40 in the afternoon

d 3 hours after 8 am

e 8:30 in the morning

f 2 hours before noon

Question 4 Convert the following 24-hour times to 12-hour time (using am or pm). a 0700

b 2317

c 1825

d 1921

e 0625

f 0900

Question 5 Convert the following 12-hour times to 24-hour time. a 6 am

b 2:45 pm

c 4:30 pm

d 6:30 am

e 3:25 am

f 10:20 am

g 7:48 pm

h 9:10 pm

81





UNIT 13: P roblem solving using 12– and 24-hour time

1 Write the plane arrival times in 12-hour time. State whether each time is am or pm.

a 0835 hours

b 0943 hours

c 1025 hours

d 1520 hours

e 2036 hours

f 2340 hours

2 Write the following times in 24-hour notation.

a

11

12

1

11

9

9

84 7

6

11

1

12 b 1 1 11

12 11

102

10 2 10 3

9 8

12

102

10

5

morning

3 9

7

6

5

7

3

9

7 6

5 7

5 6

21010

6

3

48 8

8 57

6

66

33

9

84 4

4 77 5

11

102 2

2

9 93

9

4

1212 12 11 1111 1

1 11 10

3

84

8 4 8

12 2

7

55

12 12 c 111 11 111

9

6

75

6

7 57

6

2 3

9

4

84 8

8

84 6

5

12

1 11 102

3

3 9

9

12 1

2

102 10

10

afternoon

12

3

111

11 2

3

4 8 57

d1

2

75

6

6

1 2

4

3

9 4

8

5

12

10 3

4

morning

12

3 9 8

6

12 2 10

9

4

5 7

111 10

7

6

5

night

3 Write the times in 24-hour notation for the following digital clocks.

a

b

c

d

4 Work out the time in hours and minutes between:

a 1130 hours and 1750 hours

b 0820 hours and 1320 hours

5 Write the time in 24-hour notation.

a 15 minutes after 1630 hours

b 20 minutes before 2300 hours

6 Write 2120 h in 12-hour time. 7 How long is it between 1800 h and 1955 h? 8 Convert the following times into 12-hour time indicating whether the time is am or pm.

a 1610

b 0935

9 Convert the following 12-hour times into 24-hour time. a 5:30 am

b 3:20 pm

c 2330

c 10:40 pm

10 Liam is to fly from Sydney to Melbourne on a flight that leaves Sydney at 1830. The flight time is

1 hour and 50 minutes. What is the time in Sydney when Liam’s flight arrives in Melbourne? Give the time in 24-hour time.





UNIT 14: P roblem solving with length, mass and time

Pages 152–154

1 A room is measured as 10.34 m long and 6.58 m

2 An equilateral triangle has a side of 9 cm. What is the

wide. Calculate the difference between the length and breadth in metres.

perimeter of the shape in centimetres?

3 I walked 5.347 km in the morning and 5283

4 Find the perimeter of a square whose side

metres in the evening. How many kilometres did I walk altogether?

length is 8.25 cm.

5 Find the perimeter of a rectangular block of

6 A ship has a mass of 45 960 000 kg. What is this

land which is 150 m long and 70 m wide.

in tonnes?

7 Find the mass of the load if the mass of a

8 Jill needs 3 tonnes of salt. If a packet of salt weighs

loaded truck is 25.64 tonnes and the mass of the empty truck is 12.63 tonnes.

600 g how many packets does she need?

9 There are 11 members in a team and the average 10 Find the mass of a container of a product if the

mass is 55 kg. What is the total mass? product’s gross mass is 2.75 kg and the net mass is 2125 g.

11 If a pulse beats 75 times a minute, how

12 How many hours are there in two weeks?

many beats would there be in 30 minutes?

83



Length, mass and time TOPIC TEST

PART A





1 9 m equals:

A 90 mm

B 900 mm

C 900 cm

D 9000 cm

1

D 9

1

C 64 cm

D 56 cm

1

C 0.4 m

D 90 cm

1

B $10.94

C $11.96

D $12.63

1

B 5250 g

C

23 kg 4

D 5125 g

1

C tonne

D kilogram

1

B 62.5

C 6200

D 6250

1

B 9:30 pm

C 7:30 am

D 7:30 pm

1

D 11:05 am

1

D 60

1

D 2:10 pm

1

2 How many 4-m lengths can be made from a piece 28 m long?

A 6

B 5

C 7

3 What is the perimeter of a rectangle 30 cm long and 14 cm wide?

A 88 cm

B 60 cm

4 The height of a door would be closest to:

A 2 m

B 10 m

5 What is the cost of 4 kg of beans at $2.99 per kg?

A $8.97 1

6 5 4 kg can be written as:

A 5.005 kg

7 What is the most suitable unit to use to measure the mass of a lamb?

A metre

B gram

8 What is the number of grams in 6.25 kg?

A 625

9 1930 h is the same as:

A 9:30 am 1

10 If a 1 2 hour test starts at 9:35 am what time should it finish?

A 10:05 am

1

B 11:35 am

C 11:30 am

11 A tap drips every 1 2 seconds. How many times will it drip in 2 minutes?

A 90

B 80

C 70

12 A plane due at 3 pm arrived 28 minutes early. When did it arrive?

A 2:28 pm

B 2:32 pm

C 2:15 pm



12


Length, mass and time TOPIC TEST

PART B





1 Find the perimeter of a square whose side

length is 7 metres.

1

2 Find the perimeter of a rectangle whose

length is 20 cm and width 12 cm.

1

3 Find the perimeter of a rectangular block

of land 50 m long and 30 m wide.

1

1

4 How many metres are in 3 2 km?

1

5 What fraction of 4 metres is 25 cm?

1

6 Jack needs half a tonne of sugar. If a packet of sugar weighs

800 g how many packets does he need?

7 Convert 3000 kg to tonnes.

1 1

8 A carton has a mass of 12 kg. If it contains

30 cans of beans, what is the mass of each can (ignoring the weight of the carton)?

1

1

9 The weight of a dog is 5 2 kg and he then

puts on 640 g in 6 months. What is his weight now?

1

10 A cruise ship has a mass of

35 000 000 kg. What is this in tonnes?

1

11 How many minutes are there from

2:00 am to 5:00 am?

1

12 Express 5 days in hours.

1

13 How many hours are in a year?

1

14 Change 160 seconds into minutes and seconds.

1

15 Add 5 days, 7 hours and 45 minutes

to 3 days, 8 hours and 25 minutes.

1


85


15


Chapter 8

Area, volume and capacity


UNIT 1: Units of measurement Question 1 Complete the following. a 1 cm2 =

mm2 b 1 m2 =

c 1 ha =

cm2

m2 d 1 km2 =

e 1 km2 =

ha

m2

f 1 cm3 =

g 1 m3 =

cm2 h 1 L =

i

1 kL =

L

j 1 cm3 =

k 1 m3 =

L

l

mm3 mL mL

1 m3 =

kL

Question 2 Complete the following table. a b c d e f g

Capacity/water

Volume

1 mL

10 mL

100 mL

10 cm3

100 g 500 g

500 cm3

600 cm3

600 mL

800 mL

1L

1 000 cm3

Question 3 Complete the following.

mm2 b 80 000 m2 =

1g

a 7 cm2 =

Mass

800 g

ha

c 9 m2 =

cm2 d 350 ha =

km2

e 5 ha =

m2 f 230 m2 =

cm2

g 6 cm3 = i

mm3 h 5 000 000 cm3 = cm3 j 49 cm3 =

15 000 mm3 =

k 8 m3 =

kL


l

50 000 L =

m3 mm3 m3




UNIT 2: Formulae for plane shapes and solids

Pages 137–174

Complete the following table by writing the formulae of the given plane shapes and solids. Name

Diagram

1 Parallelogram

Area =

Formula

h

b

Area =

a

2 Trapezium

h

b

Area = d

3 Rhombus

D

Area = d

4 Kite

D

Area = r

5 Circle

Circumference = Volume =

6 Cube

x

l

Volume =

b

7 Rectangular prism

h

Volume =

r

8 Cylinder

h

Volume =

9 Triangular prism

A

h

Chapter 8: Area, volume and capacity © Pascal Press ISBN 978 1 74020 033 2


87



UNIT 3: Area of parallelograms Question 1 Find the area of each parallelogram. a

b

6 cm

6 cm

8 cm 8 cm

6 cm 10 cm

6 cm

8 cm14 cm 14 cm

10 cm

10 cm

10 cm

8 cm

14 cm

14 cm

c

d

8 cm

9 cm

9 cm 9 cm

9 cm 16 cm 16 cm 16 cm

16 cm

Question 2 Use the formula A = bh to find the area of each parallelogram given in the table below. Base

Height

5 cm 5 cm 5 cm

8 cm 8 cm

8 cm

5 cm

Question 3 Complete the following table for the area of parallelograms.

Area

Base

Height

a

12 m

5 m

a

b

24 cm

9 cm

b

c

16 cm

21 cm

c

8 mm

11 mm

d

14 m

9 m

d

22 cm

15 cm

e

7 cm

18 cm

e

16 m

f

12 m

10 m

f

10 mm

g

6 cm

19 cm

g

h

14 m

12 m

h

i

32 cm

10 cm

i

j

15 mm

20 mm

j


8 m

160 m2 20 cm

180 cm2

128 m2 17 mm 12 cm

24 m

108 cm2 432 m2

23 cm 28 cm

Area

253 cm2

15 cm




UNIT 4: Area of trapeziums Question 1 Find the area of each trapezium.

9 cm 10 m a b c 8 cm 5 cm

12 m 22 m

10 cm

15 cm

18 cm

27 m 10 km d e f 9 cm

11 m

7 km 15 km

4 cm

6 cm

19 m

1.2 m

g h i 91.7 m 57 cm 39 cm

3.8 m

5.4 m

52.5 m

59.5 m

87 cm

2m

63.7 m

Question 2

a Find the shaded area.

10 m

8m

26 m (not to scale)

b Is it possible to find the individual triangular areas? Briefly explain why or why not. Chapter 8: Area, volume and capacity © Pascal Press ISBN 978 1 74020 033 2


89



UNIT 5: Area of rhombuses

Question 1 Find the area of each rhombus. All measurements are in centimetres. a b c 3 20 5

3 3

53 5 5

3 35 3

3

20

5 5 5

15 15 15

15

d

12 12 12

12

20 20

8

8 8 8

e f 18 18 18

18

11

10

11 11 11

10

7

Height

Area

7 cm

a

6 m

b

12 cm

3 cm

b

8 cm

c

14 m

5 m

c

18 cm

d

11 mm

6 mm

d

12 cm

10 m

6 m

e

13 m

f

15 cm

8 cm

f

14 cm

g

25 mm

6 mm

g


Diagonal 1 (d1)

Area

e

90

Base

9 cm

Diagonal 2 (d2)

18

Question 3 Complete the following for the area of each rhombus.

a

Diagonal 1 (d1)

Question 2 F ind the area of each of the following rhombuses. Base

10

7

Height

Area

5 m 32 cm2 4 cm 84 cm2 Diagonal 2 (d2)

Area 65 m2

8 cm 9 cm

99 cm2




UNIT 6: Area of kites

Question 1 Find the area of the following kites. All measurements are in centimetres. a b c 3 3

54 54

34 4

5 94 9

2

4

2 3

3 23 3 8

9

d 5 6 6

5

5

5 2 2 5

3

3

8

3

6

6

4 6

8

32 2

2

4 7

3

4 7

4 7

3

7

7

12 12

7

12

2

Diagonal 2 (d2)

Question 2 F ind the area of each of the following kites. Diagonal 1 (d1)

8

4

11

8

e f

5

6

11 11

8

3

6

6

3

4

6

Question 3 C omplete the following for the area of each kite. Diagonal 1 (d1)

Area

Diagonal 2 (d2)

Area

a

9 cm

7 cm

a

6 m

5 m

b

14 m

5 m

b

18 cm

4 cm

c

11 mm

6 mm

c

12 cm

84 cm2

d

10 m

6 m

d

13 m

65 m2

e

15 cm

8 cm

e

14 cm

f

25 mm

6 mm

f

8 cm 9 cm



99 cm2

91



UNIT 7: Area of plane shapes

Question 1 Find the area of the following shapes. All measurements are in centimetres. a

b

c

4.8

5.2

12.6

6.8

9.4

d

e 7

57.2

31.5

f

15

65.3

12

9

4

h i 7

8

10

6

15

12

13

17

15

13

7

j

15

10

g

13

k

11

l

21

25.6


11.8


Area, volume and capacity UNIT 8: Problem solving with area


1 Calculate the number of square centimetres (cm2) in a square metre (m2). 2 Calculate the number of square metres (m2) in a square kilometre (km2). 3 Calculate the number of square metres (m2) in a hectare. 4 A rectangular playground measures 150 m by 250 m. Find its area in hectares (ha). 5 A garden is in the shape of a parallelogram with the base 30 m and the height 16 m. What is the cost of top

dressing the garden at $28 per square metre?

6 In a hotel, a reception area is in the form of a rhombus with its base length 50 m and height 20 m.

a Calculate its area in square metres.

b Find the cost of tiling the floor if tiling costs $130 per square metre.

7 The area of a parallelogram is the same as the area of a square with side length 30 cm. Calculate the height of

the parallelogram if its base is 45 cm.

8 A farm has an area of 180 km2. Calculate this area in hectares. 9 Another farm has an area of 320 ha (hectares). Calculate its area in:

a m2

b km2 (square kilometres)

10 A rectangular mirror measures 190 cm by 20 cm and is surrounded by a frame of width 5 cm. Calculate the:

a area of the mirror

b area of the frame

c

total area



93



UNIT 9: Volume of cubes

Question 1 C alculate the volume of each of the following cubes whose side length is given. a 2 cm

b 3 cm

c 10 cm

d 1.2 m

e 3.4 m

g 9 cm

h 4.1 m

f 12 m

i

1.8 m

Question 2 Find the volume of each cube. (All measurements are in metres.)

a b c 7

7

11

9

7

9

9

11

11

d e f 15

15

13

15

14

13 13

14

14

Question 3 Find the side length of the cube with given volume.

a 512 cm3 b 1728 cm3





UNIT 10: Volume of rectangular prisms

Question 1 Find the volume of each rectangular prism whose dimensions are given below. (All measurements are in centimetres.) Length

Breadth

Height

a

8

6

4

b

7

5

3

c

20

8

9

Volume

Length

Breadth

Height

d

14

7

8

e

12

5

7

f

9

6

4

Volume

Question 2 Insert the missing measurements in the table for the volume of various rectangular prisms. (All measurements are in centimetres.) Length

Breadth

Height

Volume

a

8

5

7

d

b

10

6

5

e

12

c

7

4

f

15

140 cm3

Length

Breadth

Height

Volume

6

9

594 cm3

8

384 cm3

6

9

Question 3 Find the volume of each rectangular prism. (All measurements are in centimetres.)

a b c 6

12

3

8

6

7 5

4

10

d e f

9

9

8

3

11

12

4 4


4


95



UNIT 11: Volume of triangular prisms

Question 1 Find the volume of the following triangular prisms. All lengths are in centimetres and areas in square centimetres. a b c

15 A = 34

A = 25

15

A = 34

5

d

18

A = 42

10

A = 25 4

A = 42

8

15

33

3

8

4

18

15

25

12

33

3

Question 2 F ind the volume of each of the following triangular prisms whose dimensions are given below. Cross-sectional area

12

25 e f

12

5

12

10

Height

Question 3 Complete the following table for triangular prisms with these dimensions. Cross-sectional area

Volume

a

64 cm2

10 cm

a

b

45 m2

8m

b

c

80 cm2

9 cm

c

25 m2

d

32 cm2

6 cm

d

42 m2

e

88 m2

12 m

e


36 m2

Height

Volume

8m 11 cm

286 cm3

9m 756 m3 12 cm

276 cm3




UNIT 12: Volume of prisms—miscellaneous

Question 1 Find the volume of the following prisms. All lengths are in centimetres and areas in square centimetres. a b c 11

12

11 11

11

11

11

d

9

18

9

18

12

5

12

5

12

29

29

e f 11 15

A = 96

3

11

15

A = 96

3

Question 2 For the given solid: a divide it into a rectangular prism and a triangular prism b find the volume of the rectangular prism c find the volume of the triangular prism

A = 84

12

21

A = 84

12

12 cm 10 cm

18 cm 21 15 cm

15 cm

18 cm cm 26 24 cm

10 cm

8 cm 9 cm

9 cm 24 cm

12 cm

8 cm 26 cm

d find the total volume of the solid

Question 3 For the given solid: a find the area of the front outer rectangle b find the area of the front inner rectangle c find the cross-sectional area

16 cm 8 cm 48 cm 16 cm

d find the volume of the solid Chapter 8: Area, volume and capacity © Pascal Press ISBN 978 1 74020 033 2

9 cm 5 cm

8 cm

16 cm8 Excel Essential Skills Mathematics Revision & Exam Workbook Year

16 cm

5 cm

27 cm 10 cm

10 cm 8 cm 3 cm

27 cm 9 cm

3 cm97

8 cm

Area, volume and capacity UNIT 13: Problem solving with volume


1 Calculate the volume of a rectangular prism with base area of 120 cm2 and height of 25 cm.

2 Find the side length of a cube whose volume is 343 cm3.

3 A rectangular prism has dimensions 60 mm × 100 mm × 140 mm. Calculate the volume of the prism in:

a cubic millimetres

b cubic centimetres

4 A small cube has dimensions 3 cm × 3 cm × 3 cm.

a Calculate the volume of one small cube.

b Calculate the volume of 30 small cubes.

c Calculate the number of small cubes of this size that would fit into a rectangular box with dimensions 18 cm × 20 cm × 30 cm.

5 If the side lengths of a cube are doubled, how many times greater is the volume of the prism.

6 The cross-sectional area of a triangular prism is 280 cm2 and its height is 30 cm. What is its volume?

7 A triangular prism has a volume of 900 cm3 and a height of 15 cm. Find its cross-sectional area.

8 A prism has its side face in the form of a parallelogram, with its base 20 cm and height 8 cm.

If the depth of the prism is 35 cm, find its volume.





UNIT 14: Capacity and volume Question 1 Convert the following to the units given. a 50 000 mL = d 18.5 L =

L b 10.253 L = e 8.3 kL =

mL

g 4 kL =

L

j 9350 mL =

mL

L

L

c 9.6 kL =

L

f 18.35 L =

h 9863 mL =

L

i

2384 mL =

k 12.78 L =

mL

l

8.8 kL =

mL L L

Question 2 Convert the following to the units given. a 9000 mm3 =

cm3

d 20 000 L = g 3000 cm3 = j

b 4 mL =

c 2648 cm3 =

cm3

L

kL e 6000 mm3 =

cm3

f

19 000 cm3 =

L

h 15 000 cm3 =

L

i

9530 mm3 =

cm3

cm3

l

7685 L =

L

m3 k 9875 mL =

5 000 000 cm3 =

cm3

Question 3

a A jug has a volume of 18 000 cm3. How many litres of water can it hold? b A swimming pool holds 35 000 L of water. How many kilolitres is this? c A bottle contains

5 of a litre of drink. How many millilitres is this? 8

Question 4 A fish tank measures 85 cm × 60 cm × 40 cm. a Find the volume of the tank in cubic centimetres. b How many litres of water will the tank hold?

Question 5 Find the volume of the following prisms and then find how many millilitres of liquid each would hold. a b c 14 cm

14 cm

9 cm

14 cm

18 cm

50 cm

12 cm

A = 70 cm2



99

Area, volume and capacity UNIT 15: P roblem solving with area, volume and capacity


1 A rectangular tank with dimensions 60 cm × 65 cm × 80 cm is filled with water.

How much water will it hold?

2 A dripping tap loses 10 mL of water every 45 seconds. How much water will be lost in 6 hours? 3 Find the side length of a cube that has a volume of 6859 cm3. 4 Madeleine drank

7 of a litre of milk. How many millilitres is this? 8

5 Sixty-five children went on a picnic. Each child drank a can of drink containing 300 mL. How many litres

was this?

6 A rectangular prism has dimensions 12 cm × 10 cm × 20 cm.

a What is its volume?

b What would be its volume if all the dimensions were doubled?

7 Find the area of a photograph that is 70 cm long and 40 cm wide. 8 The perimeter of a square is 60 cm. Find its area. 9 A triangle has an area of 1750 cm2. If the base of the triangle is 70 cm long, find its height. 10 Jasbir drank 1.250 litres of milk. How many millilitres is this? 11 One of the faces of a cube has an area of 256 cm2. What is the volume of the cube? 12 Find the total area of the four walls of a room 14 m long, 8 m wide and 5 m high.



Area, volume and capacity TOPIC TEST

PART A





1 Which formula can be used to find the area of any trapezium?

A A = 12bh

C A = 12(a + b)h

B A = bh

D A = 2(a + b)h

2 How many tiles, each measuring 20 cm × 20 cm, are needed to cover a floor 2 m × 5 m?

A 250

B 2500

C 5000

D 40

1

3 A rhombus has diagonals of lengths 14 cm and 18 cm. What is the area of the rhombus?

A 63 cm

B 126 cm

2

C 252 cm

2

4 What is the area of this shape?

D 504 cm

2

2

2

1

14 m

A 80 m B 112 m C 140 m D There is not enough information to determine the area. 2

1

2

8m

1

10 m

5 A triangular prism has perpendicular height 12 cm. The area of the triangular face is

15 cm2. What is the volume of the prism? 45 cm3 60 cm3

A

C 90 cm 3

B

6 If the volume of cube is 125 cm3, what is its side length?

A 15 cm

B 5 cm

C 25 cm

7 How many square millimetres are in 5 cm2?

A 5 mm

B 50 mm

2

2

2 2

3

2

3

1

B 70 000 cm 3

B 48 cm 3

B 350 mL

12 cm

13 cm

1

C 700 000 cm

D 7 000 000 cm

1

C 480 cm

D 80 cm

1

C 3500 mL

D 35 000 mL

1

3

3

3

3



1

30 cm

11 Which is the capacity of a glass closest to?

A 35 mL

D 12.5 cm 2

20 cm

2

10 The volume of a rectangular prism 6 cm × 8 cm × 10 cm equals:

A 4.8 cm

1

D 5000 mm

2

B 266.5 cm D 410 cm

9 How many cubic centimetres are in 7 m3?

A 7000 cm

3

11 cm

8 What is the area of this trapezium?

A 246 cm C 330 cm

C 500 mm

D 180 cm


11

101

Area, volume and capacity TOPIC TEST

PART B





1 Find the area of the following shapes.

a b 20 cm

15 cm

90 cm

c

13 cm

2.1 m

25 cm

7 cm

1

1

1

4m d e 8 cm

10 cm

5m

f

3m

15 cm

9 cm

12 cm

8m

1

1

1

2 Find the volume of these prisms.

a b 5m

4m 3m

70 cm2 2m

5 cm

3 Find the volume of a cube with sides 7 cm.

8 cm × 10 cm × 12 cm.

1

5 How many cubic centimetres are in one cubic metre? 6 A jug has a volume of 5000 cm3.

How many litres of water can it hold?

1 1



1 1

4 Find the volume of a rectangular prism

102

1

12


Chapter 9

Circles


UNIT 1: Parts of circles Question 1 Name the part of the circle indicated.

a b c O

d e f

a lo n g thlo n a g nc e s t a s st

Di

Di Di

Di

e

a ry un d bo a ry un d b o d a ry un b o d a ry un

bo

g h i s ta a nctaenacleo nngec teh ea ltoh en g th

j k l c e a lo n g th e

Di

an

bo

st

un d a ry

Question 2 Find the fraction of the circle given in the following diagrams.

a b c d 270°

120°

45°

Question 3

a If the diameter of a circle is b If the radius of a circle is 12 cm, what is 18 cm, find its radius. its diameter?

103

Chapter 9: Circles © Pascal Press ISBN 978 1 74020 033 2


Circles


UNIT 2: Circumference of circles

Question 1 Calculate the circumference of the following circles correct to one decimal place. a b

c

6c

m

3

4 cm

cm

d e f 15

26 cm

cm

32

cm

10

cm

2

cm

g h i 9

cm

22

Question 2 B y using as the value of π, find the approximate length of the circumference for 7 these circles. a b 7

cm

m

c

49 c

21 cm

Question 3 Find, to one decimal place, the circumference of a circle with: a radius 11 km

b diameter 57 m

c radius 23 cm

d diameter 94 cm

e diameter 78 mm

f radius 19 m



12 cm 12 cm

Circles UNIT

14 cm

12 cm 14 cm

cm 3:12Applications 12 cm

20 cm

14 cm

Excel Mathematics Study Guide Year 8 Pages 142–151 20 cm

of circumference 14 cm

20 cm

20 cm 20 cm cm Question 1 12 Calculate the total perimeter 14 of cm the following semicircles correct to one decimal place. cm 15.814cm

12 cm a b 1520 cmcm 14 17cm 20.7 cm 15.8 cm

15.8 cm

15.8 cm

20.7 cm

15.8 cm 15.8 13.5 cmcm 7 cm 15.8 cm 18.3 cm 13.5 cm

c

20.7 cm 20 cm 21 cm 13.5 cm 20.7 cm

20.7 cm 20.7 cm 7 cm 20.7 17.9cm cm

13.5 cm 13.5 cm 13.5 24.6 cm cm 21 cm

7 cm

Question 2 Find the total perimeter of these quadrants. 21 cm 7 cm

7 cm a b 15.4 cm

14 cm

15.4 cm 15.4 cm 15.4 35.7 cm 20 cmcm

14.2 cm

14 cm 21 cm 21.7 cm

c

21.7 cm 21 cm 15.4 cm

14 cm 15.4 cm

14 cm

21 cm 21 cm 21.7 cm

21 14cm cm 21.7 cm 21.7 cm 20 cm 21.7 cm 28 cm 2018 cmcm

21.7 cm

14.2 cm

a b 20 cm 2018 cmcm 20 cm 15 cm 15 cm

d

14.2 cm

14.2 cm

14 21 cm cm

14.2 cm 14.2 cm

c

15 cm

5 cm

5 cm

15 cm 15 cm

7 cm

14.2 cm

14.2 cm 14 cm 14 cm

15 cm

15 cm 14.2 Question 3 Find18the correct to one decimal 14.7 cm cm place. cm perimeter of each of these figures 18 cm

18 cm 20 15cm cm 18 cm

1

13.5 cm

7 cm

77cm cm 15.4 cm

8 cm 40 cm 8 cm 40 cm 8 cm

15 cm

14 cm 14 cm 14 cm

20 cm g h 89cm cm 18 cm

14cm cm 14

20 cm

5 cm

20 cm

20 cm

15 cm

5 cm

5 cm

5 cm 5 cm 5 cm 85 20 cm cm 20 cm 7 cm 51 cm 54 cm 54 cm 14.7 cm cm cm 5.3 cm 20 cm 28 68 cm cm 85 cm 5.3 cm 5.3 cm 51 cm e f 85 cm 68 cm 85 cm 7 cm 85 cm 51 cm 5.3 cm 7 cm 51 cm cm 51 cm 40 8 cm 85 14cm cmcm 68 85 cm 714cm 51 cm cm68 cm 68 cm 5.3 cm 51 cm 8 cm 8 cm5.3 cm 26 cm 14 cm 14 cm 68 cm 20 cm 40 cm 68 cm 5.3 6.7cm cm 5 cm 5 18 cmcm 18 cm 7 cm20 cm 5 cm 5 cm 20 cm 7 cm

i

40 cm 40 cm 18 cm 40 cm 40 cm 18 cm 18 cm 18 cm 36cm cm 18

9 cm

18 cm

20 cm 20 cm 20 cm cm 2020cm

105


1


5

5

Circles


UNIT 4: Area of circles

Question 1 Calculate the area of the following circles correct to one decimal place using the calculator value of π. a b m

m 3c

5c

c

m

9c

d e f 13

cm

17

cm

19

cm

g h i cm

22

cm

cm

8

10

22 as the value of π, find the approximate area of these circles. 7 a b c

Question 2 By using m

35

7c

cm

14

Question 3 Find the area, to one decimal place, of a circle with:

cm

a radius 25 km

b radius 1.8 m

c diameter 37 mm

d radius 73 cm

e diameter 400 km

f diameter 13.9 cm



15 cm

17 cm

15 cm

Circles 15 cm

15 cm

17 cm

21 cm

17 cm

Excel 21 Mathematics Study Guide Year 8 cm

17 cm

Pages 142–151

UNIT 5: Applications of area

15 cm 17 cm 21 cm 17.9 Question 18.3 1 cmCalculate the area of the following semicircles correct to 18.3cm cm 15cm cm 15 a b 17cm cm 15 cm 17 17 cm 18.3 cm 17.9 cm 15 cm 17 cm 18.3 cm 17.9 cm

18.3 cm 24.6 cm cm 18.37cm cm 18.3 18.3 cm 7 cm 18.3 cm

7 cm

7 cm

17.9 cm 17.9cm cm 17.9 17.9 cm 17.9 cm

14 cm

21 cm 24.6 cm one decimal 17.9place. cm

c

21cm cm 21 21 cm 24.6 cm 21 cm

24.6 cm 24.6 cm

24.6cm cm 24.6 24.6 cm 24.6 cm 21 cm 14 cm

Question 2 7Find the area of these quadrants correct to one decimal place. cm 14 cm28 cm a b 35.7 cm cm 77cm 7 cm 7 cm35.7 cm

35.7 cm 21 cm

35.7 cm 15 cm

cm

14 cm 28 cm

21 cm

35.7 cm

14 cm 28 cm 14 cm 2814 cmcm 14 cm 14 cm 15 cm 28cm cm 28 28 cm18 cm

c

21 cm

28 cm

cm 14.721cm

14.7 cm

1

21 cm

21cm cm 21 21 cm 14.7 cm21 cm

14.7 cm

18 cm cm 35.7 cm 35.7 cm 4 cm 4 cm 35.7 cm 14.7 cm 15 cmthe area of these shapes correct 28 cm Question 3 Find to one decimal 14.7 place. 14.7cm cm 14.7 28 cm 35.7 cm a b c 14.7 cm 1518 cmcm 14.7 cm 4 cm 4 cm 14.7 cm 1815cm cm 28 cm 14.7 cm 4 cm 4 cm 18 cm 28 cm 15cm cm 14.7 cm 4 cm 4 cm 14 cm 15 14 cm 15 cm 14.7 cm 4 cm 4 cm 28 cm 26 cm 18cm cm 15 cm 18 28 cm 14.7 cm 4 cm cm 18 cm 6.7 cm cm 6.7 cm 14.7 4 cm 44cm 14 cm 14.7 cm 4 cm 4 cm 18 cm 28 cm cm 2628cm 14.7 cm 4 cm 4cm cm 14 cm 4028 cm 6.7 cm 28 cm d e f 26 cm 40 cm 14 cm 6.7 cm m 9 cm 726c cm 14 cm 9 cm 114 4020 cmcm cm 14cm cm 26 cm 6.7 cm 40 cm 14 14 cm 9 cm 26cm cm 9 cm 26 9 cm 40 cm 26 14 cm 14 cm cm 6.7 cm 36 cm 20 cm 6.7 cm 26 cm 6.7 cm 9 cm 14 cm 9 cm 40 cm 20 cm 6.7 cm 40 cm 36 cm 9 cm 14 cm 9 cm 40cm cm 20 cm 40 g h i 36 cm40 cm 20 cm 9 cm cm 99cm 14cm cm 40 cm 14 20cm cm 9 cm 20 36 cm 14 cm 20 cm 936 cmcm cm 14 cm 99cm 20 cm 9 cm 36cm cm 36 9 cm 36 cm 36 cm 14.7 cm

107



Circles


UNIT 6: Miscellaneous questions

Question 1 Calculate the circumference of each circle correct to one decimal place. cm

a b 11

77

cm

c

12

cm

Question 2 Calculate the area of each circle correct to two decimal places. 9 a b c m

c

7

m

cm

c 54

Question 3 Calculate the perimeter of the following shapes correct to three significant figures. 18 cm a b 7 cm

7 cm

8 cm

5c

m

8 cm

8 cm

7 cm 5 cm

cm

c

12 cm

6

7 cm

9 cm 20 cm 9 cm

5

6

cm Question 4 Calculate the shaded area of the following shapes correct to two decimal places.

cm

8 8cm 8cm cm

a b 8 cm 8 cm

c

cm

cm

10 cm

6

10 cm cm 158cm

9 cm

12 cm

6

c

cmcmcm 66 6 m

8 cm

5c 5 cm 5 cm 10 cm m5 cm 8 cm 8 cm 8 cm 8 cm5

12 cm 18 12 cm

20 cm 9 cm 9 cm 9 cm 5 cm

20 cm 20 cm 20 cm 20 cm 9 cm 10 cm 5 cm

20 cm

5 cm

5 cm10 cm 5 cm 5 cm

10 cm 12 12 cm cm 10 cm d e f 18cm cm 10 cm 12

15 cm

10 cm

18 18 cm cm

18 cm 18 cm

15 cm 15 cm 15 cm 15 cm

15 cm


5 cm10 cm

12 cm

10 cm 10 cm 10 cm

10 cm

18 cm


Circles


UNIT 7: Problem solving with circles

Pages 142–151

1 A circular track has a radius of 28 metres. Calculate the distance round the track. 2 Calculate the area of the circle formed by the circular track in Question 1. 3 Calculate the radius of a circle with a circumference of 220 cm. 4 Find the area of the top of a can 16 cm in diameter and with 12 cm height to one decimal place. 5 The circumference of a circle is 200 cm. Find the area of the circle. 6 Find the circumference of a circle with diameter equal to 18 cm. 7 What distance do you ride in one turn of a merry-go-round when you sit 6.3 metres from the centre? 8 The wheel of a bicycle has a radius of 25 cm. How far does the bicycle travel when its

wheels make one complete turn?

9 What is the cooking area of a circular barbecue grill having a radius of 18 cm? 10 A revolving sprinkler sprays a lawn for a distance of 14 metres in all directions. How much area does the

sprinkler water in one revolution?

11 Two cylindrical cans are both 25 cm high. One can has a base with a radius of 10 cm, and the other has a

radius of 20 cm. Find the ratio of the area of their bases.

12 Find the circumference of a circle with diameter of 68 cm. 13 Find the area of a round tablecloth if its diameter is 3 metres. 14 A circular ring has a radius of 1.5 metres. What is the perimeter of the ring?

109



Circles TOPIC TEST

PART A





1 What is the formula for the circumference of a circle? C = 2π C = 2π r d

A

B

2 What is the formula for the area of a circle?

A A = πr

B A = πd

2

2

D C = 2πd

1

C A = rπ

D A = dπ

1

D none of these

1

D none of these

1

D segment

1

D 14 cm

1

2

3 What is the exact value of π?

A 3.14

C C = 2πr

C 227

B 3.142

4 What is the relationship between the diameter and radius of a circle?

A d = 2r

B r = 2d

C rd = 2

5 Which of these is a name for part of the circumference of a circle?

A arc

B radius

C sector

6 The circumference of a circle of radius 7 cm is closest to:

A 44 cm

B 24 cm

C 22 cm

7 The area of a circle of diameter 28 cm is closest to:

A 88 cm

B 616 cm

2

2

C 1232 cm 2

D 2463 cm

2

1

C 78.5 cm

D 314.2 cm

2

1

C 24 cm

D 12π cm

1

D none of these

1

8 The area of a quadrant with a radius 10 cm is closest to:

A 157.1 cm 2

B 31.4 cm

2

9 The radius of a circle is 12 cm. Its diameter equals:

A 6 cm

B 12 cm

10 The area of a circle of radius 3 cm is approximately equal to:

A 27 cm 2

B 28 cm 2

2

2

C 29 cm 2

11 The circumference of a circle is 154 cm. Which is closest to the length of the diameter?

A 24 cm

B 49 cm

C 98 cm

12 In how many places does a chord meet the circumference?

A 1

B 2

C 3

D 242 cm

1

D 0

1



12


Circles TOPIC TEST

PART B

Instructions • This part consists of 7 questions. • Answer each question in the space provided Time allowed: 20 minutes


1 If the diameter of a circle is 24 cm, what is its radius?

1

2 What name is given to the shaded part of each circle?

a

b

O

O

O

O

1

1

3 A circle has radius 21 cm. To one decimal place, find the:

a circumference b area

1

1

4 A circular pond has a diameter of 4 m. To one decimal place, find the:

a area b circumference

1

5 A semicircle has radius 48 cm. Find the:

1

a perimeter to the nearest centimetre

b area to the nearest square centimetre

1

1

6 A quadrant has radius 9 cm. Find, to one decimal place, the:

a area b perimeter

1

1

7 Find the shaded area to the nearest square centimetre.

a b 16 cm

12 cm 20 cm

12 cm

16 cm

20 cm


1

13

111


1


Linear relationships

Chapter 10 Excel Mathematics Study Guide Year 8 Pages 66–86

UNIT 1: The number plane Question 1 Write the letter used to name the following points. a (0, 0)

b (1, 1)

e (4, 4)

f (0, 1)

4

j (1, 0)

3

n (2, 1)

2

c (2, 2)

d (3, 3)

g (0, 2) i

D

E

F

C

S

T

U

I

B

R

Y

V

J

A

Q

X

W

K

O

P

N

M

L

h (0, 3)

(0, 4)

k (2, 0)

l

m (4, 0) o (2, 3)

(3, 0)

p (2, 4)

q (1, 2)

r (1, 3)

s (1, 4)

1

t (3, 1)

u (3, 2)

v (3, 4)

w (4, 1)

x (4, 2)

0

1

G

2

H

3

4

Question 2 Write down the coordinates of the following points shown in the number plane. a A

c C

b B

d D

e E

f F

g G

h H

i

I

j J

k K l

y M

n N

o O p P

q Q

u U y Y

E

B

A

7 6

K

5

F

G

4 3 2 1

S

T

–4 –5 –6

D

C 2

–2 –3

J

I

H

N O –x –7 –6 –5 –4 –3 –2 –1 0 1 –1 U Y X

L

m M

L

R

3

V

P Z

4

5

6

7

x

W

Q

–7

–y

r

v z

R V

s

w

S W

t

x

T X

Z





UNIT 2: Tables of values Question 1 Complete each table of values.

a y = x b y = 2x x

0

1

2

3

y

x

–1

0

1

2

y

d y = –x c y = 3x x

–2 –1

0

1

y

x

0

1

2

0

1

2

y

e y = x + 2 x

–1

–2 –1

0

f y = x – 3

1

y

x

–1

y

Question 2 Complete each table of values and list the coordinates of the points. a y = 2x + 1 x

–1

0

1

b p = 2q – 1

2

y

q

c c = 2d + 3

–1

0

1

n

2

0

1

2

3

0

1

2

m

e s = 4t – 3

1

d m = 3n + 2

2

c

t

0

p

d

–1

–1

0

1

f a = 3b – 2

2

s

b

–1

a

113

Chapter 10: Linear relationships © Pascal Press ISBN 978 1 74020 033 2




UNIT 3: Graphing straight lines

Question 1 Complete each table of values and then graph the equation on the number plane. a y = x + 2 x

–1

0

1

2

x

y

b y = x – 1

–1

0

1

c y = –x + 3

2

y

y

–1

x

1

2

y

y

y

x

x

0

x

Question 2 Complete each table of values and then graph the equation on the number plane. a x = 2

b y = 3

x y

x 0

1

2

3

0

1

2

c y = x

3

y

y

0

x

2

3

y

y

y

x

x

1

x

Question 3 On the same number plane, graph the following equations by first completing the tables of values. Find their point of intersection. a y = x x

–1

0

1

2

x

y

b y = x + 2

y = –x

–1

0

y

1

2

x

–1

y = 2x + 1

0

1

2

x

y

–1

1

2

y

Point of intersection

Point of intersection y

y

x

0


x




UNIT 4: Using the intercept method to graph lines Question 1

Pages 66–86

Find the x-intercept for each equation.

a x + y = 2

b x – y = 4

c 2x + y = 6

d 2x – y = 8

e x – 3y = 6

f 2x – 3y = 12

Question 2 Find the y-intercept for each equation. a x – 2y = 4

b x – y = 8

c 2x + y = 6

d 2x – y = 3

e 3x – 4y = 12

f 3x – y = 3

Question 3 Draw the graph of each equation, given the x-intercept and the y-intercept:

a x-intercept = 3, y-intercept = 2

b x-intercept = –1, y-intercept = 3

y

y

x

x

Question 4 For each equation, find the x-intercept and the y-intercept and then draw its graph. a y = –2x + 3 y

x

0

y 0 x

x

c y = 2x – 3 x y

4

d y = 3x – 1

y

0 0

x

0

y

y 0 x

y

0

x 0

y

b x + y – 5 = 0

115


x




UNIT 5: Intersection of two lines Question 1

a x = 1; y = 3

Graph each pair of lines on the same number plane and find their point of intersection.

x = 1

x y

y

y x

x = 3

x y

y=3 x

b x = 3; y = –2

Pages 66–86

y = –2

y

x

y x

Question 2 Graph each pair of lines on the same number plane and find their point of intersection. a y = 2x – 1; y = –x + 2

y = 2x – 1

x y

y x

y = 3x – 1

x y

y

x

b y = 3x – 1; y = x – 3

y = –x + 2

y=x–3

y

x

y x





UNIT 6: D etermining whether or not a point lies on a line Question 1 a (0, 3)

Pages 66–86

Which of the following points lie on the line 3x + 4y = 12? b (0, 0)

c (–4, 6)

d (4, 3)

e (4, 0)

f (8, –3)

Question 2 Which of the following lines pass through the origin, (0, 0)? a 2x – y + 2 = 0

b 2y = 3x

c x – 5y = 0

d 2x + 3y = 6

e y = –2x

f y = 5x – 4

Question 3 Does the given point lie on the given line? a x + 2y = 3 (3, 0)

b x + y = 2 (0, 2)

c 2x + 3y = 6 (3, –2)

d y = 5x – 3 (1, 2)

e y = –x + 7 (4, 3)

f 2x + y = 5 (2, –1)

Question 4 A straight line y = mx + 8 passes through the point (–2, 2). Find the value of m.

Question 5 If the point (–3, –6) is on the line ax – 4y – 9 = 0, what is the value of a?

Question 6 F ind the missing coordinates to make each of the following points satisfy the equation

b (

)

d (5,

, –5)

f (

a (0,

)

c (1, e (

y = 3x – 2.

, 4) ) , –8)

117





UNIT 7: Using graphs to solve linear equations 1 Use the graph of y = x + 1 on the right to write the x-value, when:

a y = 3

x=

b y = –2

x =

c y = 5

4

x=

2 –4

b x + 1 = –2

c x + 1 = 5

x

4

3 The graph of y = 2x – 3 is drawn opposite. Use the graph to solve each of the

following equations. a 2x – 3 = 3

8

b 2x – 3 = –4

6 4

y = 2x – 3

2

d 2x – 3 = 5

y

10

c 2x – 3 = 1

2

–2

a x + 1 = 3

0

–2

–4

2 Use your answers from Question 1 to solve the following equations.

y=x+1

y

–2

0

2

–2

4

8x

6

4 The graph of y = 3x + 2 is drawn opposite. Use the graph to solve each of the

following linear equations. a 3x + 2 = –1 b 3x + 2 = 5

2

c 3x + 2 = –4

y 4

d 3x + 2 = 8

–4

10


x

y

4

y = –x + 2

2

d –x + 2 = 0

4

6

2

8

b –x + 2 = 6

c –x + 2 = –2

–2

y = 3x + 2

–4

Question 5 T he graph of y = –x + 2 is drawn opposite. Use the graph to solve each of the following equations. a –x + 2 = 3

–2

0

–2

0 –2

2

4

6

8x


Linear relationships TOPIC TEST

PART A





1 The straight line y = 2x – 1 passes through one of the following points. Which one?

A (0, 2)

B (0, –2)

2 Which graph best represents y = x?

A asd

B

y

y

x

C (0, 1)

D (0, –1)

C

D

y

3 The equation of the line l is:

A C

x = –3 y = –3

B D

y

x

x

x=3 y=3

B 4

y

l

0

3

x

B 4

1

D 2

1

D (6, 0)

1

D y = 3 + x

1

D 5x + 4y = 15

1

C (–1, 6)

D (–2, 3)

1

C 2

D –2

1

C 3

D –3

1

D (3, –5)

1

C 3

6 Which one of the following points lies on the y-axis?

A (2, 3)

B (3, 2)

C (0, 6)

7 Which linear rule states that y is always 3 less than x?

A y = 3 – x

B y = x – 3

C y = –x – 3

8 On which of the following lines does the point (5, 1) lie?

A 4x + 5y = 15

B 5x – 4y = 15

C 4x – 5y = 15

9 Which one of the following points lies on the line 2x – y = 4?

A (1, –4)

B (2, 0)

10 What is the x-intercept of the line x + 2y = 4?

A 4

B –4

11 What is the y-intercept of the line 2x – 3y = 6?

A 2

B –2

12 The coordinates of the point of intersection of the lines x = 3 and y = –5 are:

A (–5, 3)

B (5, –3)

C (–3, 5)


12

119


1

D 6

C 5

5 If the y-coordinate of a point on the line y = 5 + 3x is 20, what is the x-coordinate?

A 5

1 x

4 If the x-coordinate of a point on the line y = 8 – 2x is 1, what is the y-coordinate?

A 3

1


Linear relationships TOPIC TEST

PART B





1 Match each table of values with an equation.

a

x

–2 –1

0

1

–5 –3 –1

1

b

x

–2 –1

0

1

1

1

y –2 1 4 7 c d x –2 –1 0 1 x –3 0 3 6 y

y

i

9

7

0

1

y –1 0 1 2 e f x –2 –1 0 1 x –3 0 3 6 y

–4 –2

1

5

2

3

y = 2x

y 9 ii y=

x 3

1

–9 –18

y

iii y = 2x – 1 iv y = 5 – 2x

v y = 3x + 4

vi y = –3x

0

2 a O n the same number plane, draw the graphs of the following lines.

0

1

i

x = –3

ii

2

x

y=1

b Write the coordinates of the point of intersection of the lines x = –3 and y = 1.

y

1

3 a Complete the table of values below for the

equation y = x + 2.

x –3 –2 –1 0 1 2 y b Draw the graph of y = x + 2.

3

0

x

1 1

c What is the value of y when x = –7?

1

d Where does the graph cut the x-axis?

1

e Where does this graph cut the y-axis?

1

f Using the graph, solve x + 2 = –3.

1



15


Chapter 11

Equations


UNIT 1: Solving equations by inspection

Pages 88–108

Question 1 Solve the following one-step equations by inspection and then check by substitution. a x + 2 = 5 b a + 3 = 7 c m – 4 = 8

d b + 1 = 7

g x – 2 = 4

j p – 3 = 7

m y – 2 = –7

e a + 2 = 10

h x + 3 = 9

k t – 2 = 8

n x – 4 = –6

f n + 5 = 12

i y + 8 = 14

l a – 9 = 3

o 8 + x = 12

Question 2 Solve the following equations by inspection and then check by substitution. a m + 1 = 9 b x + 2 = 12 c 3 + y = 15

d 9 + n = –3

g m + 5 = 9

j m – 3 = 7

m y – 5 = –3

e x – 4 = 7

h y – 3 = 18

k n – 6 = 10

n t – 2 = –4

f x – 2 = 16

i a + 6 = 8

l a – 4 = 11

o 15 + a = 21

121

Chapter 11: Equations © Pascal Press ISBN 978 1 74020 033 2


Equations


UNIT 2: O ne-step equations (addition and subtraction)

Question 1 Solve the following one-step equations. a x + 5 = 9 b a + 7 = 15

Pages 88–108

c m – 3 = 4

d b + 3 = 11

g x – 3 = 12

j p – 2 = 10

m y – 2 = –3

e a + 4 = 10

h x + 5 = 16

k t – 4 = 1

n x – 5 = –6

f n + 9 = 12

i y + 8 = 20

l a – 9 = 9

o 5 + x = 20

Question 2 Solve the following equations. Check your solutions by substitution. a m + 7 = 2 b x + 3 = 1 c 9 + y = 14

d 12 + n = 18

g m + 15 = 30

j m – 4 = 11

m y – 5 = –5


e x – 10 = 12

h y – 12 = 27

k n – 12 = 19

n t – 6 = –3

f x – 1 = 8

i a + 5 = 13

l a – 7 = 1

o 10 + a = 14


Equations


UNIT 3: O ne-step equations (multiplication and division)

Question 1 Solve the following one-step equations. x = 3 a 4a = 16 b 2

Pages 88–108

c 5y = 15

x y d = 7 e = 6 f 8x = –32 3 5

t g 6m = –18 h 2x = 6 i = –5 4

y j 2p = –8 k = –4 l 7t = 28 5

a x m = 9 n 3a = 24 o = –3 2 7

Question 2 Solve the following equations. Check your solutions by substitution. a

x x x = 5 b = –2 c =6 6 6 7

a a b d = –20 e = –2 f =9 9 3 8

m x y g = 12 h = 9 i = –14 3 3 2

j 3a = 18

m 5x = 35

k –2b = –10

n 8x = 48

l –3x = –12

o 7x = 49

123



Equations


UNIT 4: Two-step equations Question 1 Solve the following two-step equations. a 2x + 1 = 3 b 18 = 3x – 6

c 10 = 5y – 15

5m d 3 = 10

x–3 e 4 =5

x g 2 – 1 = 7

a–2 h 3x + 5 = 11 i 7 =3

j 8x – 7 = 33

f 2a + 9 = 19

k 5x + 3 = 28

l 6t – 3 = 39

m m 7y – 5 = 9 n 3 – 4 = 6

o 2k + 3 = 21

Question 2 Solve the following equations. Verify your solutions by substitution. a 3x – 3 = 9

m

x–5 c 7 =4

b 2 + 6 = 9

x–2 d 6 = 8

5m e 5x – 9 = 26 f 6 = 10

g 10 – 2m = 0

j 2x + 8 = 14

m 3a – 2.3 = 7

h 3y – 9 = 21

k 8x – 7 = 17

n 6a –


1 12

=

1 42

i 7y + 4 = –3

l 9x – 7 = 56

o 8p + 0.3 = 2.7


Equations


UNIT 5: Three-step equations Question 1 Solve the following three-step equations.

a

b 2x – 7 = x – 3

4x + 9 = 3x – 12

c

d

6t – 10 = 4t + 12

e

9m – 3 = 7m + 9

f

4a – 3 = 3a + 9

g

10y – 6 = 5y + 19

h

i

7y – 3 = 4y + 15

j

5x – 1 = 6x – 9

k

3a + 5 = 21 – a

l

11m – 6 = 7m + 14

6x – 4 = 2x + 16

12p – 3 = 7p + 32

Question 2 Solve the following equations. Check your solutions by substitution.

a

b 2x – 6 = 3 – x

6x – 20 = 4x + 48

c

d

6x – 2 = 3x – 6

e

2x – 14 = x – 12

f

5x + 17 = 3 – 4x

g

3m – 2 = 2m + 7

h

i

3y + 1 = 2y + 7

j

6m + 7 = 7m + 10

k

2x + 3 = x – 9

l

6x – 21 = 2x – 2

4y – 3 = 2y + 11

125


7y – 14 = 5y + 20


Equations


UNIT 6: Equations with grouping symbols Question 1 Solve the following equations. b 2(m + 1) = 5 a 3(x + 4) = 18

e

3(a – 3) = 10

f

4(n – 3) = 36

c

6(m – 1) = 24

d

g

5(2n – 1) = 25

h

i

5(2x + 3) = 45

j

4(a – 4) = 8

Question 2 Solve the following equations. b 3(x – 5) = 2(x + 4) a 5(a + 4) = 4(a – 3)

e

8(3 – x) = 7(x – 6)

m 6(a + 7) = 5(a – 3)

f

3(3a – 2) = 4(4 – a)

i

j

c

2(a + 1) + a + 3 = 0

g

2(a + 1) – a + 7 = 9

k


4(y – 3) = 3(y + 2)

l

3(m + 2) = m + 14

n 8(2a + 7) = 5(3a – 8) o

k

2(3p – 1) = 22

2(3x + 2) = 16

d

3(x + 7) + x + 3 = 18 h

3(a – 3) – 2a + 9 = 15 l

9(3a – 4) = 13(2a – 1)

2(x + 5) = 18

7(x – 8) = 6(x + 2)

5(a + 3) = 4(a + 9)

2(5a – 10) – 9a + 6 = 0


Equations


UNIT 7: Formulae Question 1 Given the formula V = Ah, find V if: a A = 10, h = 3 b A = 15, h = 5

Question 2 Given the formula P = 2L + 2B, find P if: a L = 18, B = 10 b L = 12, B = 5

c A = 9, h = 4

c L = 9, B = 4

Question 3 If y = mx + b, find y for the given values of m, x and b. 1 a m = 1, x = 3, b = 2 b m = 2, x = 6, b = 3 c m = 2 , x = 8, b = 4

Question 4 If A = 12 bh, find A for the given values of b and h. a b = 4, h = 3 b b = 6, h = 4

c b = 9, h = 6

Question 5 If C = 2πr, find the value of C to one decimal place when: a r = 8

Question 6 If A =

b r = 37

1 2

h(a + b), find A when:

a h = 6, a = 8 and b = 10

b h = 17, a = 13 and b = 19

c r = 63.5

c h = 23, a = 35 and b = 44

127



Equations


UNIT 8: Problem solving with equations

In the following questions, suppose the unknown number is represented by x. Write the statement as an equation and find the value of x. 1 The sum of a number

2 Multiply a number by 3 and

3 I think of a number and

and 8 is 24. then take away 9. The answer is 21.

add 12. The result is 26.

4 A number increased by 9

5 The difference between

6 I think of a number, double it,

is 27.

5 times a number and 3 is 7.

and the result is 30.

7 I think of a number, double it

8 I think of a number, divide it

9 The difference between

and add 12. The result is 48. by 4, subtract 2 and the result is 7.

7 times a number and 6 is 29.

In the following questions, write an equation using the pronumeral x for the unknown number and then find the value of x. 10 A rectangle is 5 cm longer than it is wide.

If its perimeter is 26 cm, find the width and the length of the rectangle.

11 If the perimeter of an equilateral triangle is 36 cm,

12 The length of a rectangle is 8 cm and its

perimeter is 22 cm. Find its width.

13 If I subtract 29 from a certain number the result is 23.

14 Find x if the sum of 3, 5, 8, x is 28.


What is the number?

15 I think of a number, add 3 to it, multiply this sum

128

what is the length of each side?

by 7 and then subtract 9. The result is 47. What is the number?


Equations


UNIT 9: Simple equations with one fraction

Pages 88–108

Question 1 Solve the following equations. a

x a y = 9 b = 8 c =7 4 3 6

m m x d = 10 e = 7 f =9 3 4 6

a+3 3x 5x – 4 g = 2 h = 9 i =7 7 4 3

j

x x+2 m+5 = 2 k = 6 l =9 3 2 3

Question 2 Solve the following equations. Check your solutions by substitution. 5

3y – 1 b 2 = 10

t–5 c 2 =5

m–7 3 =4

2a + 8 e 4 =6

3p – 5 f 2 =8

h 4x – 2 = 3 5

3x + 4 i 2 =2

k 5 – 3x = 1 2

l 2m + 9 = 4 6

6p n 5 +3=9

3a + 4 o 2 = 14

a 2x = 8

d

g 3x + 1 = 7

j

4

3m – 1 4 =8

m 3x = –2

5

129



Equations TOPIC TEST

PART A





n 1 If 3 = 7, n equals:

A 7

2 If x – 10 = –2, x equals:

A –12

B 11

C 17

D 21

1

B –8

C 8

D 12

1

3 If 2x – 5 = 21, what is the value of x?

A 6

B 8

C 13

D 26

1

A 2

B 3

C 9

D 18

1

C 14

D 28

1

C 1

D 7

1

C x = 9

D x = 7

1

C 8

D none of these

1

m 4 If 3 = 6, find the value of m. 5 If 2p – 5 = 23, then p equals:

A 8

B 9

6 If n + 3 = –4 then n equals:

A –7

B –1

7 Solve for x: 5x + 3 = 2(x + 12).

A x = 3

B x = 5

8 If 2(t + 3) = t – 4 then t equals:

A –10

B 2

9 If 2(7 – x) = 3 then x equals:

A 11

B 17

10 2(x – 3) = 3(2x + 4) then x equals: 1

A 1 2

1

B 4

1

C 8 2 1

C –4 2

11 If y = ax2 what is the value of y when a = 4 and x = 3?

A 36

B 144

C 49

1

D 5 2

1 3

D –3 4

1

D 1849

1

D 567

1

1

12 If A = 2 h(a + b) and h = 12, a = 9 and b = 21, what is the value of A?

A 90

B 180

C 36



12


Equations TOPIC TEST

PART B





Solve the following equations. 1 a x – 7 = 30

c 7n = 147

e 2x – 3 = 5

g

x–2 3 = 10

i

3(x – 1) = 9

x d 12 = 96

1

h

1 1

1

1

4x – 3 = 2x + 9

m 4(2x – 5) = 0

n 3(x + 4) = x + 19

1

x 2 = 4 3

j 4(p + 7) = 30

l

1

f 5a + 17 = –3

k 3x + 10 = 5x – 2

1

1

1

b m + 9 = 15

1 1

1 1

2 I think of a number, double it, add 8 and the result is 42. Find the number.

1


131


15


Chapter 12

Reasoning in geometry


UNIT 1: Angles and the value of the pronumerals Question 1 Find the value of the pronumeral(s) in each of the following.

a b c

m°

50°

y°

50°

75°

a°

n°

d e f 40°

130°

k°

20°

30°

110°

m°

60°

m°

Question 2 Find the value of the pronumeral(s).

a b c

t°

20°

15°

y° 70°

70°

40°

a°

d e f 50° 155°

70°

y°

115°

65°

85°

m°

x°

n° p°

82°

Question 3 Find the value of the pronumeral.

a b c 80° 2a° n° a° a° a° a° 30°



76° 76° 76° n°nGuide ° Excel Mathematics Study Year 8 Pages 199–230 n° 76° 76°76° nn°° n° 76° n° 76° 76° n° n°


60° 60° mm ° ° 60° a °a° m ° UNITa2: Parallel lines and angles ° 120° 120° 60° m 120° m°°min° each60° Question a1 Find the value of the pronumeral of60°the following. ° a° a° 120° a b c 60° 120° m° 120° a° 60° m° 120° 60° a° m° a° 120°

d

50°

25°

25° 25°

n°n°

n°

75° x°x°25° n75° ° 50° 75° n° 25°25° x ° 50°50° n° e f

y°y°

y°

yy°° 50° y° y° y°

xx°° x°

50° 50°

y°

120° 50° 50°

25° 25°

x°

75°n° 75°75° n° 75°n°

25°

x° x°

75° 75°

d°d° Question 2 Find the value of each pronumeral. d°110° b°b° 110° x ° x ° a°a° y°y° 120° 120° ba° °a° 110° a b c a° yb°°b° x° a°d° c°c° y120° °y°x°x° 120° 120° dc°°d° y° x° mm b° 120° x° 110° b° ° ° 110° aa°° yy°° x° aa°° b° b° 110° m° 120° x ° 120° y° d° acc°°° yy°° xx°° 120° bba°°° 120° 120° y ° x ° b°c° 110° m ° x° a° b°y° 120° m120° °m° da°° y° x° 110° d° cb°° a°b° 120° y° xx°° 110° a° b° 120° m° a° y° a° c° 120° y ° x ° b° 120° c° y ° x ° m° b° 120° m° x°x° 125° 110° 125° 110° x ° 125° 110° Question 3 Find the value of each pronumeral. a

a°a°

a°

b x° 125°

aa°° a°

a°

a° a°

x° x°

125° 125°

125°

x°

125° 125°

x° x°

c

a110° °a°

110° 110°

a°

aa°° 110° a°

a°

110° 110°

a° a°

d e f x°x° 20°

20° 20°

x°

x°x°

xx°° 20° 45° 20°20° 45° x° 45°

x° 45° 45° 20° 45°x° x° 20° 45° 20°

y°

y°y°

yy°° y° y°

y° Chapter 12: Reasoning in geometry 45° 45°

y°


40°

40° 40°

x°

xx°° yx°y°

30°

30° 30°

60°

60° 60°

a°

a°a°

b°b60° ° y°30° 30° 30° 60°60° 40° 30°30°b° 40°40° x° 30° aa°° a° yy°° bb°° 60° 40° 30° x° y° 30° 30°30°x° b° a° 60° 40° y° 30° b° 60° a° 30° 40° 30° a° y° b° 30° y° b° 30° Excel Essential Skills Mathematics Revision & Exam Workbook Year 8

133

x° xx°°

110° 110° 110° Reasoning in geometry 50°50° 50° a° aa°°


UNIT 3: The20°angle sum of a trianglea° aa°° 65°65° 65° 20° 20°

45°45° 45°

110° Question in each of the following. 50° 110° 110°110° a°a°1 Find the value of the pronumeral 110° 50° 50° 50° 110° a ° ° 50° a b c a° 50°110° a°a° 65° a° 20° 50° a ° a ° 65° 20° 65° 20° a°a°° 65°65° 20°20° 65° 20° a° 65° 20°

b° bb°°

50°50° 50° 50°50° 50°

35°35° 35°

60°60° 60°

a° aa°°

x° xx°120° ° 120° 120°

a° aa°n° ° nn°° 35° m°mm 35° 35° °°35° 35°

c

35°35° 35°

30°30° 30°

30° 30° 30° 30°30° 30° 30°

35° 35°

a° °n° ° an°° n° m°ma°°a am°n° °n°° ° m°m° a° n° m°

c° c° a° aba°°°bb°°c° Question 3 Find the value of each pronumeral. 50°50° 50° a b c° x° xxy°°° yy°° 75°75° 75° a°ab°° c°c°° c° 60° 60° a ° 60° ° a°ab°°b°° cc°°b° a° bb°° 50° 75° x° y° 50° 50° 50° °° y 75° x x°° y° 50° 60° 50° x°x75° 75°75° 60° 60° °y° y° 75° 60° 50° 60° 75° x° y° 60° 60°

Question 2 Find the value of each pronumeral. 30°30° 30° x° xx°° y° yy°° a b x°x°120° a°a°° a° 35° x° 120° a°a° 35° 35° 120° 120° x°x°°120° 35°35° 35° 120° a° 30° x° 120° x° 35° y° ° 30° 30° °° x° y ° 30°30° x y ° 30° x°x° y°y° 30° x° y°

45° 45° 45° 45°45° 45° 45°

y° yy°° 50° 60° x°x° 50° 50° 50° 60°60° 60° 60° b65° ° 65°65° x ° 50°50° e f x ° ° xx60° °° b°° bx°° xx°° x ° b°b° 60° x°y° 50° 60° 60°x60° ° y°° y° b° y° y°y° 60°60° 60° y° 50°50° 50° 50° y°y°° y° 60° y° 50°50° x ° 65° x°yx°° 50° 65° 65° x°° x° x°x° 65°65° x°x°° x° 65° x° 65° x°

d

x° xx°° 60°60° 60°y° yy°°

x°x° x°x°° x° x°

c

m°mm°° m°m° m°m°° m° m°

d e f a° aa°° 85° 85° 145° 145° 145°

145° 145° 145°145° 145° 145° 145°

80°80° 80°

y° yy°° x° xx°°

80° 80° 80° 80°80° 80° y°80° y° y°yx°° ° y°° x° yx° °xx°° x°


a° aa°° c° cc°°

b° bb°°

85°

c° c° 130° 130° 50°50° 50° 130° b°abb°°° 40° c° a°a° 40°85° 40° a ° 85° b ° 85° ° a° 85°85° ba°° °ab°° a°ca°°°c°°a°c° 85° b ° b° a° ca°°c° 85° b° c ° c ° 130° b° 50° 40° c° c° 130° b°° b° 50°50° 40° 130°130° 50° 50° ° c°° 40°c40° 130° b ° 40° 130° b° 50° 40° c° 130° b° 50° 40° Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook Excel Essential Skills Mathematics Revision & Exam Workbook Year 8



UNIT 4: Triangles and the value of the pronumerals Question 1 Find the value of each pronumeral. a

63°

b

x°

x°

65°

65°

y° y°

65°

c

y°

d e f

x°

35°

a°

30°

a°

140°

20°

Question 2 Find the value of each pronumeral. a

45°

a°

b 62°

100°

a°

118°

x°

c

35°

130°

105°

b

x°

110°

Question 3 Find the value of each pronumeral. a

x°

y°

58°

115°

c

80°

d e f 55°

a°

35°

m° x°

a°

y°

x°

88° 110°

65°

135

Chapter 12: Reasoning in geometry © Pascal Press ISBN 978 1 74020 033 2

75°


Reasoning in geometry m°mm°°

Excel 80° 80° 80°

80°80° 80°

110° 110° angle sum of a quadrilateral UNIT 5:110° The m° 80° m°° 145° 145° 145° 80° 80° mm °

80°p° pp°° n° nn°° 110° aa°° value of each pronumeral. Question 1 70° 70°70° 110° Finda°the m° ° 110° 80° m 110° 80° a 145° b n° m ° 145° 110° 145° ° p 80° a° 70° 145° n° p° a° 70° 110° 70° n°n° p°p° a°a° 70° 145°110° 145° 70° nn° ° pp° ° 145° aa° ° 70° n° p° a° 70°

Mathematics Study Guide Year 8

140° 140° 140° Pages 199–230

c

80° 80° 140° 80° 80° 140° 140° 140° 80° 80° 140° 140° 80° 140°

a° aa°°b° bb°° a° b°b° a° a°a° b°b° aa° ° bb° ° a° b°

130° 130° 130°

130° 130° 130° a° aa°° n ° nn°° 130° 130° 130° 130° 140° 140° 140° 130° d e f 130° 60°60° 60° n ° a ° 55° 55° 55° 120° 120° 120°m ° m m ° ° 130° n n °° 130° x ° x x ° ° a°° 130° n° 130° 140° a°a140° 130° 60° 140° n°55° ° 140°a° 60° 60° 120° m° 130° n x ° 60° a° 55° 120° m m°° 55° 120° x ° x ° n °55° 140° 120° m° 130° a° x° 130° 140° 60° 60° 55° 120° m° 140° x ° 55° 120° m° 60° x° 55° m° 120° x°

a° aa°° x°° Find the unknown m°mm°° 135° 135°x° x Q135° uestion 2 angles. a

m° 135° x°xx°° y° yy°° 120° 120° 120° m°° 135° 135° mm ° 135° x° 220° 220° 220° m° ° 135° x° y° 135° x° yy°° 120° 120° m 120° x ° m ° y ° 135° 220° 120° 220° 220° 220° 120° y°y° 120° 220° y° 120° 220° 220°

b° bb°°

m°mm°°

b a° b°

a° a°a° aa° ° a°

b° b°b°

bb° ° b°

145° 145° 145°

145° 145° 145° 145° 145° 145° 145°

c

n° nn°°

n° m° n° m°° 110° 110° n°n° p° pp°° mm ° 110° m° ° npn°°° m 110° n° pp°° m°110° 110° p° 110° 110° pp° ° 110° p° 110°

87°87° 87°

2a2a °2a°° Question 3 Find the value of the following pronumerals. p° pp°n° ° nn°° 87° a ° a a ° ° 50° 50° 50° a b c 87° 87° 2a° 3a3a °3a°° 20°20° 20° 87° 70°70° 70° p°p 2a°° 2a p°°n°nm° °mm°° 2a ° 4a4a a° 87°50° p ° ° 4a ° ° a ° a a ° ° n°n° aa°° 87° 50° 50° 2a ° a ° 50° 3a ° ° ° 87° 20° 70° 2a° 3a°° 3a pp° m 20° 70° 20° 70° m n°mn°°°° a ° 4a 2a ° ° 3a° 50° p ° 20° 70° a ° m a° 50° 4a ° 4a ° n° a° 4a° 3a° ° 50° a°a° 20° a° 70° 3a 20° 70° mm° ° 4a° °3a° a° 70° 20° 4a m° a° 4a° a °

d e f

m°mm°°

30° 30°30°

m° m°° mm ° 30° 30°m° 30° ° 30° m m ° 30° 30° 30°

136

60°60° 60°

60° 60° 60° n° n60° n°° 60° 60° 60° n° n° n°n° nn° ° n°


100° 100° 100°

2a2a °2a°° 3a3a °3a°°

2a°

° 2a°° 3a3a 2a 3a°° 2a ° 3a ° 2a ° 3a° ° 2a° 3a 2a° 3a°

100° 100° 100° 100° 3a 3a °3a°° 100° 100° 3a ° 3a 3a100° ° 3a° ° 3a° 3a° 3a°

3a3a °3a°°

3a° 3a °° 4a3a 4a 3a °°4a°° 3a° 4a° 3a° 4a3a °° ° 4a4a ° 4a° ° 4a 4a°

Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook




UNIT 6: Transformations Question 1 Complete the following sentences. a Under a

a shape is moved from one position to another.

b If the shape is moved by sliding, the transformation is

.

c If the shape is moved by flipping, the transformation is

.

d If the shape is moved by turning, the transformation is

.

Question 2 N ame the transformation used when each of the following shapes is moved to its new position. a b Q' Q A B A' B' D

C D'

X

C'

P

Y

R

P'

R'

G

c d Z'

Z

Y'

H H'

X'

I I'

G'

O

P

e f M L' O' L

T'

M'

N N'

P' Q'

S'

T

Q

S

R

R'

A g h V W B

C F'

Y D

V'

Y'

W'

X'

X

E

F

C' E'

D'

B'

A'

137





UNIT 7: C ongruence of plane shapes using transformation Question 1 Complete the following. a The symbol for congruence is

.

b Congruent shapes have the

shape and the

size.

c Two plane shapes are called congruent if one shape fits exactly on top of the

other by Ba

B

B

90°

90°

.

D

D

90°

90°

D

90° d The congruence statement of a ABC and 90° a DEF is written as A

60°

60°

A

60° 2 N Question ame A B

a

90°

A

30°

30° 60° C E C E the 30° transformation has AC E A60° that D D A D 30°

30°

30°

60°

30°

90° 30°

60°

30°

30° 30°

B

60°

F

90° 90°60° 60° 60° 60°90° 90° B C C E F 30° E 30° 90° 60° 90° C E FE E

B

F

30°

A D b

30° F

30° in each pair of congruent triangles below. been D used F

60°

C E

.

E

60°

F

60°

60° B 90° D 90° D 90° 60° 60° 90° 90°90° BB C E F 90° D 90° E30° c 30° 60° 60° 30° 30° 60° A A 30° C C 60° 30° A C B 90° D 90° B

30°

60° 30° A C

Question 3 For each A pair A of congruent D D triangles below, write the congruence statement. A

D

L P a b P P

B B

A B CE

CE

D

F Q

138

B

F Q

CE

E 1 74020 033F2 Q © Pascal Press ISBN C 978

L

R M

G

R M R M

F Q

P

L

L

G c G

J

J

I K

I K

J

HN

N

N GH

H JI K

L

L

L

Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook R Skills M MathematicsNRevision H & Exam Workbook I K Year 8 Excel Essential

L



UNIT 8: Recognising congruent figures Question 1 Complete the following sentences. a Congruent figures have exactly the

size and the

shape.

b In congruent figures, i

.

matching sides are

ii matching angles are

.

iii matching areas are

.

c The symbol for congruence is

.

Question 2 Name the congruent faces in each prism.

B C a b S A

D

P

F

T

U

G

E

Q

H

R

Question 3 Name the pairs of congruent figures. A

A

B

B

C

G

H

G

C

D

H

I

I

J

N

D

E

E J

K

L

K

F

F

L M

M

N

Question 4 The following pairs of figures are congruent. a Name all pairs of matching angles. b Name all matching sides.

I L

O J

K

M

N

139


P




UNIT 9: Recognising congruent triangles Question 1 Complete the following sentences:

a b c d

Two right-angled triangles are congruent if two sides and the one triangle are equal to Two right-angled triangles are congruent if three of the other triangle. Two right-angled triangles are congruent if one triangle are equal to Two right-angled triangles are congruent if two sides and one are equal to

and the included

of of the other triangle. of one triangle are equal to

and the h of one of the other triangle. and one of one triangle of the other triangle.

Question 2 Name the pairs of congruent triangles.

M A E G J K

L

T

I

D

B

C

P

F

H

Q

V

S

X

Y

A

W

U

R

O

N

A

R

Z

T

Question 3 T he following pairs of triangles are congruent. Fill in the blanks for the corresponding P angles. X A D a b

F

C

B

E

Q

R

Y

∠P = ∠R =

∠BCA =

Z

∠Q =

Question 4 Divide each shape into two congruent triangles using a single line. a

b

c

d

Question 5 There are four pairs of congruent triangles in each shape. Name the different pairs. A a b

C

B

G

F E

D


P

T

U Q

S R




UNIT 10: Naming congruent triangles Question 1 Two pairs of congruent triangles are drawn below.

a b D A

45°

B 70°

P

45°

65°

E 70°

C

13 cm

65°

D

A

Q

F

45° i Which45° side corresponds to AC

B 70°

65°

C

EA 70°

65°

i

D

F

S

13 cm

12 cm 12 cm

R

5 cm P

T

U

5 cm

S

Which angle corresponds to ∠QRP? 13 cm

13 cm

Q

12 cm 12 cm

5 cm

R

T

5 cmP

U

S

45° ii Name these congruent triangles, ii Name these congruent 45° triangles, 13 cm 13 cm in the 12matching cm giving the vertices in the matching order. giving the vertices order.

B 70°

65°

C

E 70°

iii Write the congruence statement. E

F

R

T

U

5 cm

E

F

H E

H

G F

G

Complete the following statements for the parallelogram EFGH:

a ∠EFH =

S

b H EF =

P

∠EHF =

P

∠HEF =

S

T

FH =

Q

R

Question 3

T

HE =

P

S

c ΔEFH ≡Δ G

U

U

W

Q W

R

5 cm

iii Write the congruence statement. F

Question 2

65°

12 cm

Q

V V

T

U

W

V

Q

R

Complete the following statements:

a SP =

b ∠SPQ =

PQ =

∠PSQ =

QS =

∠PQS =

c ΔPQS ≡ Δ

141





UNIT 11: Tests for congruent triangles Question 1 Complete the following sentences.

a Two triangles are congruent if three sides of one triangle are equal to of the other triangle. b Two triangles are congruent if two sides and the included angle of one triangle are equal to

of the other triangle.

c Two triangles are congruent if two angles and a side of one triangle are equal to


d Two right-angled triangles are congruent if the hypotenuse and one side of one triangle


are equal to

e The symbol for congruence is

.

Question 2 In each pair of triangles below, write the congruence test that would be used to prove that the triangles are congruent. a b

c d

A

Question 3 a Name the common side in ∆ABC and ∆ADC. b

Are the triangles congruent?

c

If they are, name the test that you can use to prove it.


B C

D




UNIT 12: A pplying properties to solve numerical problems

Question 1 Find the value of the pronumerals in these quadrilaterals. c° 120°

96°

x° y° a b c c° c° 96° a° a° 96° 120° 120° b° b° 48° x° y° x° b°y° a° a°

a°

b°

120°

120°

a°

a°

a°

c° a°

120° a° a°

95°

b°

c°

120°

120° 95°

48°

b°

c °

48°

x° a°

96°

y°x°

96°

b°120°

48°

95°

130°

y °

a°

y°

48° 48° a° 96° b° c° b°x° 96° y° x° a°120° y° a°

a°

48° 130°

a°

c°

c°

b°

b°

a°

a° b°

130°

6

cb° °

65°

y° c°

70° 70° x° Question 2 Find the value of each pronumeral in the following quadrilaterals.

88°

c° x°

y°

c°

65°

70° 88°

a b c

a° a°

a95° °

x120° °

95°

95°

60°

a°

a° 120°

120°

130° ax°°

95° 150° x° 120° 150°

130°

y°

60°

60° 130°

a°

65°

y°

130° a° 150°

a°

y° y°

a°

70°

y°

125°

125°

a° 150° 150° x° x° Question 3 Find the value of each pronumeral.

70°

65°

y°

b°

y° 70°

b°

a65° ° x° 88°

c°

a°

b°

x°

88°

b° c°

125° 88°

70° x° 88°

65°

x° c°

b°

a b c

x° 60°

60°150°x° 60° 60°

y°

150°

y°

y°a°

y°

125°


a°125° a°

50° 10°

a° a°

125°

b125° °

a° 50°

50° 10°

b°

a° 50°

50° a° 50° 10° 10° 50°

c°

50°

b°

b° c°

50°

c°

c°

a°

50° 10°

50°

b°

b°

50°

b °

50° 50° b° b° 10° Skills Mathematics 10° Excel Essential Revision & Exam Workbook Year 8

143



UNIT 13: More numerical problems

Question 1 F or each of the following quadrilaterals, (i) write an equation first (ii) solve the equation to find the value of the pronumeral (iii) find the size of each angle. a b c x° x°

x°

x°

x°

x°x°

x°

x°

x°

x°

6x° x°

6x° (10x + 7)°

(8x + 3)°

(10x + 7)°

(8x + 3)°

y° y°y°

y°

y°

3y°

3y°

y°2y°

2y°

y°

3y° 3y° 3y°

3y°

2y° + (x3)° + 40)° x° (8x2y°

(x + 40)°

110°

(10x + x° 7)° 3y°

a°

3y°

2y° 2y° 2y°

2y° 6x° x°

2y°

x°

2y° 2y° 2y°

a°

2y°

2y°

y°

x°x°

x°

2y° x°

x° x°

2a° 2y° a°

2a°

a°a°

2a° 2a° 2a° a° (a + 30)° (a + 30)° 110° x° a° 2a° 2a° 2a° 2a°

110°

2a° (x + 40)° a°

x°2a°

a°

x°

30)° d e f (a + 30)° (a(a ++ 30)° x° 110° 6x° 6x° 6x° 7)°7)° (10x (10x + (10x 7)°+ +

(8x ++ 3)°3)° (8x +(8x 3)° 6x°

6x°

x°

(10x + 7)° (10x + 7)°

(8x + 3)° a° (8x + 3)° b°

a°

b° Question

30°

c°

x°

b°

c°c° 2 b°c°b° Find

40)° (x + 40)° (x(x ++ 40)°

x°x°

x°

30° a° x° x°

c°

30° 30° 30° a°a°

110° 110°

x°

x°

b°

c°

a°

a°a°

a° x°

a°

x°x°

110°

30°

a° a° (x + 40)° (x + 40)°

2a° 2a° 2a° 2a° 2a° 2a°

x°

110°

x°

c°

a°a° (a + 30)° (a + 30)° 2a°

a°

115°

a°

a°

c°

c° b°

b° 115° 115° 115°

c°

the value of each pronumeral.

2a° 115° 2a°

115° 2a°

b°

c°c°

b°b°

b°

115° a b c a° b°

30°a°

b° c°

30°

a° e° a° 35°

c° d°

b° d°

e°

35° 35° e°e° 35°

d° d°d°

e°


e° 35°

115° a°

35°

e° b°

c° 80° c°

a°

a°a°

a°

a°

b°

e°

35°

80°d°

c°

b°

80°

Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook b°

80° Exceld°Essential Skills Mathematics Revision & Exam Workbook Year 8 c°

d°

a°

c°

b° b°b° 80° c°c°80° 80°

c°

35°

a°

b°

c°

c°

b°

80°

2a°

Reasoning in geometry TOPIC TEST

PART A





1 Two triangles are congruent if they are the:

A same shape only B same size only

C same shape and size D none of these

2 What is another name for the transformation known as translation?

A flipping

B sliding

C turning

3 All congruent triangles are:

A equilateral

4 What is the value of x?

A 36 C 45

5 What is the value of a?

A 50 C 75 A

55° 50°

≡

C

B 90°

=

B equilateral

50°

1 a°

D 360°

1

C congruent

D none of these

1

C 180°

D 90°

1

D none of these

1

C congruent


10

145


1

1

10 The longer diagonal of a kite divides it into two triangles that are:

A isosceles

3x°

D none of these

C 270°

B isosceles B 270°

1

a° 55°

9 The angle sum of a quadrilateral is always equal to:

A 360°

D right-angled 2x°

8 A diagonal of a parallelogram divides it into two triangles that are:

A equilateral

1

x°

7 The angle sum of a triangle is always equal to:

A 180°

D enlarging 2x° 4x°

B 55 D 105 B

3x°

x°

B 40 D 54

6 The symbol for congruence is:

|||

C similar 4x°

B isosceles

1


Reasoning in geometry TOPIC TEST

PART B





1 a

1 C

c Name triangles that are congruent.

D 1

d Name a congruence test.

1

B

Name the pairs of equal sides.

e Under what single transformation will one triangle map onto the other?

1

P

b Name the pairs of equal angles.

A

c Name the triangles that are congruent.

D

QA y°

d Name a congruence test.

D

A A

a Find the value of x.

b Find the value of y.

c Write the congruence statement applying to the two congruent triangles shown. d State the congruence test.

e Under what single transformation will one triangle map onto the other?

D

1

30°

110° C

B

S x° T

R

y° D

30°

B B

x°

110° C

30°

1

1

110° C x°A

y°

B

x°

y°

30°

D

110° C

B

1 1

C

A

1

D

B

1

A

4 In the kite drawn opposite, ∠ADC = 96° and ∠DAC = 54°.

Find the size of ∠DCB.

1

1

3 For the parallelogram, drawn opposite:

E

A

b Name the pairs of equal angles.

2 a

Name the pairs of equal sides.

D

1

A

B C

D

B

Total marks achieved for PART B C

1

15

C



Chapter 13

Probability


UNIT 1: The language of probability Question 1

sing the terms of probability, rate the chance of these events as certain, likely, unlikely, U impossible or even.

a The sun will rise tomorrow.

b There will be at least one cloud in the sky tomorrow.

c If a die is rolled, a seven appears.

d I can win the raffle if I have just one ticket.

e Sunday will follow Monday next week.

f John will live to the age of 142 years.

g scoring an even number when a die is thrown

h A year will have 460 days.

Question 2 S elect the most appropriate from 0%, 30%, 50%, 70% or 100% to describe the chance implied by each of the following words. a maybe b definitely

c perhaps d sure

e an outside chance

f 50–50

g against all odds

h probably

Question 3 Choose from certain, most likely, even chance, unlikely or impossible to best describe an event which has a probability of: a 10% d

b 0

c 100%

7 1 e f 95% 8 2

3 4 g 0.005 h i 97 5 j 1

k

1 l 75% 64

147

Chapter 13: Probability © Pascal Press ISBN 978 1 74020 033 2


Probability


UNIT 2: Sample space Question 1 Write the sample space for each of the following. a choosing a month of the year

b selecting a primary colour c choosing a letter that comes before I in the alphabet d choosing a letter that comes after V in the alphabet e choosing a square number less than 50 f choosing a letter from the word MATHEMATICS g choosing a whole number greater than 25 and less than 30 h choosing a season

Question 2 The letters of the word CONSCIENTIOUS are written on cards and turned face down. A card is then selected at random. a Write the sample space. b How many elements does the sample space have? c How many different elements does the sample space have?

Question 3 For each of the following events, write the number of elements in the sample space. a selecting a letter from the alphabet b selecting a day of the week to visit a relative on c selecting a colour from the rainbow (red, orange, yellow, green, blue, indigo, violet) d selecting a captain from a 15-player soccer team



Probability


UNIT 3: Outcomes

Question 1 F or each of the following, state whether each element of the sample space is equally likely to occur. a choosing a letter from the word PINEAPPLE

b the weather on a given day c the gender of a baby being born d choosing a whole number between 21 and 30 e the result of a horse race

Question 2 Write the outcomes for each of the following. a selecting a letter from the word HAPPINESS

b selecting a sock from a drawer containing black and grey socks c tossing two coins at once d rolling two dice and adding the numbers together

Question 3 F or each of the following, state whether each of the possible outcomes is equally likely to occur. a tossing a coin

b tossing two coins at the same time c choosing a letter from the word ELEPHANT d the result of a football match e choosing a card from a standard pack of cards.

Question 4 The season of each Year 8 student’s birthday in a particular school is recorded below.

Boys Girls Total

Summer (Dec.–Feb.) 15 8 23

Autumn (Mar.–May) 15 20 35

Winter (June–Aug.) 14 16 30

Spring (Sept.–Nov.) 18 16 34

Total 62 60 122

How many outcomes are there for each event below?

a boys born in winter

b girls born in spring or autumn c boys or girls born in summer d girls born in a season beginning with the letter Q e boys born in a season beginning with the letter S

149



Probability


UNIT 4: Theoretical probability

Question 1 A card is drawn at random from a normal pack of 52 cards. Find the probability that the card is: a a club

b a black card

c an ace

d not a spade

e a black ace

f a red card

Question 2 From the letters of the word CHANCE, one letter is selected at random. What is the probability that the letter is: a a vowel?

b a consonant?

c the letter C?

Question 3 A die is thrown once. Find the probability that it is: a a five

b an odd number

c a number greater than 2

d zero

e a prime number

f a square number

Question 4 A bag contains 6 yellow, 4 blue and 5 red balls. If a ball is drawn at random, find the probability that it is: a yellow

b red

c blue

d not yellow

e white

f either blue or red

Question 5 The numbers 1 to 15 are written on separate cards. One card is chosen at random. What is the probability that the number is: a even?

b odd?

c less than 5?

d divisible by 3?

e divisible by 5?

f greater than 10?

Question 6 The numbers from 1 to 7 are written on separate cards. One card is chosen at random. What is the probability that: a the number is odd?

b the number is even?

c it is 6?

d it is zero?

e it is a prime number?

f it is divisible by 3?

Question 7 A letter is chosen from the word PROBABILITY. What is the probability that the letter is: a a vowel?

b a consonant?

c the letter B?

d the letters P or B?

e the letter M?

f the letter Y?



Probability


UNIT 5: Complementary events Question 1 A die is rolled, what is the probability of: a not getting a 6?

b not getting a 3?

c not getting a 4 or 5?

d not getting an even number?

Question 2 F rom a pack of 52 playing cards one card is drawn at random, what is, the probability that it is not a club? Question 3 The probability of winning a competition is

1 . What is the probability of losing? 500

Question 4 A coin is tossed once. What is the probability that the result is: a not a head?

b neither a head nor a tail? c either a head or a tail? 19

Question 5 T he probability of a train arriving on time is , what is the probability that it will not 32 arrive on time? 1 5

Question 6 The probability of it raining today is , what is the probability of it not raining today?

Question 7 A bag holds only two-dollar coins. If a coin is selected at random from the bag, what is the probability that it is not a two-dollar coin? Question 8 T here is a 27% chance of winning a game, what is the probability of not winning the game? Question 9 T he probability of a baby being born with a particular defect is 0.005, what is the probability of the baby being born without that defect? Question 10 A s the result of an experiment it is determined that the chance that any motorist at a particular location is exceeding the speed limit is 1 in 5. If a motorist at that location is randomly selected, what is the probability that she or he is travelling at, or less than, the speed limit? 151



Probability


UNIT 6: Venn diagrams

Question 1 For the Venn diagram shown, fill in the missing words to make the statements true. There are

students who play both soccer and hockey;

students who play soccer or hockey, but not both; students who play neither sport; soccer or hockey or both; and

students who play students in Year 8.

Sport played by Year 8 Soccer

32

12

Hockey

18

23

Question 2 For the Venn diagram shown, fill in the missing words to make the statements true. There are

students who study Japanese;

students who study French; neither language; and

students who study students who study both languages;

students in Year 8.

Languages studied by Year 8 Japanese

French

27

41

19

Question 3 Use the following information to work out the missing values in the Venn diagram shown. There are 120 students in Year 8, of whom 46 own neither a dog nor a cat. 62 own a dog or a cat but not both, while 35 own cats. A=

B=

C=

D=

Pets owned by Year 8 Dog

A

B

Cat

C

D

Question 4 In a Year 8 class, students play cricket or basketball or both. Eighteen play cricket, 15 play basketball and 6 play both cricket and basketball. a Show this information by drawing a Venn diagram

b How many students play cricket but not basketball? c How many students play basketball but not cricket? d How many students play cricket or basketball but do not play both? e Find the total number of students in class.



Probability


UNIT 7: Using language of ‘at least’, exclusive ‘or’, inclusive ‘or’ and ‘and’

Pages 252–268

Question 1 In a family of three children, find the probability that there is at least one girl. Question 2 When a coin is tossed four times, find the probability of getting at least one head. Question 3 F rom a pack of cards numbered 1 to 10, one card is selected at random. Find the probability that the number drawn is: a odd b greater than 5 c less than 4 d greater than 5 or less than 4 e odd or greater than 5 f odd and greater than 5 g odd and less than 5 h greater than 5 and less than 4 i

less than 5 or divisible by 6

j less than 5 or divisible by 3

Question 4 F rom a pack of 52 playing cards, one card is drawn at random. Find the probability that it is: a a black card or a ten b a black ten or a king c a spade or a ten

Question 5 Two dice are thrown. Find the probability that the throw gives: a a double or a total of 10 b a double or a total of 15

153



Probability


UNIT 8: Two-way tables

Question 1 L achlan takes note of the occupants of cars as they leave a car park. He records whether the drivers are male or female and whether or not there are passengers. The results are shown in the two-way table. Male Female Total

Passengers 48 X 102

No passengers 36 62 Y

Total 84 116

a What is the value of: i

X?

ii Y?

b How many cars were there altogether? c What fraction of the drivers were female? d Of the male drivers, what fraction had passengers? e What percentage of cars did not have passengers? f What is the probability that a driver, selected at random, is a male with passengers? g What is the probability that a female driver, selected at random, has passengers?

Question 2 A survey was conducted to see whether students preferred strawberry- or chocolateflavoured milk. The results are shown in the table. Male Female Total

Strawberry 98 66 164

Chocolate 52 84 136

Total 150 150 300

a What is the probability that a student chosen at random from the group: i

is male?

ii preferred strawberry?

iii is a female who preferred chocolate?

iv is a female or preferred chocolate?

b What is the probability that: i

a male student preferred strawberry?

ii a student who preferred strawberry was male?

Question 3 185 out of 300 boys and 165 out of 250 girls surveyed had seen a particular movie. a Complete the two-way table to display the information. Boys Girls Total

Seen the movie

Not seen

Total

b W hat is the probability that a person who has seen the movie chosen at random from the surveyed group is a girl?



Probability TOPIC TEST

PART A




Total marks: 12

1 How could you describe the chance of getting a number less than 3 when rolling a die?

A impossible

B unlikely

C even chance

2 One of these cards is selected at random. What is the probability

3

4 5

6

7

8

9

D likely

that the number on the card is either odd or less than 5? 1 2 3 4 5 5 5 5 A bowl holds 9 red, 5 green and 6 black jellybeans. If a jellybean is taken at random from the bowl, what is the probability that it is either red or black? 2 3 7 9 3 4 10 11 The probability of an event is 1. How could you describe the chance of that event occurring? impossible unlikely likely certain A card is drawn at random from a standard pack of playing cards. What is the probability that the card is a black heart? 1 1 3 0 4 2 4 A card is drawn at random from a standard pack of playing cards. What is the probability that the card is either black or a heart? 1 1 3 0 4 2 4 A letter is chosen at random from the word EXCELLENT. How many different elements are in the sample space? 6 7 8 9 A bag contains 3 white, 2 yellow and 5 black balls. If a ball is drawn at random, the probability of a white ball is: 1 1 3 3 10 3 7 10 This two-way table shows the number and colour of ribbons Blue Red Boys 12 18 won in a competition by some students. What is the probability Girls 20 10 that a boy chosen at random won a blue ribbon?

Marks

1

A

B

C

D

1

A

B

C

D

1

A

B

C

D

1

A

B

C

D

1

A

B

C

D

1

A

B

C

D

1

A

B

C

D

1

2

A 3

2

B 5

3

C 8

1

D 3

1

10 Referring to the table in question 9, what is the probability that a red ribbon was won by a girl? 5

A 9

5

B 14

1

C 2

1

D 3

1

11 A ticket is chosen at random from a hat. The probability that the ticket is green is

1 5 and the probability that it is blue is . What is the probability that the ticket is neither blue 12 12

nor green? 1 5 1 7 12 12 2 12 12 A number is chosen at random from the whole numbers 1 to 12 inclusive. What is the probability that the number is even or less than 8, but not both? 5 1 7 5

A

B

C

D

1

A 12

B 2

C 12

D 6

1


155


12


Probability TOPIC TEST

PART B





1 Of a group of 40 students in Year 8, 20 study

Italian, 25 study French and 5 study neither. a Show this information on a Venn diagram.

1

b How many students study both the languages?

1

c How many study Italian or French but not both?

1

d What is the probability that a randomly chosen student from the group studies:

i

French?

ii Italian but not French?

1 1

2 A card is drawn at random from a normal pack

of 52 cards. Find the probability that the card is:

1

1

a a diamond

b a queen

1

c black and a heart

d a king or a jack

1

e

not a club

1

3 Write the complement of the following.

a tossing a head with a coin

1

b not winning a cricket match

1

4 In a normal pack of playing cards, E represents the

event ‘drawing a red card’. If one card is drawn at random, find:

a P (E)

1

b P (Ẽ)

1

c P (E) + P (Ẽ)

1



15


Chapter 14

Statistics


UNIT 1: Review of basic statistics

Question 1 Some students sat for a quiz. The results are shown in the table. Score 6 7 8 9 10

Frequency 2 5 9 7 3

a How many students scored 7?

d Show these results in a frequency histogram.

b Which score has a frequency of 7? c How many students were there altogether?

Frequency (f)

Score (x)

Question 2 A die was rolled many times. a Complete the frequency distribution table.

Score 1 2 3 4 5 6

Tally |||| |||| |||| || |||| |||| |||| | |||| ||| |||| |||| |

Frequency

Cumulative frequency

b How many times did a score of 4 occur? c Which score occurred a total of 8 times? d How many times was the die rolled?

f How many scores were less than 5? g How many scores were greater than 2? h Draw a cumulative frequency histogram.

Cumulative Frequency (f)

e How many scores were there of 3 or less?

Score (x)

157

Chapter 14: Statistics © Pascal Press ISBN 978 1 74020 033 2


Statistics


UNIT 2: Collecting data Question 1 Complete the following.

a When a surveyor collects information about a whole class of objects or the total number of people,

the process is called

b When each and every member of the population is surveyed it is called a c When only a part of the population is surveyed it is called a

Question 2 State whether a census or a sample should be used in each of the following. a the average number of lollies in a box of lollies b the total number of books available for sale in a bookshop c the number of students who travel to school by car d the number of people who bought two tickets for a movie e all the students and teachers in a high school who voted for the selection of a new school captain. f the yearly exam results of all the students in a high school

Question 3 State whether a sample or a census is used in the following. a the total number of people working in a hotel b the number of adults who went to a hall to attend a meeting c the total number of students in a high school d the number of students who were selected to participate in a swimming carnival e the number of teachers who work in the state of NSW f the number of people who travel to work by bus



Statistics


UNIT 3: Types of sampling Question 1 Complete the following.

a A random sample may be defined as a sample in which each member of the population has the same

of selection.

b A systematic random sample is a sample where those chosen for the sample are chosen in a

way.

c In a stratified sample, the population is divided into different sample is taken from each group.

and a

Question 2 S tate whether the sample chosen is a random sample, systematic sample or a stratified sample. a Every 20th bottle of juice coming off the production line is to be tested for quality and quantity. b In a survey, the names are drawn from a box. c I n a high school, there are 500 boys and 400 girls. The sample of students chosen consists of 50 boys and 40 girls to represent the school in a function.

Question 3 Which sampling method would be most suitable for each of the following? a A sample of milk bottles is to be inspected to check the quality of the milk. b The people of each state are to be surveyed to determine whether Australia needs a new flag. c to determine what new books the school library needs d checking the quality of shirts made by the manufacturer e A student is chosen from a class to give a message to the school office.

159



Statistics


UNIT 4: Classification of data Question 1 Answer the following questions.

a Briefly explain the difference between a census and a sample. b Briefly explain the difference between categorical (qualitative) data and numerical (quantitative) data.

c Briefly explain the difference between data that is discrete and data that is continuous.

Question 2 State whether the data is numerical or categorical. a the heights of horses

b the number of petals on flowers c the number of messages sent in a day d the colour of cars e the lengths of newborn babies f the type of pet that students have g the minimum temperature each day h the number of students in each class

Question 3 State whether the data is discrete or continuous. a the number of children in families b the lengths of cars c the number of days in months d the number of pencils in boxes e the heights of buildings f the number of biscuits in packets g the weights of babies h the masses of containers i the number of marks in tests j the diameters of tanks k the temperatures of patients



Statistics


UNIT 5: Classification of data and sample types

Pages 232–250

Question 1 S tate whether the data is numerical or categorical. If numerical, also state whether it is discrete or continuous. a the mass of packets of noodles

b the day of the week on which your birthday falls c the type of trees growing in a backyard d favourite colours e the number of students in each class at school f the heights of buildings g the heights of saplings h the ages of people at a concert i

the breed of dogs at a dog shelter

j the number of medals won at Olympic games k the type of medal (gold, silver or bronze) won at Olympic games l

maximum temperatures recorded

m favourite movies n sex of chickens o the weight of babies

Question 2 Determine whether the type of sample is random, systematic or stratified. a choosing the first 100 people that arrive

b selecting a boy and a girl from every class c picking names out of a hat d every 100th name from the telephone book e all the members of a club whose membership numbers end in 7

Question 3 J ulie wants to conduct a survey of teachers. She knows that quite a few of the teachers are attending a lunchtime meeting and decides to use these people as her sample. Explain why this is not a random sample. Question 4 G reg wants to conduct a survey of the opinion of students about the school uniform. He decides to select a stratified sample. There are 1250 students at the school, 215 in Year 7, 200 in Year 8, 210 in Year 9, 220 in Year 10, 225 in Year 11 and 180 in Year 12. If Greg decides to survey 250 students, how many should he choose from each year? 161



Statistics


UNIT 6: Mean Question 1 Find the mean of the following sets of scores. a 3, 5, 7

b 4, 7, 8, 12, 13

c 60, 62, 69, 75

d 5, 6, 6, 8, 11, 18

e 0, 1, 3, 4, 6, 7, 7, 8, 9

f 14, 15, 17, 19, 23, 25, 27

g 2, 2, 2, 2, 3, 3, 3, 4

h 6, 7, 7, 8, 8, 8, 9, 9, 10, 10

i

3, 4, 4, 4, 5, 6, 7, 7, 8, 9, 9

Question 2 Find the mean, giving each answer correct to one decimal place. a 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7

b 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 6, 6

c 11, 12, 14, 14, 16, 17, 17, 17, 20

d 44, 44, 44, 44, 45, 46, 46, 47, 48, 48, 49

Question 3 Complete the tables below and calculate the mean. a

x f fx

b c x f fx x f fx

1

5

0

11

6

3

2

8

1

13

7

5

3

6

2

14

8

6

4

9

3

12

9

7

5

12

4

10

10

4

Total

Total

Total

Question 4 Answer the following questions.

a Find the sum of the scores if the mean of 50 scores is 78.6.

b The mean of 9 scores was 12. A new score of 15 is included. What is the new mean?

c F rom 8 tests, Max has a mean mark of 73%. What must Max score in his ninth test to increase his mean mark to 75%?



Statistics


UNIT 7: Median and mode Question 1 Find the median of each set of scores. a 12, 13, 15, 17, 20

b 5, 5, 6, 7, 7, 8, 8, 8, 9, 9

c 73, 81, 76, 79, 80, 74, 70, 84, 74

d 29, 26, 30, 22, 29, 24, 30, 27, 22, 29

e 121, 108, 112, 123, 102, 120, 123, 105

f 56, 60, 68, 49, 66, 87, 67, 56

Question 2 Find the mode of each set of scores. a 2, 2, 3, 4, 4, 5, 5, 6, 5, 6

b 4, 8, 8, 9, 9, 9, 9, 9

c 2, 3, 3, 2, 4, 2, 5, 6, 5, 3, 3

d 52, 17, 18, 52, 53, 54, 52, 52, 53, 52

e 8, 9, 10, 8, 11, 8, 9, 8, 10, 8, 6, 8

f 5, 6, 5, 5, 7, 6, 6, 7, 6, 5

Question 3 Complete the table, then find the mode and median. a

Score Frequency Cumulative frequency b 1 3 2 6 3 8 4 7 5 5 6 4

mode =

median =

c

Score 5 6 7 8 9 10

Frequency Cumulative frequency 12 19 18 15 10 13

mode = median =

Score Frequency Cumulative frequency

d

Score

Frequency Cumulative frequency

16

8

16

5

17

6

17

7

18

7

18

8

19

10

19

14

20

5

20

6

mode =

median =

mode = median =

163



Statistics


UNIT 8: Using the mean, mode and median

Question 1 A foreign language class has just 6 students. The class sat for a test and the following marks resulted: 7, 93, 95, 96, 96, 99. a Find the:

i median

ii mean

iii mode

b B arry scored 93. ‘I did well in the test,’ Barry told his mother. ‘I was way above average.’ Do you agree with Barry’s statement? Briefly comment.

Question 2 When talking about real estate, people in the industry and the media refer to the median house price. Why is the median a better means of describing the data than the mean or mode? Question 3 A shop sells women’s clothes. The table shows the number of each size of dress sold over the previous month.

Size Number sold

8 2

10 13

12 28

14 42

16 35

18 26

20 23

22 19

24 21

a Find the mean dress size.

b W hat is the modal dress size? c W hat is the median? d T he shop owner is most interested in the modal dress size. Why do you think she would find that important?



Statistics


UNIT 9: Range Question 1 Find the range of the following sets of scores. a 3, 5, 8, 12, 17

b 1, 4, 9, 12

c 0, 5, 9, 11, 13, 18

d 56, 59, 65, 69, 77, 78, 84, 84, 91

e 23, 28, 35, 38, 44, 46

f 6, 23, 34, 49, 51, 68, 70

g 12, 9, 10, 17, 22, 9, 8

h 11, 13, 8, 21, 7, 24

i

7, 9, 6, 13, 15, 11, 9

k 109, 107, 123, 110, 101, 107, 105

l

j 30, 26, 24, 13, 3, 17, 35, 17, 21, 16, 7 69, 47, 53, 80, 37, 55, 64, 71, 83, 81

Question 2 Find the range for the scores in each dot plot.

• a b • • •

•

5

• • • • •

6

• • • • • • •

7

• • • • • •

8

• • • • •

9

• •

10

•

• • • •

0 1

• • • • • •

2

• • • • • • •

3

• • • • • • •

4

• • • • • • •

5

• • • • • • •

6

• • • • • •

7

• • • •

8

•

9

Question 3 Find the range for the scores in each stem-and-leaf plot.

a b 4 6 8 9 13 8 9 5 4 5 5 6 7 7 14 0 5 7 9 6 2 3 3 3 6 8 9 15 1 2 2 5 7 8 7 0 4 4 5 7 8 16 0 3 4 6 8 9 8 1 5 6 9 9 17 1 4 5 9 0 18 2

Question 4 Answer the following questions.

a The range of a set of scores is 25. If the lowest score is 13, what is the highest score? b The range of a set of 9 scores is 14. The highest score is 91. What is the lowest score?

165



Statistics TOPIC TEST

PART A





1 Niamh wanted to test a theory that older students preferred a different type of music to younger

students. She chose the youngest person from each Year 7 class and the oldest person from each Year 12 class to answer her questions. What type of sample is this? random stratified systematic census

A

B

C

D

1

2 A motoring organistion did a survey of the number of breakdowns experienced by motorists

over a month. This data is categorical.

A C numerical discrete.

B numerical continuous. D none of these.

For Questions 3, 4, 5 consider the scores 5, 7, 3, 3, 8, 2, 6, 3, 9 and answer the questions. 3 What is the median? 3 5 7 8

A

4 What is the range?

A 3

5 What is the mode?

A 3

1

B

C

D

1

B 5

C 7

D 8

1

B 5

C 7

D 8

1

6 Which of the following is not numerical data?

A values of cards chosen from a standard pack B weights of children C population of flying foxes in a colony D number of visitors to a theme park

7 For this set of data, which is the greatest?

Score

Frequency

A the mean C the mode

5

13

6

7

22

35

8

1

9

26

11

B the median D The mean, mode and median are all equal.

1

8 30% of a country’s population is aged over 60. How many people aged over 60 should be

included in a stratified sample of 250 people? 30 50

A

B

C 60

D 75

9 The mean of 8 scores is 12.5. A new score of 8 is included. What is the new mean?

A 12

B 12.5

C 13

D 13.5



1

1

9


Statistics TOPIC TEST

PART B





1 Patrick conducted a survey of opinions of an excursion. He chose the first five people to get

off each of the buses as they arrived back at school to answer his questions.

a Explain why this is not a random sample.

b If Patrick wanted to conduct a census what would he need to do?

1

1

2 40 people were randomly selected at a concert and asked their age.

The results were recorded in the table below. Age 12 13 14 15 16

Frequency

7

6

9

a What is the mode?

8

c Find the mean.

18

4

3

17

2

19 1

b What is the median?

d What is the range?

1 1 1 1

e What fraction of the people were more than 15 years old? 1

3 A high school has 500 girls and 700 boys.

a How many girls should be chosen in a stratified sample of 180 students?

b In another stratified sample of 300 students, 45 were in Year 12. How many Year 12 students are at the school?

1

1

4 The range of a set of 12 scores is 19. The lowest score is 8 and the mean is 11.

a What is the highest score?

b What is the sum of all the scores?


1

11

167


1


Exam Paper 1 Instructions for all parts • Attempt all questions. Time allowed: 1 hour Part A: Allow about 10 minutes for this part. Part B: Allow about 20 minutes for this part. Part C: Allow about 30 minutes for this part.

Total marks: 50

EXAM PAPER 1

PART A

Fill in only one circle for each question. Fill in only one circle for each question.

1

6 50

is equivalent to:

Marks 1

A 3%

B 6%

C 8 3%

D 12%

1

A −12 48

B −8

C 8

D 12

1

A 6

B 8

C 18

D 48

1

A 28

B 18

C 24

D 21

1

A –17

B –12

C 1

D 17

1

A x – 2

B x – 2x

C –x

D –2x

1

A 20

B –15

C 36

D 5

1

A The mode is 3. B The mean is 3.

C The median is 3.

D The range is 3.

1

A 16 mm

C 1600 mm

D 16 000 mm

1

2 If x – 10 = –2, then x equals: 3 2 × 4 equals:

4 The ratio of boys to girls is 4 : 3. If there are 42 children, how many girls are there? 5 (–3)2 + (–2)3 equals: 6 x(x – 2) equals: 2

2

7 –7 + 2 × –4 equals:

2

8 For the set of scores 2, 3, 4, 5, 5, 5, which statement is true? 9 1.6 m equals:

B 160 mm

10 When a die is thrown, what is the probability of getting an odd number? 1

1

1

2

A 4

B 3

C 2

D 3

1

A 0.02

B 0.2

C 0.5

D 5

1

11 A car uses 20 L of petrol for 100 km. At this rate, how many litres are needed to travel 1 km? 12 The area of a quadrant with radius 12 cm is:

A 6π cm 2

B 24π cm


2

C 36π cm 2

D 144π cm

2


1

12


EXAM PAPER 1

PART B

Answer each question in the space provided. Marks

1 Calculate 80 635 – 43 419.

1

2 Complete the table of values for y = 3x − 2.

x y

–1

0

1

1

2

3 How many litres are there in 3645 mL?

1

4 Simplify 8ab + 2ba.

1

5 Simplify 22 × 24 × 25.

1

6 How many thousands are there in 3 million?

1

1

7 Find 5 of 3.8 tonnes.

1

8 Write 48% as a fraction in its simplest form.

1

9 Simplify 4 – 2(a + 1).

1 1

10 Edwina draws a sketch of a building using a scale of 1 cm to 2 metre.

1

How long is a line representing a wall of length 12 metres?

11 What is the area of the figure shown? 12 Find the value of a 13 Calculate

2

1

10 m

b when a =12 and b = 9.

14 m

1 256 × 53 × .

14 Find the value of x.

7 m

1 1

4

135°

x°

1

15 A rectangular prism measures 8 cm × 3 cm × 5 cm. Find its volume.

1

16 How many metres are there in 0.95 km?

1

17 What is the sum of two complementary angles?

1

18 Factorise 6ab – 3b2 + 12a2b.

1

19 Seven tickets cost $27.65. How much would two tickets cost?

1

20 On a sports afternoon, half of Year 8 went swimming, a third of

Year 8 played basketball and the rest stayed at school. If 52 stayed at school, how many students were in Year 8?


20

169

Exam Papers © Pascal Press ISBN 978 1 74020 033 2

1


EXAM PAPER 1

PART C

Show all working for each question. Marks

D E 1 a ∆ABC ≡ ∆EFD b Find the area B of the 3 cm 4 cm

parallelogram 4 cm 3 cm F ABCD A

C

15 cm

i Name the side in ∆EFD that matches to BC.

7 cm

1

ii Name the angle in ∆EFD that matches to ∠ABC. 2 a

Simplify: 3a + 2a × 4 − 5a

1

b Expand: 5(2x − 3)

c Factorise: 3x − 24

1 1

3 Peta surveyed the staff and students at her

1

high school to see how many wore glasses and Staff how many didn’t wear glasses. Her results are Students partly displayed in the table below Total

a What number should be written at (a)?

Glasses 30 (b) 180

1

No glasses (a) 480 520

Total 70 630 700

b What number should be written at (b)?

1

1

If one person is selected at random from Peta’s school, what is the probability that he or she is: c a student who wears glasses? d a person who doesn’t wear glasses?

1

4 Calculate the time:

1 1

a 35 minutes after 11:43 am b 24 minutes before 8:15 pm c 1 hour and 52 minutes before 1:17 am

5 Find the value of the pronumeral in each of the following.

a

6 a

x°

75°

b

c

50° 15°

On the set of axes shown plot the line y = x + 1.

b Where does this line cut the x-axis?


1

1

3x° 130°

y

1

4

72° 65°

2

1 0

–4 –2

2

4

x

1

–2

1

–4

1

Total marks achieved for PART C

18



Total marks: 47

EXAM PAPER 2

PART A

Fill in only one circle for each question. Marks

1 (0.3)2 equals:

A 0.09

B 0.9

2 (5m2 × 8n4) ÷ (4m0 × 3n2) = 40 m 2 n 2 3

A

10 m 2 n 2 3

B

C 9.0

C

10 m 2 3n 2

D 0.03 10 m 2 3n 6

1

D

1

3 An article costing $4.00 is sold for $4.50. The profit as a percentage of the cost price is:

A 20%

B 12.5%

C 25%

D 37.5%

1

A 0

B 1

C 3

D 4

1

A 7x + 13

B 7x – 7

C 4x – 5

D 4x – 10

1

A $40

B $24

C $80

D $120

1

4 If x = 3 and y = 2, the value of x2 – xy is: 5 x + 3 + 2 (3x – 5) equals:

6 The interest on $500 for 3 years at an interest rate of 8% per annum is:

7 What is the capacity of an animal water trough in the shape of a rectangular prism with

dimensions 1.1 m by 2 m by 80 cm?

A 1.76 L

B 176 L

C 1760 L

D 176 000 L

1

A $30

B $40

C $50

D $60

1

A 1.189

B 0.8019

C 1.319

D 1.519

1

A y

B y + xz

C yz

D y + z

1

A 10

B 100

C 360

D 3600

1

A a

B a

C 2a

D 2a

1

8 If $80 is divided in the ratio 5:3, the bigger amount is:

9 The sum of the smallest and the largest of the numbers 0.519, 0.9, 0.89 and 0.289 is: 10 x is a factor of xy + xz. What is the other factor?

11 Express 360 tonnes per hour as kilograms per second. 12 a4 + a4 equals: 8

16

4


12

171


8


EXAM PAPER 2

PART B


1 Write 4:35 pm in 24-hour time. 15.6 2 Evaluate 4.2 − 2.54 .

1

3 Factorise 8a – 8.

1

1

4 Find the third angle in a triangle if the other two angles measure 53° and 42°. 5 Calculate the area of the kite where AC = 32 mm and BD = 18 mm.

1 D

A

E B

6 Adrian bought a case of 64 apples for $16.95. He wants to make a profit

1 C

of 30%. For how much, to the nearest cent, should he sell each apple?

2x 8 7 Solve 3 = 6 . 3

1 1

2

8 Simplify 3 4 – 1 5 .

1

9 A die is rolled. What is the probability that the number rolled is not a six?

1

10 Expand and simplify 8x – 3(x + 2).

1

11 Find the mean of the set of scores: 8, 6, 4, 6, 5, 6, 10

1

12 The area of a square is 20 4 cm2. What is its perimeter?

1

1

13 If A = 4b2 and A = 5, what is the exact value of b (b > 0)?

1

2

14 Find 3 of 1.5 litres.

1

15 What percentage is 43 seconds of 2 minutes?

1

16 If the bill at a restaurant for three people came to $129.90, how much

should each person pay? 7

1

17 Express 9 as a recurring decimal.

1

18 If m = –3, find the value of (–m – 1)3.

1

19 Increase $100 by 10% and then decrease this amount by 10%.

1

20 Three parcels weigh 5.3 kg, 8.7 kg and 3.7 kg.

What is the average weight of the parcels?


1


20


EXAM PAPER 2

PART C


1 Correctly name the feature of the circle shown below.

a b c Q P A

B

1

PQ is a

AB is a

The shaded region is a

2 Solve the following equations.

a x – 5 = 31

b

3x + 10 = 5x – 6

c

1 1

4(a – 8) = 48

1

1

1

3 For the following scores — 10, 15, 11, 9, 14, 14, 12, 10, 10, 15 — state the:

a mode

b median

2

c range

d mean

2

4 A car is travelling at 60 km/h. How many metres does it travel in 4 seconds?

1

5 Find the length of the missing side.

a b 1.5 m

x

6 cm

y

2 m

1

6.5 cm

1

6 It is known that the wheels of a toy truck rotate 100 times per minute. If the radius of the

wheels is 70 mm, calculate, using π =

22 , 7

how far the truck will travel in 10 minutes.

7 The diagram shows a quadrilateral and a semicircle.

Find the value of x.

15 cm

x 10 cm


1

15

173


1



Total marks: 44

EXAM PAPER 3

PART A

Fill in only one circle for each question. Fill in only one circle for each question. 1 What is the perimeter of a rectangle with height 4 cm and length 8 cm?

Marks

A 12 cm

B 16 cm

C 24 cm

D 32 cm

1

A 7000

B 6800

C 6850

D 6900

1

A 0.65 1

B 6.5

C 65

D 650

1

A 0.65

B 0.62

C 0.062

D 0.065

1

A 5%

B 10%

C 20%

D 45%

1

A 5 × a × 2 × b

B 5a × 5a × b

C 5ab × 5ab

D 5 × a × a × b

1

A 4

B 4

C 4

D 1

1

A 6

B 8

C 13

D 26

1

A 8

B 9

C 10

D 11

1

A $1500

B $4500

C $6200

D $6000

1

A 3 : 250

B 4 : 1

C 1 : 250

D 1 : 4

1

C 27 m

D 270 m

2 What is the number 6848 rounded to the nearest hundred?

3 On a plan, the length of a building is shown as 65 000 mm. How many metres is this? 4 Write 6 2 % as a decimal.

5 A toy was reduced in price from $50 to $45. What is the percentage discount? 6 5a2b equals:

7 (23)2 ÷ (22)3 equals:

3

1

8 If 3x – 8 = 31, what is the value of x?

9 A letter is chosen at random from the word MATHEMATICS. How many different elements are

there in the sample space?

10 A car was bought for $5000 and sold at a profit of 20%. What was its selling price? 11 The ratio of 12 grams to 3 kilograms is

12 Find in square metres the area of a rectangle 3 m long and 90 cm wide.

A 0.27 m 2

B 2.7 m


2

2

2


1

12


EXAM PAPER 3

PART B

Answer each question in the space provided. Marks 2

1 Write 9 as a recurring decimal.

1

2 A man’s wage is $250. If he spends 40% of this on rent and 35% on

household expenses, how much money does he have left?

1

3 Solve for x: 12(x – 1) = 2(5x + 4).

1

4 A concrete mixture contains two parts cement, three parts sand

and three parts gravel. What percentage of the mixture is sand?

1

5 A road map is drawn to a scale of 50 mm to 1 km. How far apart

are two towns if they are 275 mm apart on the map?

1

6 Simplify 8x + 6y − x + 2y.

1

7 Calculate the mean of 34, 37, 42, 45 and 48.

1

8 Simplify 5x + (5x)0.

1

9 Factorise fully 9m − 3m2.

1 120°

10 Find the value of x.

1

x°

3

11 Change 8 to a decimal.

1

12 The numbers 1 to 12 are written on separate cards and placed face down on a table.

If one card is chosen at random, what is the probability of selecting a number divisible by 5?

13 What type of angles are α and β?

1

α

14 Simplify 105 × 102 × 100.

β

1 1

15 If the volume of a cube is 729 cm3, what is its side length?

1

16 Solve 4x − 5 = 2x + 7.

1

17 Convert 3 hours 20 minutes to minutes.

1

18 A car travels at an average speed of 80 km/h. How long will it take

to cover 400 km?

19 Kate earns $90.80 for 20 hours babysitting. How much

will she earn for 45 hours at the same rate?

1

20 Calculate the area correct to

one decimal place.

1 15 cm


20

175


1


EXAM PAPER 3

PART C


1 Calculate the area of the following shapes.

b

a

c

6 cm 15 cm

14 cm

8 cm

1

20 cm

1

1

2 Calculate the volume of the following prism. 5 cm

20 cm

1

12 cm 3 A swimming club has 40 members and an athletics club has 55 members. There are 16 people

who are in both clubs. a Draw a Venn diagram to show this information.

1

b How many people are in either the swimming club or the athletics club or both.

4 a

y

Complete the table of values for y = 2x – 1.

x –3 –2 –1 0 1 2 y b Draw the graph of y = 2x – 1.

1

1

3 0

x

c What is the y-intercept?

1 1

d For what value of x does y = 7?

1

5 A pair of congruent triangles is drawn below.

a Write all pairs of matching sides

A

1

b Write the congruence statement.


1 C

M

B


12


Exam Paper 4 Instructions for all parts • Attempt all questions. Time allowed: 1 hour • Calculators are NOT allowed for Part A. Part A: Allow about 10 minutes for this part. Part B: Allow about 20 minutes for this part. Part C: Allow about 30 minutes for this part.

Total marks: 50

EXAM PAPER 4

PART A

Fill in only one circle for each question.

1

4 25

is equivalent to:

A 4%

Marks

B 8%

C 16%

D 20%

2 Which clock correctly shows the same time in the evening as this clock?

A C

3 (0.25)2 equals:

11

B D

12

1 1

1 2

10

3

9 4

8 7

6

5

A 0.125

B 0.0125

C 0.0625

D 0.625

1

A $40

B $50

C $80

D $120

1

4 If $200 is divided in the ratio 2:3, the smaller amount is: 5 The area of this triangle is:

4 cm

5 cm

A 15 cm C 9 cm

B 18 cm D 22.5 cm

A –2

B 2

C 1

D –1

1

A 3

B 14

C 32

D 38

1

A 5x + 6

B 12x + 1

C 5x + 8

D 5x + 12

1

A $72

B $24

C $216

D $320

1

A 9500

B 9600

C 9700

D 10 000

1

A a

B a + 7b

C ab

D a + b

1

A 30 : 2

B 3 : 2

C 3 : 200

D 3 : 2000

1

2

2

6 (–1)2 – (–1)3 equals:

2

9 Interest on $800 for 3 years at 9% per annum is:

10 The number 9659 rounded to the nearest hundred is: 11 If 7 is a factor of 7a + 7b, what is the other factor? 12 The ratio of 30 mL to 2 L is:


12

177


1

6 cm

7 What is the range of the following set of scores: 32, 32, 43, 46, 37, 41, 35? 8 7 + 5(x + 1) equals:

3 cm

2


EXAM PAPER 4

PART B


1 Decrease $720 by 5%. ab + ac 2 Find the value of abc if a = 2, b = 3 and c = 4.

1 1 y

3 How many millilitres are there in 3.5 litres?

1 y = 2x

4 What is the point of intersection for the lines y = 2x and y = 3 – x?

0

x y=3–x

5 Write 84% as a fraction in its simplest form. 6 Simplify 8y2 ÷ 8y2.

1 1 1

7 A bicycle wheel has a diameter of 65 cm. How far, correct to the nearest metre, will

the rider travel if the wheel turns 200 times?

1

8 Find the size of a quantity if 20% of it is 30 metres.

1

9 What is the probability of rolling a number less than 3 when rolling a normal die?

1

10 How many grams are there in 1.4 kg?

1

98°

11 What is the value of x?

140°

x°

12 Write 500 minutes as hours and minutes.

1 1

13 What is the area (to the nearest whole number) of a circular speed limit sign with

a diameter of 35 cm?

1

14 Factorise 8m – 10.

1

15 A square has a perimeter of 20 cm. What is its area?

1

16 A cube has a volume of 216 cm3. What is its side length?

1

17 Expand and simplify x(3x – 5) + 2x(5 – 3x).

1

18 Calculate the circumference of a wheel with a diameter of 42 cm.

Answer to the nearest centimetre.

1 62°

19 If v = u + at, find v when u = 10, a = 6 and t = 5.6. 20 Find the value of the pronumeral

in the given diagram.


x° Total marks achieved for PART B

1

1

20


EXAM PAPER 4

PART C


1 Find the value of the pronumeral, giving reasons.

P a b c R S A

P

67°

45°

2x°

T

Q

C

Q

R

a

1

1

1

b A

B

ABCD is a rhombus. AC = 19 cm, BD = 15 cm

9 cm

12.5 cm

104° 92°

71°

D

S

2 Find the area of the following plane shapes.

7 cm

128°

a°

3x°

B

D

C

1

1

3 Find the volume of the given solid.

12 mm

47 mm

1 62 mm

4 In the rectangle given opposite, a diagonal is drawn

to divide it into two congruent triangles. Write: a all pairs of equal sides

48 mm A

B

1

b all pairs of equal angles

1

c the congruence statement

1

D

C

Continued on the next page

179



EXAM PAPER 4

PART C


5 Nine students did a short test. The results are recorded below.

6, 7, 4, 7, 8, 7, 7, 3, 9

a Determine the range.

1

b What is the mode?

1

c What is the median?

1

d What is the mean?

1

6 Solve the following. 2 a 9 = y 3

a−2 = 10 4

b

1

1

7 Find the value of the pronumeral in each of the following.

a b c 120°

50°

x°

25°

3x°

x°

1

1

1



18


Answers Chapter 1 – Basic arithmetic and the calculator

Page 1 1 a 40 b 70 c 90 d 30 e 160 f 230 g 630 h 830 i 390 j 5670 k 9650 l 6380 2 a 800 b 500 c 200 d 2400 e 5400 f 6300 g 8900 h 6400 i 8500 j 500 k 900 l 600 3 a 3.6 b 0.8 c 9.7 d 31.6 e 0.2 f 16.1 g 18.4 h 91.5 i 62.9 j 43.2 k 83.3 l 55.1 4 a 5.67 b 8.94 c 9.62 d 33.26 e 41.67 f 83.19 g 52.37 h 81.29 i 63.14 j 59.33 k 129.64 l 538.63 5 a 50 b 3 c 90 d 9 e 0.007 f 0.05 6 a 84 b 240 c 8.9 d 92 e 330 f 82 g 250 h 0.000 65 i 0.0076 Page 2 1 a 17 b 46 c 48 d 59 e 45 f 100 g 360 h 112 i 20 j 23 k 11 l 29 m 32 n 109 o 11 2 a 244.52 b 678.804 3

11

4

4

c 121.7 d 38.1 e 114.632 f 223.1 g 27.62 h 22.35 i 11.02 j 59.94 k 25.346 l 114.53 3 a 9 4 b 1215 c 515 d 17 e 6

7

6

36

1

16 173 39 f 1175 11 212

4 a 100.15 b 10.98 c 72 d 2363.75 e 8.122 f 5.2 g 4754.65 h 498.015 i 158 5 a 118 b 2 35 c 35 d 2125 e 13 8 f Page 3 1 a 25 b 36 c 225 d 1521 e 4225 f 7921 g 12.25 h 4.41 i 44.89 j 232.5625 k 265.69 l 14 713.69 2 a 512 b 64 c 125 d 216 e 32 f 2401 g 3125 h 512 i 243 j 1.728 k 13.824 l 1296 m 5.0625 n 0.343 o 13.0321 3 a 104.86 b 4.91 1

27

9

c 571.79 d 753.57 e 2138.14 f 3442.95 g 39 283.24 h 3763.82 i 20 730.72 j 6512.49 k 316.84 l 2766.76 4 a 2 4 b 125 c 116 4

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d 28 9 e 40 25 f 72 4 g 15 8 h 42 8 i 41016 j 3 81 k 2125 l 5 9 Page 4 1 a 3 b 5 c 6 d 11 e 13 f 15 g 9 h 14 i 8 j 5 k 2 l 2 m 7 n 36 o 2 2 a 2 b 4 c 3 d 9 e 7 f 6 g 13 h 8 i 2 j 33 k 40 l 1.2 3 a 7.5 b 1.5 c 1.4 d 2.4 e 4.2 f 0.2 g 5.8 h 4.4 i 2.1 4 a 2.50 b 0.88 c 2.92 d 2.48 e 2.05 f 3.09 g 1.60 h 7.31 i 0.34 j 2.77 k 7.61 l 2.09 m 1.71 n 2.34 o 1.13 Page 5 1 16.8 cm 2 148.877 cm3 3 1219.68 cm3 4 17 cm 5 85 000 6 50 7 $830.40 8 $148.75 9 $111.88 10 24 11 48.54 1

12 $1891 13 6.06 14 2 2 15 2.38 16 159 17 $30.49 18 132.01 19 32.939 20 $1375 Page 6 1 C 2 A 3 B 4 C 5 A 6 C 7 A 8 A 9 A 10 A 11 D 12 C Page 7 1 558.13 2 4700 3 0.50 4 2.38 5 1436.03 6 21.95 7 0.61 8 20.9 9 11.1 10 2 11 66.0 12 0.1 13 20.5 14 6.9 15 5.0

Chapter 2 – Percentages

Page 8 1 a 100 b 100 c 100 d 100 e %, 100 2 a 48% b 52% 3 a 35% b 42% c 97% 4 a 75% b 80% c 90% d 33% e 11% f 49% g 36% h 22% i 91% 5 a 68% b 53% c 9% d 31% e 63% f 23% 6 a 77% b 85% c 77% d 81% 7 a 88% b 14% Page 9 7

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g 200 h 500 i 8 j 200 k 11

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j 200 k 200 l 8 m 200 n 200 o

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1 3 17 17 9 19 49 19 23 1 41 9 73 4 j 4 k 20 l 1 m 100 n 10 o 20 p 100 q 100 r 100 2 a 40 b 500 c 200 d 200 1 21 17 183 37 81 131 1 1 1 1 9 21 11 1 l 125 m 200 n 200 o 1000 p 400 q 200 r 200 3 a 200 b 300 c 400 d 800 e 40 f 40 g 200 h 3 171 31 81 19 14 31 19 49 13 19 43 6 37 69 13 p 200 q 200 r 400 4 a 50 b 25 c 50 d 75 e 400 f 400 g 200 h 500 i 125 j 1000 k 1000 l 250

1 a 2 b 5 c 10 d 10 e 5 f 5 g 10 h

18

9 40 71 200

4 5

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m 50 n 20 o 25 Page 10 1 a 30% b 50% c 80% d 40% e 43% f 84% g 62% h 39% i 56% j 25% k 16% l 72% 2 a 50% b 160% 1

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c 70% d 80% e 30% f 18% g 36% h 28% i 14% 3 a 75% b 6 4 % c 65% d 11 3% e 25% f 17 2 % g 15% h 60% i 17 2 % 1

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4 a 37 2 % b 55 9 % c 62 2 % d 6311% e 41 3% f 33 3% Page 11 1 a 0.1 b 0.8 c 0.3 d 0.5 e 0.4 f 0.6 g 0.2 h 0.7 i 0.9 j 1 k 0.15 l 0.65 2 a 0.16 b 0.19 c 0.39 d 0.12 e 0.61 f 0.56 g 0.14 h 0.73 i 0.67 j 0.98 k 0.81 l 0.78 m 0.62 n 0.43 o 0.49 3 a 0.05 b 0.02 c 0.08 d 0.09 e 0.06 f 0.07 g 0.03 h 0.01 i 0.04 j 0.015 k 0.025 l 0.033 m 0.021 n 0.017 o 0.049 4 a 0.455 b 0.892 c 0.574 d 0.639 e 0.632 f 0.365 •

•

•

•

g 0.538 h 0.927 i 0.697 j 0.237 k 0.158 l 0.213 5 a 0. 3 b 0.0083 c 0.003 75 d 0.015 e 0. 6 f 0.125 g 0.0925 h 0.2075 i 0.007 Page 12 1 a 15% b 25% c 35% d 95% e 14% f 85% g 18% h 55% i 17% j 45% k 67% l 65% m 91% n 75% o 72% 2 a 80% b 60% c 10% d 50% e 90% f 20% g 70% h 40% i 30% j 1% k 2% l 5% m 4% n 6% o 3% 3 a 12.3% b 62.5% c 53.7% d 18.9% e 42.7% f 13.9% g 83.5% h 56.7% i 68.3% j 12.9% k 81.6% l 92.7% m 68.7% n 25.7% o 36.9 % 4 a 0.1% b 91% c 0.6% d 0.7% e 0.2% f 0.9% g 81% h 3.7% i 2.1% j 0.4% k 0.5% l 0.3% m 5.7% n 8.9% o 6.5% 5 a 120% b 250% c 360% d 256% e 131% f 357% g 825% h 341% i 563% j 284% k 534% l 813% m 527% n 803% o 206% Page 13 1 a 30 b 1000 c 270 d 252 e 290 f 630 g 92.5 h 50.4 i 10.5 j 135 k 623 l 79 m 56.25 n 664 o 313.65 p 650 2 a 0.48 b 8.84 c 0.9 d 7.82 e 5.727 f 207.936 g 2.365 h 677.875 i 556.25 j 302.95 k 11 l 105 m 45 n 516.6 o 60 p 46.8 3 a 85 b $224 c 6.03 d 67.71 days e 46.2 f $2 g $18 h 1.2 kg i 80c j 120 k 200 g l $203 m $60 n $170.40 o 45 p 68 Page 14 1 a $58.50 b $9200 c $116 d $4800 e $420 f $1012.50 g 1260 g h 1 hour i 640 kg j 360 L k 72 h l 140 t m $810 n $372.13 o $209.95 p $168.64 q 96 ha r 1020 cm 2 a $51.03 b $57.12 c 2.6 m d 197.6 L e $837 f $5083.20 g $100.50 h $402.50 i $789.23 j $121.90 k 36 h l $252 m $310.25 n $528 o $57.60 p $12.10 q $676.80 r $403 3 a $414 000 b $1800 c $24 000 d $97.50 1

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Page 15 1 a 10% b 40% c 57 7 % d 35 7 % e 3611% 2 a 25% b 25% c 40% d 25% e 50% f 33 3% g 12.5% h 90% 1

2

2

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i 25% j 5% k 8 3% l 63% m 66 3% n 7.5% 3 a 12.5% b 16 3% c 13 3% d 2% e 20% f 25% g 33 3% h 25% i 30% j 10% 1

2

1

5

1

1

1

1

k 25% l 40% m 4% n 1.6% o 83 3% p 6 3% 4 a 8 3% b 25% c 15 9 % d 12 2 % e 16 4 % f 87 2 % g 20% h 333 3% i 2% j 25%

181

Answers © Pascal Press ISBN 978 1 74020 033 2


Answers 5

1

k 55 9 % l 30% m 7 2 % n 25% Page 16 1 a 64 b $150 c 50 d 40 2 a 160 b 630 c 2400 d 700 3 a 200 b 460 c 480 d 400 e 140 f 600 g 1660 • h 264. 4 i 4700 j 425 k 287.5 l 1840 4 a 27 b $21 500 c $575 d $168 000 e $550 f $54.17 g 5000 Page 17 1 $2430 2 a $2700 b $4400 3 a $4125 b $4475 4 $15 800 5 a $733.75 b $8400 Page 18 1 2$56, $504; $9, $36; $5.12, $58.88; $6.50, $123.50; $142.50, $807.50; $35, $105 2 a $81.60 b $598.40 3 a $300 b 21 3% 4 a $31 b $217 5 a $209.41 b $31.41 6 a $1520 b $684 Page 19 1 a $660 b 25.98% c 20.63% 2 a $12 360 b $18 540 3 a $5.16 b $51.64 4 $600 Page 20 1 44% 2 36 3 318 4 85% 5 500 kg 6 $495 7 20% 8 $2950 9 $190 10 $881.10 11 $969.50 12 3 13 $110.50 1

14 a 144 b 56 4 % Page 21 1 D 2 D 3 A 4 D 5 C 6 D 7 A 8 D 9 B 10 C 11 D 12 D 1

Page 22 1 $111 2 257.40 kg 3 58.33% 4 $933.33 5 $106.67 6 33 3% 7 7 8 $72 9 12.5% 10 245 11 $50 714.29 12 28.78% 13 $2000 14 $2880 15 $2100

Chapter 3 – Four operations with integers

Page 23 1 a 11 b 5 c 11 d 9 e 13 f –1 g 14 h 8 i 26 2 a 13 b 4 c 31 d 4 e 24 f 13 g 12 h –2 i 54 3 a 5 b 3 c 19 d –5 e 30 f 2 g 27 h – 2 i 9 4 a 24 b –5 c 15 d 7 e 36 f –14 g 12 h –11 i 8 5 a 11 b 8 c 15 d –5 e 8 f –13 g 0 h –17 i 3 6 a 9 b 15 c 6 d – 15 e 4 f –15 g 14 h –12 i 20 Page 24 1 a 4 b 11 c 3 d 10 e 12 f 28 g –7 h 22 i 17 2 a 11 b 31 c 5 d 18 e 14 f 87 g 15 h 58 i 9 3 a – 21 b –6 c –13 d –12 e –10 f –6 g –17 h –4 i –28 4 a –17 b –2 c –17 d –4 e –23 f –5 g –32 h –2 i –25 5 a –26 b –14 c 43 d –8 e –46 f –3 g –24 h –10 i –40 6 a –4 b –7 c –12 d 14 e –14 f –2 g –18 h –17 i –9 Page 25 1 a 10 b –84 c 150 d –24 e 12 f –96 g 54 h –90 i 52 2 a 6 b –15 c 189 d –120 e 44 f –42 g 27 h –63 i 360 3 a –36 b 12 c –55 d 45 e –6 f 140 g –24 h 27 i –20 4 a –21 b 24 c –32 d 24 e –45 f 60 g –60 h 32 i –48 5 a 64 b 18 c –350 d 36 e 60 f –24 g –48 h –210 i 30 6 a b c 7 11 –4 –5 –9 8 12 –25 –100 × × × 3 21 33 –12 7 –35 –63 56 –4 –48 100 400 –7 –49 –77 28 –10 50 90 –80 12 144 –300 –1200 Page 26 1 a 6 b –7 c 6 d –4 e 4 f –7 g 2 h –11 i 6 2 a 6 b –3 c 3 d –5 e 9 f –4 g 2 h –12 i 7 3 a –9 b 4 c 3 d 3 e –9 f –1 g –3 h 12 i 9 4 a 6 b –2 c –3 d –1 e –16 f 3 g –1 h 2 i –3 5 a 6 b –5 c –9 d 35 e –7 f –80 g 6 h –24 i –1 6 a –5 b 4 c –5 d 3 e –5 f –1 g –2 h 5 i –1 Page 27 1 a –6 b –1 c 7 d –4 e 10 f –2 g –1 h –12 i 7 2 a –32 b 2 c –9 d –21 e –77 f –8 g 90 h 25 i –72 3 a –8 b 15 c –5 d 12 e –28 f 3 g 11 h 0 i –64 4 a –14 b –5 c –16 d –2 e –4 f –18 g 0 h 49 i –4 5 a –2 b –42 c 1 d 50 e –5 f 8 g –9 h –9 i –8 6 a + 3 –7 –9 12 –15 b × –4 5 –10 8 –9 –1

2

–8

–8

–5

–15 –17

6

9

–1

–10 –3

11

–16

–5

4

–23

–6

18

–9

11

20

–25

24

–30

–44

55

50

–40

60

–48

–110

88

45

–99 54

Page 28 1 a 8 b 25 c –27 d 9 e 16 f 1 g 125 h 64 i –1 j 64 k –8 l 1 m 32 n 81 o 16 p 81 q –25 r –125 2 a 1 b 625 c –125 d –1 e –32 f 32 g –1 h –1000 i 64 j –216 k 64 l 108 m 81 n 343 o 100 p –64 q 81 r 162 3 a –72 b 85 c –63 d 41 e 125 f 2 g –28 h –49 i –150 j 4 k 56 l –288 m 441 n 208 o 100 p –4 q –11 r –16 4 a –5 b 1 c –1 d 21 e 2500 f 8 g 2100 h –15 i –100 000 j –6000 k 24 l –116 m 63 n 176 o –241 p 19 q –964 r 5000 Page 29 1 a 17 b –3 c 4 d 0 e 11 f 3 g –1 h 1 i –25 j 3 k –5 l –1 2 a 6 b 12 c –10 d –60 e 64 f –2 g –1 h –4 i –25 3 a –24 b 81 c –55 d –18 e 7 f 19 g 0 h 26 i –6 4 a (5 + 7) ÷ 6 = 2 b (–3 + 5) × –1 = –2 c 5 × (4 – 6) × 3 = –30 d (6 + 3 × 5) ÷ –7 = –3 e (–4 + 7 – 9) × 2 = –12 f 54 ÷ –9 – (2 + 7) = –15 g (–4 × 7 – 5) × –2 = 66 h (7 – 10) × (3 – 8) = 15 i 10 – (7 + 4 × –3 ÷ 12) = 4 Page 30 1 4° 2 3 km east 3 70° 4 –4 5 –1 kg 6 –3 7 a $1750 b $2545 8 loss of $3000 9 –3 and –5 10 5 cm 11 $575 12 fall of 13 degrees 13 –2 and 6 14 –5 15 –42 Page 31 1 C 2 D 3 B 4 B 5 A 6 A 7 C 8 D 9 C 10 A 11 D 12 A Page 32 1 –11 2 13 3 –18 4 –15 5 8 6 11 7 5 8 –1000 9 –10 10 –29 11 –76 12 –60 13 28 14 –12 15 12 °C

Chapter 4 – Indices

Page 33 1 a 2 × 2 × 2 × 2 b 5 × 5 c 7 × 7 × 7 d 6 × 6 × 6 × 6 × 6 e 10 × 10 × 10 × 10 × 10 × 10 f 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 g 2 × 2 × 2 × 2 × 2 × 2 × 2 h 7 × 7 × 7 × 7 × 7 × 7 × 7 × 7 2 a 26 b 75 c 57 d 38 e 104 f 65 g 123 h 29 3 a 16 b 27 c 121 d 125 e 169 f 100 000 g 216 h 64 i 81 4 a 52 b 23 c 104 d 62 e 25 f 72 g 107 h 32 i 63



Answers

5 a2×2×2×3×3 b6×6×7×7×7×7 c5×5×5×2×2×2×2 d3×3×3×3×3×5 e7×7×7×2×2 f 3 × 3 × 3 × 3 × 2 × 2 × 2 × 5 × 5 6 a 23 × 5 b 24 × 3 c 23 × 32 d 32 × 52 e 22 × 34 f 2 × 35 g 25 × 72 h 22 × 3 × 52 Page 34 1 a 28 b 39 c 510 d 711 e 211 f 109 g 69 h 114 i 512 j 316 k 222 l 717 2 a 65 b 59 c 38 d 76 e 28 f 511 g 237 h 1018 i 153 j 310 k 1224 l 55 3 a 45 b 512 c 511 d 214 e 49 f 812 g 312 h 712 i 314 j 210 k 321 l 232 4 a 55 b 99 c 411 d 811 e 211 f 510 g 35 × 47 h 310 i 65 j 65 k 78 l 810 5 a 55 b 38 c 65 d 76 e 55 f 712 g 414 h 815 i 410 j 64 k 29 l 315 6 a 53 b 53 c 77 d 82 e 43 f 8 g 37 h 3 i 94 j 66 k 73 l 72 Page 35 1 a 73 b 22 c 36 d 53 e 25 f 64 g 108 h 72 i 310 j 29 k 116 l 5 2 a 5 b 9 c 2 d 49 e 125 f 3 g 36 h 16 i 5 j 1 000 000 k 27 l 8 3 a 212 b 515 c 742 d 312 e 24 f 56 g 6 h 314 i 215 j 108 k 730 l 1212 4 a 38 b 96 c 55 d 56 e 29 f 76 g 78 h 415 i 912 j 87 k 614 l 1026 5 a 33 b 57 c 8 d 95 e 123 f 9 g 23 h 75 i 53 × 46 j 82 × 33 k 22 × 35 l 25 × 3 6 a 55 b 56 c 85 d 37 e 73 f 33 g 84 h 69 i 42 j 2 × 32 k 58 l 23 × 36 Page 36 1 a 210 b 318 c 516 d 715 e 228 f 618 g 550 h 316 i 114 j 1018 k 560 l 336 2 a 6561 b 1024 c 4 035 607 d 1 048 576 e 244 140 625 f 1 679 616 g 4 782 969 h 262 144 i 2401 j 4096 k 1 771 561 l 14 348 907 3 a 321 b 220 c 614 d 536 e 76 f 1121 g 2100 h 1010 i 612 j 128 k 749 l 230 4 a 415 b 335 c 840 d 5144 e 290 f 584 g 718 h 480 i 266 j 948 k 763 l 3126 5 a 64 b (23)3, 29 c (34)2, 38 d (53)2, 56 e (72)4, 78 f (25)3, 215 6 a 212 b 236 c 340 d 396 e 1116 f 330 g 512 h 1045 i 240 j 372 Page 37 1 a 1 b 8, 8, 1 c 10 000, 10 000, 1 d 125, 125, 1 e 49, 49, 1 f 32, 32, 1 2 a 30 b 20 c 100 d 50 e 70 f 20 3 1 4 a 1 b 1 c 1 d 1 e 1 f 1 g 1 h 1 i 1 5 a 2 b 0 c 1 d 7 e 8 f –1 g –1 h 15 i 6 j 2 k 1 l 10 6 a 1 b 1 c 1 d 2 e 3 f 5 g 1 h 1 i 1 j 1 k 1 l p m 10 n 8 o 6 Page 38 1 a 79 b 27 c 78 d 412 e 39 f 86 g 85 h 55 i 63 2 a 43 b 23 c 62 d 52 e 43 f 32 g 34 h 52 i 43 3 a 36 b 26 c 76 d 412 e 610 f 88 g 522 h 330 i 512 4 a 4 b 1 c 8 d 5 e 64 f 1 g 1 h 1 i 81 5 a 85 b 611 c 220 d 56 e 52 f 54 g 26 × 66 h 4 × 32 i 33 j 9 k 72 × 42 l 44 Page 39 1 C 2 A 3 C 4 B 5 B 6 D 7 C 8 C 9 B 10 D 11 B 12 B Page 40 1 66 2 52 3 86 4 6 5 312 6 314 7 94 8 72 × 52 9 36 10 9 11 314 12 34 13 1 14 3 15 58 × 236

Chapter 5 – Rational numbers

Page 41 1 a 8 b 12 c 15 d 9 e 7 f 8 g 6 h 35 i 23 2 a 70 b 50 c 90 d 400 e 70 f 80 g 150 h 380 i 570 3 a 200 b 600 c 400 d 700 e 800 f 1000 g 300 h 300 i 2500 4 a 6000 b 8000 c 8000 d 5000 e 2000 f 3000 g 5000 h 6000 i 6000 j 9000 5 a 20 000 b 90 000 c 30 000 d 50 000 e 50 000 f 60 000 g 70 000 h 80 000 i 50 000 j 20 000 6 a 3 000 000 b 6 000 000 c 8 000 000 d 6 000 000 e 29 000 000 f 32 000 000 g 48 000 000 h 92 000 000 i 9 000 000 j 31 000 000 Page 42 1 a 2.3 b 8.9 c 30.6 d 81.1 e 92.8 f 41.4 g 89.5 h 32.1 i 54.2 j 53.3 k 91.8 l 39.4 2 a 81.3 b 32.1 c 36.5 d 41.9 e 62.5 f 92.4 g 51.3 h 39.6 i 42.8 j 28.5 k 58.7 l 73.9 3 a 7.81 b 19.63 c 21.54 d 63.83 e 51.37 f 72.12 g 84.35 h 63.84 i 41.64 j 64.84 k 75.61 l 81.14 4 a 7.42 b 15.63 c 28.14 d 0.94 e 33.46 f 47.44 g 53.24 h 64.83 i 78.36 j 81.89 k 92.64 l 125.84 5 a 5.678 b 25.831 c 19.716 d 37.840 e 42.839 f 59.235 g 63.615 h 72.819 i 81.342 j 93.145 k 120.616 l 92.184 6 a 88.615 b 63.341 c 230.361 d 95.649 e 94.833 f 512.158 g 120.158 h 134.643 i 832.325 j 435.235 k 437.130 l 531.641 Page 43 1 a 0.3 b 0.9 c 0.7 d 4.3 e 0.07 f 0.12 g 0.93 h 2.39 i 0.783 j 0.549 k 0.6342 l 0.0764 2 a 5.3 b 8.9 c 15.07 d 28.05 e 16.01 f 94.7 g 123.03 h 128.8 i 532.37 j 81.3 k 58.7 l 94.19 3 a 0.1 b 0.6 c 0.03 d 0.17 e 0.063 f 0.0415 g 0.6 h 0.14 i 0.375 j 0.25 k 0.064 l 0.875 4 a 0.1 b 0.18 c 0.2 d 2.49 e 0.068 f 2.8 g 1.26 h 3.04 i 0.935 j 0.018 k 0.044 l 0.24 5 a 0.003 b 0.0114 c 0.625 d 0.4 e 0.3 f 0.74 g 0.206 h 0.135 i 1.28 j 0.275 k 0.322 l 0.056 Page 44 1 a terminating b recurring c terminating d recurring e terminating f recurring g recurring h terminating 0.936 f 0.26 g 0.43 h 0.12 i 0.81 j 0.6 i terminating j terminating k terminating l terminating 2 a b 0.7 c 0.53 d 0.8 e 0.27 k 0.428 571 l 0.08 3 a 4.333 ... b 8.666 ... c 0.111 ... d 0.3131 ... e 0.7777 ... f 2.222 ... g 1.7272 ... h 0.227 272 7 ... e 1.63 f 5.123 g 6.230 69 h 5.06 i 3.25 i 1.2424 ... j 0.708333 ... k 0.555 ... l 0.1515 ... 4 a 0.083 b 0.2 c 1.4 d 1.6892 b 0.3 c 0.6 d 0.38 e 0.23 l 8.37 k 2.1 l 0.936 f 0.153 g 1.72 h 0.4 i 1.7 j 0.002 k 3.58 6 a 0.3 5 a 0.253 j 0.456 j 0.045 k 0.01 l 0.02 g 0.27 h 0.36 i 0.45 b 0.6 c 0.2 d 0.3 e 0.5 f 0.18 Page 45 1 a rational b rational c irrational d irrational e irrational f rational g rational h rational i irrational j rational k rational l irrational 2 a rational b rational c rational d neither e rational f irrational g rational h rational i irrational j rational k rational l irrational 3 a irrational b rational c irrational d rational e rational f irrational 4 a 2 and 3 b 4 and 5 c 8 and 9 d 14 and 15 e 5 and 6 f 9 and 10 Page 46 1 a 2 : 1 b 1 : 4 c 4 : 1 d 1 : 3 e 3 : 1 f 1 : 11 g 8 : 1 h 1 : 13 i 9 : 1 j 1 : 6 k 4 : 1 l 1 : 12 2 a 7 : 15 b 2 : 1 c 3 : 1 d 4 : 23 e 8 : 1 f 22 : 3 g 7 : 2 h 1 : 9 i 16 : 3 j 2 : 19 k 1 : 5 l 4 : 9 3 a 1 : 3 : 5 b 3 : 1 c 3 : 10 d 5 : 24 e 1 : 7 f 24 : 5 g 2 : 3 h 7 : 9 i 1 : 4 j 6 : 25 k 24 : 1 l 7 : 8 m 1 : 2 : 4 n 1 : 3 : 9 o 1 : 2 : 3 4 a 1 : 8 b 2 : 5 c 1 : 8 d 3 : 10 e 3 : 7 f 1 : 7 g 6 : 35 h 2 : 3 i 25 : 6 j 3 : 5 k 16 : 1 l 5 : 4 m 2 : 5 n 1 : 5 5 a 4 : 35 b 2 : 25 c 1 : 4 d 5 : 24 e 9 : 2 f 7 : 4 g 11 : 18 h 6 : 5 i 7 : 13 j 69 : 89 k 41 : 50 l 16 : 5 Page 47 1 a $240 and $320 b 800 kg and 1200 kg c $320 and $400 d $500 e $900 2 a 28 boys b 40°, 60°, 80° c adults = 480, children = 320 d 80 g e $15 000 3 a 70 cm b 9 : 16 c 5 : 16 d $24 000, $30 000 and $42 000 e $2400 and $3000 Page 48 1 a 80 km b 5 litres c $2.50 d $30 e $31.25 2 a 90 km/h b 90 km c 106.25 L 3 a 2.5 m/year b 50 c 2 km/min Page 49 1 a 1.5 b 1440 c 1800 d 120 e 2400 f 0.5 g 50 h 85 000 i 12 500 j 306 000 k 0.315 l 2400 2 a 2760 b 165 600 c 165.6 3 33.3 m/s 4 a 1500 b 90 000 c 90 5 a 22.8 m/s b 72 km/h Page 50 1 a 1 : 1000 b 1 : 100 c 1 : 10 000 d 1 : 10 000 e 1 : 250 f 1 : 20 g 1 : 20 000 h 1 : 5 i 1 : 6000 2 a 1 m b 3 m c 5 m

183



Answers

d 0.8 m e 0.6 m f 1200 m 3 a 8 m b 50 m c 6000 m d 95 m e 8300 m f 63.25 km 4 a 5 cm b 4 cm c 12.6 cm d 8 mm e 30 cm f 28.35 cm 5 a 35 m b 15 m c 525 m2 d 2.5 m e 150 m2 Page 51 1 a 3 : 2 b 2 : 3 2 160 bottles/h 3 a 3 : 4 b 4 : 3 4 60 km/h 5 $120, $180 6 a 4 : 9 b 1 : 2 7 90 km/h 8 75 cents 9 $36 000, $84 000 10 metal 25 m3, sand 15 m3, cement 10 m3 Page 52 1 D 2 B 3 B 4 C 5 D 6 B 7 D 8 C 9 C 10 B 11 A 12 A 1

Page 53 1 13.2 2 0.37 3 3 4 a 3 : 1 b 7 : 20 5 36, 48 6 4 h 7 $21.50 per hour 8 a 8 mm b 130 m 9 54 km/h 10 25 11 a irrational b rational c rational

Chapter 6 – Basic algebra

Page 54 1 a 5x + 6y b m – 15 c 6a d a – b e

2y 3

x

2 a 6n – 5 b 5a + 32 c x + 2y + 5z d 12ab e 6a 3 a 3x + 9 b 5 + 8

c x + 20 d x – 8 e x + 7 4 a a + 17 b 6m + 7n c 3a + 4b + 5c d 9x + 11y + 2z e 8m + 10n + 7p 5 a 6a + 5b + 7c b 20xy – 10 3a

a +b

18 + x

c 4 b + 15 d 10 e 6 Page 55 1 a 6 b 19 c 16 d 24 e 14 f 54 g 96 h 35 i 32 j 41 k 15 l 31 2 a 3a, 10a b 5x, 9x c none d 5c, 9c e 14y, 6y f 5l, 6l g 4c, 5c h 5a, 6a i 18y, y 3 a 12a b 4y c 5m d 4x e 5a f 3d g 25d h 13k i 19a 4 a 13x b 11b c 23x d 17a e 43x f 13a g 7y h 6c i 19y 5 a 9a b 5ab c xyz d 6xy e 42mnl f 8mn g 10ab h 20mn i 14ade 6 a 28 × a × b b 8 × a × b × c c 7 × x × y d 7 × m × n e 9 × a × b × c f 18 × m × m g 2 × x × y × z h 9 × a × a × b i 14 × m × n × p j 8 × a × a × a k 5 × a × c × e l 17 × a × a × b × b m 16 × x n 28 × x × x × y × y × y Page 56 1 a 4a b 3x + 4y c 4x + y d 5l + m e 3m + 2n f 3k + 3m 2 a 14x + 7y b 19a + 29 c 5a + 12b d 7x + 11y e 14m + 7n f 11a + 15b 3 a 4x + 2y b 2x + 16y c 17p + 2l d 21m + 2n e 19y + 31x f 4xyz g 11a + 17b h 14a + b 4 a 7m b 6p c 8y2 d 2x e 11a – 7b f 4y g 17x h 2d 5 a 4x b a2 – 8a + 15 c 6y – 3x d p3 + 2p2 – 10 e 8a + b f 14x + 8y g 4ab + 4b h xy + 6x 6 a xy b 18m2n + mn2 c 16a2 d 23xyz + 4x e 27xyz f 6x2 + 17y2 g 11x2y2 + 17x h 16a3 + 4b3 Page 57 1 a 8y b 8a c 5m3 d 7 × a × b e 16y 2 a 15a b 35n c a + 7b d 4x + 64 e 23

6a

m

m +n

5x

8x + 3

3x 5

f abc g 42a h 8ab2 i 20mn

j 2m + 5 k 9 + 4x l 3a + 4b m x n 11 o 10 p 5 q 3a + 2 r 2 a 3 a 9 × a b 3 × y c 12 × a d 4 × x – 5 e 8 × m + 3 f 60 – 3 × x g a × b + 3 h 2 × x – 3 × y i a × a × a × b × b j 14 × x × y × z k 7 × m × m + 4 l x × x – y × y 4 a 6a3b b 12a2b2 c 5(x + 9) d 5(m – 5) e 7a(c + 2) f 28(x – 2) g mn(p + 3) h 6(5a + 9) i 8 + (20 + 4m) j 8(6a – 2b) k 7a + 5 l 14a – 5 m 7n3 n 18a3 o x3y2 p 8m – 9 q 16a + 7 r 5a – 10 1 2 Page 58 1 a 21 b 28 c 26 d 9 e 45 f 12 g 27 h 3 i 117 j 9 k 162 l 15 2 a 4 b 19 c –85 d 15 e 31 f 24 g 240 h 30 i 26 3 j 4 k 14 l 94 3 a 2, 5, 8, 11, 14 b 2, 6, 10, 14 c –2, 3, 8, 13, 18 d –1, 5, 11, 17, 23, 29, 35 e 5, 7, 9, 11 f –7, 2, 11, 20, 29, 38, 47 4 a 6, 4, 5, 25, 1, 25 b 11, 5, 24, 64, 9, 47 c 8, 4, 12, 36, 4, 34 d 12, 2, 35, 49, 25, 53 e 13, 5, 36, 81, 16, 56 f 6, 2, 8, 16, 4, 26 g 13, 7, 30, 100, 9, 55 h 11, 3, 28, 49, 16, 48 i 9, 7, 8, 64, 1, 37 Page 59 1 a 24 b 4 c 18 d 29 e 6 f 120 g 15 h 19 i 58 j 43 k 68 l 35 2 a 17 b 45 c 32 d 9 e 5 f 20 g 49 h 4 i 125 j 100 k 4 l 50 m 8 n 21 o 18 3 a 8.9 b 14.7 c 3.1 d 15.6 e 90.5 f 42.3 g 75.9 h 13.8 i 3.7 j 3.7 k 2.7 l 1.5 m 79.2 n 3.8 o 2.4 Page 60 1 a 5x b 3x c 9a d 3y e 10y f q g 14m h 8a i 17b j 6t k 12n l 8mn m 3p n 15xy o 4p p 6x2 2 a 8p b 10m c 10x d 5xy e 13y f 9k g 15xy h 7a i 13m j 9p k 21a l 4ab m 6x2 n 11a2 o 5x p y 3 a 7x + 9y b 8a + 7b c 19m + 8n d c + 3d e 15a – 5m f 5x2 g 8x + 2y h 9mn i 8y + 2x j 3x + 3y k 8m + 13n l 3t + 9 m 13y + 4x n 3a + 9 o 12 – 5x p 3m + 5mn q 14m + 8n r 3x + y Page 61 1 a –4a b x c –3y d –5p e 5a f 11x g 3m2 h –9n i –8x j –8p k 0 l –6x m –2a n –6t o –4x p –12k 2 a 3n b –3y c 2a d –2k e 11y f 6p g –2x h –10n + 15 i 4m j 5a2 + 3a k –6x l 4x – 10y m –7t + 21 n –5k2 + 9k o –4x + 3y p –2xy – 25 3 a 5x – 6y b 2p – 4n c 5a + 11b d –4n – 2p e –6b f a – b g 15 h 8m2 + 3a2 – 6m i 7y – 5 j –3a – 4b k 3k + 17 l 8xy + 7x m 10m – 15 n a – 5b o 3a – 9t p –2ab – 3b q –4y – 11 r –4y2 – 4y Page 62 1 a 21a b 36ab c 20mn d a2b e –10x f 16m2 g –12a2 h 27m i 24b2 j 5x2 k 6ab l 12a2m m 24m2n2 n 50p2 o 30ab p 30m2n 2 a 30ab b 14a2 c –24b2 d –18a e 6m2n f –40x g ab2c h –45t2 i 56mn2p j 6k2 k xy2z l 30x m 6mn3p n –5ab o –12ab2c p 4ab q –14a2bc r 42y2 3 a 40x2 b –80xy c –60ay d –30m2 e 24a f –60mn g 18xy h –30n3 i –40p2 j –15x3y3 k –30xy l –xyz m –7a2b n 20ab o –6m2n p 100m2 q 5a2 r –30ab2c2d Page 63 1 a 5 b 6b c 3n d 4 e 3c f 3m g 9 h b i 4 j m k 4x l 2n m y n 6b o 5m p 6x 2 a 3a b 8 c 2b d 5 e –2a 5

m

3b

f –2q g 4 h 3y i 2 j –9 k –x l –6 m 18 n –3 o c p 3b q 4 r 4n 3 a –3a b –9bc c z d 3 e 20 f 3b g 10a h a i x j n k a l –3a m –6x n –7b o –2q p –7a q y r 3n Page 64 1 a 40x2 b 72 c 35m2 d 30a2b e 96a2 f 4 g 21 h 12m i 24m j 25 2 a 54x b 120x c 3 d –1 e b f 90m2 g 60a2b2 h 1 3 a y b 26x c 35p d –47x e 51t f 2a g 3 h 25x i 8a 4 a 7 b 2 c 1 d 8y e 10 f –2 Page 65 1 a 5a + 15 b 6x – 42 c –12 – 2a d –5x – 35 e 18a + 45 f 15x – 27 g 12a + 6a2 h 2x2 – 5x i 6m2 + 3m j 5x2 – 15x k 14n2 – 21n l –3a2 + 6a m –2a – 10 n –21p + 28 o 5a2 – 5a p –6x2 + 6x q –x – 9 r –4y + 7 2 a 9x + 15 b a – 30 c 6m – 12 d 5x + 1 e 4y2 + 24y f 3m – 12 g 2x + 30 h 12x – 6 i 4m – 2 3 a 7x – 2 b 11m – 30 c 8p – 29 d 10x + 22 e 2x + 10 f x2 + 3 g 3p – 28 h 5p2 + 9 i 5m – 2



Answers

Page 66 1 a 5(a + 1) b 8(x – 1) c 3(y – 1) d 2(x + 1) e 6(m + 1) f 7(m + 1) g 3(p + 2) h 4(q + 2) i 3(2x – 3y) j 4(x – 4) k 9(b – 2) l 5(a + 4) m 2(a + 3) n 3(m + 4) o 6(n – 4) p 8(x – 4) q 3(a + 5) r 2(a + 7) 2 a 3(a + b) b 5(m + n) c 6(p – q) d 7(a + 2b) e 3(l – 3m) f m(m + 7) g y(y + 6) h 9(x – 2y) i 3(a – 8b) j 4(x + y) k p(m – 3) l 8(x – 4y) m 6(x – 6) n 3m(1 + 4m) o y(5 – y) p 3(3x – 2) q 8(m – n) r 3x(2 – x) s 2x(x – 2) t 6p(q – 2p) u 10(x – y) 3 a –3(x – 2) b –5(x – 2) c –4(x – 2) d –6(x – 3) e –x(2 – x) f –6(a – 4) g –3(a – 4) h –4(a – 4) i –6(a + 2) j –4(y + 2) k –2(x + 5) l –4(2y + x) m –3(p + 3q) n –5(x + 5) o –(x + 5) 4 a 7(a + b) b 4(a – 5) c 9(x – y) d 3(m + 5) e 6(1 – t) f m(m – 4) g a(5b – a) h 7(m – 2n) i 2ab(4 – 3a) j –4(1 + 3a) k –3(1 + 5p) l –3(m + 2n) m 9(m – 4) n –4a(1 + 5a) o –(x + 7) 2 x + y + 3z

Page 67 1 2x + 3y 2 mn 3 4 2x + 3 5 x + 1 6 x2 7 5x + 2 8 4a cm 9 y3 cm3 10 2x + 4y 11 2x + 30 cm 3 12 $7x 13 a 6x + 10 b 6x + 3 c 16x 14 a 4x2 b 2x2 – 3x c x (4x + 2) 15 6p + 5q 16 40y cents Page 68 1 A 2 C 3 D 4 A 5 B 6 D 7 C 8 D 9 A 10 B 11 B 12 B Page 69 1 4a 2 9a2b2 3 16ab3 4 11ab 5 2a + 6 6 18x2 7 x 8 2pq(p + 2q) 9 –11x + 39 10 15y + 33 11 5a – 14b 12 17 13 8a 14 –2x + 22 15 –7(x + 3)

Chapter 7 – Length, mass and time

Page 70 1 a m b mm c cm d km e g f mg g kg h t i s j min k h l d 2 a M b k c h d da e d f c g m h µ 3 a m b m c km d cm Page 71 1 a 10 b 100 c 1000 d 1000 e 1000 f 1000 g 1000 h 60 i 60 j 24 2 a 365 b 366 c 12 d 26 e 52 f 2 g 10 h 100 i 1000 j 4 k day l night m midday n midnight 3 a 31 b 28 c 31 d 30 e 31 f 30 g 31 h 31 i 30 j 31 k 30 l 31 Page 72 1 a 100 b 400 c 200 d 410 e 300 f 600 g 350 h 800 i 500 j 700 k 225 l 534 m 1 n 8 o 70 p 16.7 2 a 2 b 12 c 0.9 d 0.6 e 5 f 25 g 1.5 h 0.2 i 80 j 40 k 5.6 l 15.7 m 1000 n 15 000 o 4750 p 20 070 3 a 1000 b 3500 c 2250 d 10 000 e 6000 f 12 000 g 6500 h 7900 i 8000 j 5000 k 9520 l 5500 m 200 n 800 o 255 p 501 4 a 500 b 4 c 4500 d 64 e 7000 f 46.3 g 63.5 h 2300 i 900 j 8000 k 600 l 1800 m 6000 n 530 o 8.56 p 231 5 a 80 b 400 000 c 300 d 370 e 6 f 4 g 2 h 12 690 i 9 j 0.7 k 8500 l 580 m 20 n 0.000 009 o 50 p 36.5 Page 73 1 a c = 4 b c = 15 c c = 9 d c = 5 e c = 13 f 17 2 a 25 cm b 41 m c 85 mm 3 a 9.4 cm b 29.1 mm c 10.1 cm 4 a No b Yes c Yes Page 74 1 a a = 3 b a = 8 c a = 7 2 a x = 4 mm b y = 5 m c a = 15 cm 3 a x = 14.8 cm b x = 7.1 m c x = 4.6 mm 4 6.1 m 5 36 cm Page 75 1 a 21 cm b 22 cm c 30 cm d 19 cm e 24 cm f 17.5 cm 2 a 72 cm b 36 m c 38 m d 48 m e 56 m f 32 m 3 a 28 cm b 20 cm c 26 cm d 24 m e 25 m f 42 m Page 76 1 a 36 b 40 c 52 d 56 e 48 f 24 2 a 80 b 88 c 56 d 60 3 a 18 m b 3.28 m Page 77 1 a 3000 b 3500 c 9350 d 8000 e 8320 f 4900 g 12 000 h 1250 i 5100 j 4000 k 7500 l 8392 m 5 n 0.5 o 3.6 p 8 q 0.75 r 5.675 2 a 5000 b 1 000 000 c 8 d 7000 e 12 000 f 6357 g 3250 h 15 350 i 2 000 000 j 0.009 k 3875 l 2508 m 8000 n 0.05 o 6070 p 0.3 q 6500 r 9008 3 a 7 b 38 300 c 6500 d 15 e 3.5 f 25 g 0.89 h 0.635 i 8900 j 2 k 9 l 8.605 m 1750 n 2250 o 3205 p 0.45 q 4.368 r 8.9 4 a 1 b 11 c 5100 d 2100 e 0.001 f 3 000 000 g 0.6 h 9.5 i 9 000 000 000 Page 78 1 a 36 500 t b 1250 c 212.5 kg d 22.4 t e 1.96 kg f 820 g 2 a 380 g, 1.9 kg, 3600 g, 18.8 kg, 4.2 t, 23.5 t b 4.135 t c 3140 g d 2.8 kg Page 79 1 a 60 b 60 c 24 d 7 e 2 f 4 g 52 h 12 i 365 j 366 k 10 l 100 m 1000 2 a min b h c s d min e h 3 a 40 b 8 c 300 d 730 e 540 f 300 g 49 h 120 i 6 j 4 k 3 l 600 Page 80 1 a 11 h 38 min b 21 h 58 min c 15 h 46 min d 9 h 11 min e 13 h 33 min f 8 h 24 min g 13 h 9 min h 2 h 5 min i 1 h 42 min 2 a 11 d 16 h 17 min b 12 h 13 min c 10 h d 6 h 3 a 10:40 am b 5:55 am c 3:05 pm d 6:55 am e 5:06 pm f 6:15 pm g 9:07 am h 6:47 am i 6:44 pm j 12:10 am 4 a 1 h b 2 h 10 min c 4 h d 4 h 20 min e 5 h f 5 h 20 min Page 81 1 a twenty-five minutes to four; three thirty-five b half past eight; eight thirty c ten minutes to nine; eight fifty d ten past eleven; eleven ten e five minutes to seven; six fifty-five f twenty past seven; seven twenty 2 a 4:30 b 8:00 c 10:15 d 12:00 e 12:00 f 10:20 3 a 7:00 am b 10:20 pm c 6:40 pm d 11:00 am e 8:30 am f 10:00 am 4 a 7:00 am b 11:17 pm c 6:25 pm d 7:21 pm e 6:25 am f 9:00 am 5 a 0600 b 1445 c 1630 d 0630 e 0325 f 1020 g 1948 h 2110 Page 82 1 a 8:35 am b 9:43 am c 10:25 am d 3:20 pm e 8:36 pm f 11:40 pm 2 a 0900 b 1230 c 0440 d 2310 3 a 0530 b 1445 c 2320 d 0215 4 a 6 h 20 min b 5 hours 5 a 1645 b 2240 6 9:20 pm 7 1 h 55 min 8 a 4:10 pm b 9:35 am c 11:30 pm 9 a 0530 b 1520 c 2240 10 2020 Page 83 1 3.76 m 2 27 cm 3 10.63 km 4 33 cm 5 440 m 6 45 960 t 7 13.01 t 8 5000 9 605 kg 10 625 g 11 2250 12 336 h Page 84 1 C 2 C 3 A 4 A 5 C 6 B 7 D 8 D 9 D 10 D 11 B 12 B 1

Page 85 1 28 m 2 64 cm 3 160 m 4 3500 m 5 16 6 625 7 3 t 8 400 g 9 6.14 kg 10 35 000 t 11 180 min 12 120 h 13 8760 h 14 2 min 40 s 15 8 d 16 h 10 min

Chapter 8 – Area, volume and capacity

Page 86 1 a 100 b 10 000 c 10 000 d 1 000 000 e 100 f 1000 g 1 000 000 h 1000 i 1000 j 1 k 1000 l 1 2 a 1 cm3 b 10 g

185



Answers

c 100 cm3 d 500 mL e 600 g f 800 cm3 g 1 kg 3 a 700 b 8 c 90 000 d 3.5 e 50 000 f 2 300 000 g 6000 h 5 i 15 j 49 000 k 8 l 50 1

1

1

Page 87 1 A = b × h 2 A = 2 h (a + b) 3 A = 2 dD 4 A = 2 dD 5 A = πr2, C = 2πr 6 V = x3 7 V = lbh 8 V = πr2h 9 V = Area of triangular face × length of the prism (V = Ah) Page 88 1 a 60 cm2 b 112 cm2 c 144 cm2 d 40 cm2 2 a 60 m2 b 216 cm2 c 336 cm2 d 126 m2 e 126 cm2 f 120 m2 g 114 cm2 h 168 m2 i 320 cm2 j 300 mm2 3 a 20 m b 9 cm c 88 mm2 d 330 cm2 e 8 m f 170 mm2 g 9 cm h 18 m i 11 cm j 420 cm2 Page 89 1 a 192 m2 b 60 cm2 c 130 cm2 d 87.5 km2 e 253 m2 f 30 cm2 g 2808 cm2 h 5.52 m2 i 4079.25 m2 2 a 64 m2 b No, we know the sum of their areas but we cannot find the area of each one unless we know the length of its base. Page 90 1 a 30 cm2 b 150 cm2 c 96 cm2 d 198 cm2 e 140 cm2 f 90 cm2 2 a 63 cm2 b 36 cm2 c 70 m2 d 66 mm2 e 30 m2 f 60 cm2 g 75 mm2 3 a 30 m2 b 4 cm c 72 cm2 d 7 cm e 10 m f 56 cm2 g 22 cm Page 91 1 a 48 cm2 b 30 cm2 c 90 cm2 d 40 cm2 e 30 cm2 f 112 cm2 2 a 31.5 cm2 b 35 m2 c 33 mm2 d 30 m2 e 60 cm2 f 75 mm2 3 a 15 m2 b 36 cm2 c 14 cm d 10 m e 56 cm2 f 22 cm Page 92 1 a 30.24 cm2 b 48.88 cm2 c 46.24 cm2 d 900.9 cm2 e 195 cm2 f 24 cm2 g 120 cm2 h 57 cm2 i 45.5 cm2 j 255 cm2 k 380.1 cm2 (1 d.p.) l 151.04 cm2 Page 93 1 10 000 cm2 2 1 000 000 m2 3 10 000 m2 4 3.75 ha 5 $13 440 6 a 1000 m2 b $130,000 7 20 cm 8 18 000 ha 9 a 3 200 000 m2 b 3.2 km2 10 a 3800 cm2 b 2200 cm2 c 6000 cm2 Page 94 1 a 8 cm3 b 27 cm3 c 1000 cm3 d 1.728 m3 e 39.304 m3 f 1728 m3 g 729 cm3 h 68.921 m3 i 5.832 m3 2 a 343 m3 b 729 m3 c 1331 m3 d 3375 m3 e 2197 m3 f 2744 m3 3 a 8 cm b 12 cm Page 95 1 a 192 cm3 b 105 cm3 c 1440 cm3 d 784 cm3 e 420 cm3 f 216 cm3 2 a 280 cm3 b 300 cm3 c 5 cm d 11 cm e 4 cm f 810 cm3 3 a 144 cm3 b 420 cm3 c 240 cm3 d 324 cm3 e 352 cm3 f 144 cm3 Page 96 1 a 510 cm3 b 250 cm3 c 504 cm3 d 540 cm3 e 150 cm3 f 1980 cm3 2 a 640 cm3 b 360 m3 c 720 cm3 d 192 cm3 e 1056 m3 3 a 288 m3 b 26 cm c 225 cm3 d 18 m e 23 cm2 Page 97 1 a 1331 cm3 b 1944 cm3 c 870 cm3 d 247.5 cm3 e 1152 cm3 f 1764 cm3 2 a b 1728 cm3 c 384 cm3 d 2112 cm3 3 a 1296 cm2 b 144 cm2 c 1152 cm2 d 9216 cm3 Page 98 1 a 3000 cm3 2 7 cm 3 a 840 000 mm3 b 840 cm3 4 a 27 cm3 b 810 cm3 c 360 5 8 times 6 8400 cm3 7 60 cm2 8 5600 cm3 Page 99 1 a 50 b 10 253 c 9600 d 18 500 e 8300 f 18 350 g 4000 h 9.863 i 2.384 j 9.35 k 12 780 l 18 800 2 a 9 b 4 c 2.648 d 20 e 6 f 19 g 3 h 15 i 9.53 j 5 k 9875 l 7 685 000 3 a 18 L b 35 kL c 625 mL 4 a 204 000 cm3 b 204 L 5 a 2744 cm3; 2744 mL b 1944 cm3; 1944 mL c 3500 cm3; 3500 mL Page 100 1 312 L 2 4.8 L 3 19 cm 4 875 mL 5 19.5 L 6 a 2400 cm3 b 19 200 cm3 7 2800 cm2 8 225 cm2 9 50 cm 10 1250 mL 11 4096 cm3 12 220 m2 Page 101 1 C 2 A 3 B 4 B 5 D 6 B 7 C 8 A 9 D 10 C 11 B Page 102 1 a 150 cm2 b 1.89 m2 (or 18 900 cm2) c 45.5 cm2 d 120 cm2 e 18 m2 f 108 cm2 2 a 12 m3 b 350 cm3 3 343 cm3 4 960 cm3 5 1 000 000 cm3 6 5 L

Chapter 9 – Circles

Page 103 1 a centre b diameter c radius d arc e chord f semicircle g minor segment h major segment i sector j tangent 1

3

1

1

k secant l circumference 2 a 4 b 4 c 8 d 3 3 a 9 cm b 24 cm Page 104 1 a 25.1 cm b 18.8 cm c 37.7 cm d 81.7 cm e 47.1 cm f 100.5 cm g 12.6 cm h 62.8 cm i 56.5 cm 2 a 44 cm b 154 cm c 132 cm 3 a 69.1 km b 179.1 m c 144.5 cm d 295.3 cm e 245.0 mm f 119.4 m Page 105 1 a 51.4 cm b 40.6 cm c 34.7 cm 2 a 50 cm b 55 cm c 77.5 cm 3 a 96.5 cm b 68.6 cm c 57.1 cm d 40.0 cm e 35.6 cm f 320.4 cm g 57.1 cm h 50.0 cm i 140.5 cm Page 106 1 a 28.3 cm2 b 78.5 cm2 c 254.5 cm2 d 132.7 cm2 e 227.0 cm2 f 283.5 cm2 g 201.1 cm2 h 314.2 cm2 i 380.1 cm2 2 a 154 cm2 b 3850 cm2 c 154 cm2 3 a 1963.5 km2 b 10.2 m2 c 1075.2 mm2 d 16 741.5 cm2 e 125 663.7 km2 f 151.7 cm2 Page 107 1 a 88.4 cm2 b 113.5 cm2 c 237.6 cm2 2 a 346.4 cm2 b 1001.0 cm2 c 169.7 cm2 3 a 524.5 cm2 b 300.9 cm2 c 150.8 cm2 d 384.8 cm2 e 105.8 cm2 f 692.1 cm2 g 127.2 cm3 h 140.0 cm2 i 291.1 cm2 Page 108 1 a 69.1 cm b 241.9 cm c 75.4 cm 2 a 254.47 cm2 b 2290.22 cm2 c 153.94 cm2 3 a 40.0 cm b 73.7 cm c 35.0 cm 4 a 46.54 cm2 b 41.10 cm2 c 202.08 cm2 d 98.17 cm2 e 210.90 cm2 f 289.16 cm2 Page 109 1 175.9 m 2 2463 m2 3 35 cm 4 201.1 cm2 5 3183.1 cm2 6 56.55 cm 7 39.58 m 8 157.1 cm 9 1017.88 cm2 10 615.75 m2 11 1 : 4 12 213.6 cm 13 7.07 m2 14 9.42 m Page 110 1 C 2 A 3 D 4 A 5 A 6 A 7 B 8 C 9 C 10 B 11 B 12 B Page 111 1 12 cm 2 a (minor) segment b sector 3 a 131.9 cm b 1385.4 cm2 4 a 12.6 m2 b 12.6 m 5 a 247 cm b 3619 cm2 6 a 63.6 cm2 b 32.1 cm 7 a 55 cm2 b 201 cm2

186 © Pascal Press ISBN 978 1 74020 033 2 Chapter Answers_2015 updates for future reprint.indd 186

Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook Excel Essential Skills Mathematics Revision & Exam Workbook Year 8 12/08/2015 3:15 pm

Answers Chapter 10 – Linear relationships

Page 112 1 a O b Q c Y d U e H f A g B h C i D j P k N l M m L n X o T p F q R r S s E t W u V v G w K x J 2 a (–6, 1) b (–4, 1) c (1, 1) d (4, 2) e (–3, 2) f (–5, 3) g (–2, 3) h (0, 3) i (2, 3) j (4, 4) k (2, 5) l (–2, 6) m (–6, 5) n (–2, 0) o (0, 0) p (3, 0) q (1, –5) r (1, –4) s (–3, –4) t (–2, –3) u (–4, –2) v (2, –2) w (5, –2) x (–5, –1) y (–2, –1) z (3, –1) Page 113 1 a 0, 1, 2, 3 b –2, 0, 2, 4 c –6, –3, 0, 3 d 1, 0, –1, –2 e 0, 1, 2, 3 f –4, –3, –2, –1 2 a –1, 1, 3, 5 b –3, –1, 1, 3 c 1, 3, 5, 7 d 2, 5, 8, 11 e –7, –3, 1, 5 f –5, –2, 1, 4 Page 114 1 a b c x –1 0 1 2 x –1 0 1 2 x –1 0 1 2

y

1

2

3

4

y –2

y

–1

0

1

y 4

y

3

2

y

y = –x + 3

y=x+2 x

y=x–1

y

2

0

1

2

2

b

2

3

x

0

y 3

y

x

x

2 a x 2

1

3

2

c

3

3

3

–1

0

1

2

2

y

x

–1

0

1

2

4

1

0

–1

2

3

y

–2

2

y=x+2

y = 2x + 1 x

187


x

y

x y = –x y –1 1 3 5 Their point of intersection Their point of intersection is (0, 0). is (1, 3)

y

1

3

y 1 2 3 y = –x y = 2x + 1 y=x x –1 0 1 2 x –1 0 1 y

2

y=x

3 a y = x b y = x + 2 1

1

x

0

0

y 0

y

x

–1

x

y=3

x=2

x

1


Answers

Page 115 1 a x = 2 b x = 4 c x = 3 d x = 4 e x = 6 f x = 6 2 a y = –2 b y = –8 c y = 6 d y = –3 e y = –3 f y = –3 3 a b 4 a y

y

y

x

x

b x 0 5 5

y

c x

0

d

1

x

–2 –1

1

0

–2 –1 3

1

0

3

1

1

3

3

2

x

y=3

3

x

3

3

3

2

3

–1

0

1

–1

1

3

3

2

1

0

x

–1

0

1

y –4 –1 2 y = –x + 2 y = x – 3 (1, 1) x –1 0 1 2 x –1 0 1 y

x

x

(3, –2)

y = –2

2

5

y

y = 3x – 1

2

y –4 –3 –2 –1 y = 2x – 1 Their point of intersection Their point of intersection y = –x + 2 is (1, 1). is (–1, –4). y

x=3

2

x –2 –1 0 1 2 x=1 y –2 –2 –2 –2 –2

2

–3

y

3

x

2 a y = 2x – 1 b y = 3x – 1 y

3 4

0

x

y –2 –1 0 1 (1, 3) y = 3 y = –2 y

x

x

Page 116 1 a x = 1 b x = 3 y 1

0

y

y

3

y

x

1

y

3 2

y –3 0 y –1 0

y

x

0

x

3 2

0

x

x

(–1, –4)

y=x–3

Page 117 1 a (0, 3) c (–4, 6) e (4, 0) f (8, –3) 2 b 2y = 3x c x – 5y = 0 e y = –2x 3 a yes b yes c no d yes e yes f no 4 m = 3 5 a = 5 6 a (0, –2) b (2, 4) c (1, 1) d (5, 13) e (–1, –5) f (–2, –8)

1

Page 118 1 a x = 2 b x = –3 c x = 4 2 a 2 + 1 = 3; 3 = 3 b –3 + 1 = –2; –2 = –2 c 4 + 1 = 5; 5 = 5 3 a x = 3 b x = – 2 c x = 2 d x = 4 4 a x = –1 b x = 1 c x = –2 d x = 2 5 a x = –1 b x = –4 c x = 4 d x = 2 Page 119 1 D 2 A 3 B 4 D 5 A 6 C 7 B 8 C 9 B 10 A 11 B 12 D



Answers

Page 120 1 a and iii, b and v, c and i, d and ii, e and iv, f and vi 2 a

y

b (–3, 1)

(–3, 1)

–3

•

y=1

x

x = –3

3 a y = x + 2 x

–3

–2

–1

0

1

y –1 0 1 2 3 c –5 d (–2, 0) e (0, 2) f x = –5

2

4

b

3

5

y

x

Chapter 11 – Equations

Page 121 1 a x = 3 b a = 4 c m = 12 d b = 6 e a = 8 f n = 7 g x = 6 h x = 6 i y = 6 j p = 10 k t = 10 l a = 12 m y = –5 n x = –2 o x = 4 2 a m = 8 b x = 10 c y = 12 d n = –12 e x = 11 f x = 18 g m = 4 h y = 21 i a = 2 j m = 10 k n = 16 l a = 15 m y = 2 n t = –2 o a = 6 Page 122 1 a x = 4 b a = 8 c m = 7 d b = 8 e a = 6 f n = 3 g x = 15 h x = 11 i y = 12 j p = 12 k t = 5 l a = 18 m y = –1 n x = –1 o x = 15 2 a m = –5 b x = –2 c y = 5 d n = 6 e x = 22 f x = 9 g m = 15 h y = 39 i a = 8 j m = 15 k n = 31 l a = 8 m y = 0 n t = 3 o a = 4 Page 123 1 a a = 4 b x = 6 c y = 3 d x = 21 e y = 30 f x = –4 g m = –3 h x = 3 i t = –20 j p = –4 k y = –20 l t = 4 m a = 18 n a = 8 o x = –21 2 a x = 30 b x = –12 c x = 42 d a = –60 e a = –18 f b = 72 g m = 36 h x = 27 i y = –28 j a = 6 kb=5 lx=4 mx=7 nx=6 ox=7 Page 124 1 a x = 1 b x = 8 c y = 5 d m = 6 e x = 23 f a = 5 g x = 16 h x = 2 i a = 23 j x = 5 k x = 5 l t = 7 m y = 2 n m = 30 o k = 9 2 a x = 4 b m = 6 c x = 33 d x = 50 e x = 7 f m = 12 g m = 5 h y = 10 i y = –1 j x = 3 k x = 3 l x = 7 m a = 3.1 n a = 1 o p = 0.3 Page 125 1 a x = –21 b x = 4 c t = 11 d m = 5 e m = 6 f a = 12 g y = 5 h x = 5 i y = 6 j x = 8 k a = 4 l p = 7 4

14

3

2 a x = 34 b x = 3 c x = – 3 d y = 17 e x = 2 f x = – 9 g m = 9 h x = 4 4 i y = 6 j m = –3 k x = –12 l y = 7 3

1

Page 126 1 a x = 2 b m = 2 c m = 5 d x = 4 e a = 6 3 f n = 12 g n = 3 h p = 4 i x = 3 j a = 6 k m = 4 l x = 2 2 a a = –32 2

5

3

22

b x = 23 c y = 18 d x = 68 e x = 4 5 f a = – 3 g x = – 2 h a = 21 i a = 13 j a = 0 k a = 15 l a = 14 m a = –57 n a = –96 o a = 23 Page 127 1 a 30 b 75 c 36 2 a 56 b 34 c 26 3 a 5 b 15 c 8 4 a 6 b 12 c 27 5 a 50.3 b 232.5 c 399.0 6 a 54 b 272 c 908.5 Page 128 1 16 2 10 3 14 4 18 5 2 6 15 7 18 8 36 9 5 10 width = 4 cm, length = 9 cm 11 12 cm 12 3 cm 13 52 14 x = 12 15 5 Page 129 1 a x = 36 b a = 24 c y = 42 d m = 30 e m = 28 f x = 54 g a = 11 h x = 12 i x = 5 j x = 6 k x = 10 l m = 22 1

1

1

2 a x = 20 b y = 7 c t = 15 d m = 19 e a = 8 f p = 7 g x = 8 h x = 6 4 i x = 0 j m = 11 k x = 1 l m = 7 2 m x = –3 3 np=5 oa=8 Page 130 1 D 2 C 3 C 4 D 5 C 6 A 7 D 8 A 9 D 10 C 11 A 12 B Page 131 1 a x = 37 b m = 6 c n = 21 d x = 1152 e x = 4 f a = –4 g x = 32 h x = 1

n x = 3 2 2 17

8 3

1

189


1

i x = 4 j p = 2 k x = 6 l x = 6 m x = 22


Answers Chapter 12 – Reasoning in geometry

Page 132 1 a y = 40 b a = 105 c m = 50, n = 130 d k = 120 e m = 70 f m = 40 2 a t = 90 b y = 35 c a = 20 d y = 35 e x = 55 f m = 82, n = 98, p = 98 3 a a = 45 b n = 70 c a = 90 Page 133 1 a a = 120 b m = 60 c n = 104 d y = 50 e x = 25 f n = 105 2 a a = 120, b = 60, y = 60, x = 120 b x = 60, y = 120, m = 120 c a = 70, b = 110, d = 70, c = 110 3 a a = 60 b x = 55 c a = 70 d x = 45, y = 20 e x = 30, y = 40 f a = 30, b = 60 Page 134 1 a a = 95 b a = 20 c x = 45 d x = 65, b = 50 e x = 70, y = 50 f x = 70, y = 70 2 a x = 35, y = 55 b x = 30, a = 30 c a = 115, m = 35, n = 30 3 a b = 70, a = 60, c = 50 b x = 75, y = 105 c m = 120 d y = 65, x = 115 e b = 50, c = 80, a = 100 f a = 40, b = 55, c = 55 Page 135 1 a x = 52 b x = 50 c y = 60 d a = 55 e x = 20 f a = 60 2 a a = 70 b y = 120 c x = 35 3 a x = 56 b a = 50 c x = 65 d x = 35, y = 55 e a = 35, m = 123 f a = 40, x = 75 Page 136 1 a a = 35 b m = 100, n = 80, p = 100 c a = 50, b = 130 d m = 60, n = 115 e a = 140 f x = 100 2 a x = 45, y = 140, m = 55 b a = 90, b = 145 c m = 70, n = 110, p = 70 3 a a = 203 b a = 36 c m = 90, p = 110, n = 70 d m = 150, n = 60 e a = 36 f a = 26 Page 137 1 a transformation b translation c reflection d rotation 2 a translation b reflection c rotation d reflection e rotation f translation g rotation h reflection Page 138 1 a ≡ b same, same c transformation d ΔABC ≡ ΔDEF 2 a translation b reflection c rotation 3 a ΔABC ≡ ΔDEF b ΔPQR ≡ ΔLMN c ΔGHI ≡ ΔJKL Page 139 1 a same, same b i equal ii equal iii equal c ≡ 2 a ABCD and EFGH, ABFE and DCGH, ADHE and BCGF b PQR and STU 3 A and M, B and F, C and L, D and I, E and G, H and J, K and N 4 a L and P, I and M, J and N, K and O b LI = PM, IJ = MN, JK = NO, KL = OP Page 140 1 a sides, angle, two, included angle b sides, three sides c side, hypotenuse, one side and the hypotenuse d sides, angle, two, angle 2 ΔABC and ΔZYX, ΔDEF and ΔAWV, ΔHGI and ΔATR, ΔJKL and ΔPQR, ΔMNO and ΔSUT 3 a ∠EFD b ∠P = ∠X, ∠R = ∠Z, ∠Q = ∠Y 4 a b d c 5 a ΔACF and ΔAEB; ΔBGC and ΔFGE; ΔBCE and ΔFEC; ΔCGE and ΔCDE b ΔRPS and ΔRTQ; ΔPQS and ΔTSQ; ΔPQU and ΔTSU; ΔPQT and ΔTSP Page 141 1 a i DF ii ΔABC and ΔDEF iii ABC ≡ DEF b i ∠TUS ii ΔPQR and ΔSTU iii ΔPQR ≡ ΔSTU 2 a ∠EFH = ∠GHF; ∠HEF = ∠FGH b EF = GH; FH = HF; HE = FQ c ΔEFH ≡ ΔGHF 3 a SP = SR; PQ = RQ; QS = QS b ∠SPQ = ∠SRQ; ∠PSQ = ∠RSQ; ∠PQS = ∠RQS c ΔPQS ≡ ΔRQS Page 142 1 a three matching sides b two matching sides and the included angle c two matching angles and the matching side d the hypotenuse and one matching side e ≡ 2 a SSS = SSS b RHS = RHS c SAS = SAS d AAS = AAS 3 a AC b yes c RHS Page 143 1 a a = 60, b = 120, c = 60 b x = 108, y = 108 c a = 90, b = 90, c = 90 2 a a = 55 b a = 50 c x = 92, y = 133 3 a x = 120, y = 30 b a = 55 b = 125, c = 55 c a = 40, b = 80 Page 144 1 a x = 90 b y = 45, 45, 90, 90, 135 c a = 60, 60, 60, 120, 120 d x = 14, 14, 84, 147, 115 e x = 70, 70, 70, 110, 110 f a = 55, 55, 110, 110, 85 2 a = 90, b = 30, c = 60 b a = 65, b = 115, c = 65 c a = 80, b = 65, c = 35, d = 80, e = 65 Page 145 1 C 2 B 3 C 4 A 5 C 6 B 7 A 8 C 9 A 10 C Page 146 1 a AB = ED, AC = EC, BC = DC b ∠A = ∠E, ∠B = ∠D, ∠ACB = ∠ECD c ∆ABC ≡ ∆EDC d SSS or SAS or AAS e reflection 2 a QR = ST, PQ = PT, PR = PS b ∠QPR = ∠SPT, ∠PQR = ∠PTS, ∠PRQ = ∠PST c ∆PQR ≡ ∆PTS d SSS or SAS or AAS 3 a 30 b 110 c ∆ABD ≡ ∆CDB d AAS e rotation 4 60°

Chapter 13 – Probability

Page 147 1 a certain b likely c impossible d unlikely e impossible f impossible g even chance h impossible 2 a 30% b 100% c 30% d 100% e 0% f 50% g 0% h 70% 3 a unlikely b impossible c certain d most likely e even chance f most likely g unlikely h unlikely i most likely j certain k unlikely l most likely Page 148 1 a January, February, March, April, May, June, July, August, September, October, November, December b red, blue, yellow c A, B, C, D, E, F, G, H d W, X, Y, Z e 1, 4, 9, 16, 25, 36, 49 f A, A, C, E, H, I, M, M, S, T, T g 26, 27, 28, 29 h spring, summer, autumn, winter 2 a C, C, E, I, I, N, N, O, O, S, S, T, U b 13 c 8 3 a 26 b 7 c 7 d 15 Page 149 1 a no b no c yes d yes e no 2 a A, E, H, I, N, P, S b black, grey c two heads, one head and one tail, two tails d 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 3 a yes b no c no d no e yes 4 a 14 b 36 c 23 d 0 e 33 1 4 1 1 1 4 d3 e5 f3 6 a7 5 Page 151 1 a 6

Page 150 1 a

1

1

b 2 c 13 d

3 7 5 b6

b

1 7 2 c3

c

3 4

4 7 1 3 2 2 4

d0 e d

1

1

e 26 f 2 2 a f


2 7

3

4

1 3

b

7

2 3

7 a 11 b 11 c

499 500

1

1 3 2 11

c

1

1

3 a6 b2 c 3

1

d 11 e 0 f 11

4 a2 b0 c1 5

13 32

6

4 5

2 3

1

d0 e2 f

1 3

2

4 a5 b

1 3

4

3

3

7

8

4

c 15 d 5 e 0 f 5 5 a 15 b 15 c 15

7 0 8 73% 9 0.995 10 4 in 5


Answers Page 152 1 There are 12 students who play both soccer and hockey; 50 students who play soccer or hockey, but not both; 23 students who play neither sport; 62 students who play soccer or hockey or both; and 85 students in Year 8. 2 There are 27 students who study Japanese; 41 students who study French; 19 students who study neither language; 0 students who study both languages; and 87 students in Year 8. 3 A = 39 B = 12 C = 23 D = 46 4 a b 12 c 9 d 21 e 27 C B E 12 6 9 Page 153 1

7 8

15

1

1

3

2 16 3 a 2 b 2 c 10 d

Page 154 1 a i 54 ii 98 b 200 c 3 a Boys

Girls

Total

29 50

4 5

d

Seen the movie

e 4 7

4 5

1

1

1

6

165

1

27

Total

115

300

85

350

7

41 7 75 iii 25 33 b 70

2

1

101

iv 150 b i

49 75

ii

49 82

550 5

1

b 10 c 25 d i 8 ii 4 2 a

I F 10 10 15

4

250

200

Page 155 1 B 2 D 3 B 4 D 5 A 6 D 7 A 8 D 9 B 10 B 11 C 12 C Page 156 1 a

3

e 49% f 25 g 58 2 a i 2 ii

Not seen

185

3

f 5 g 5 h 0 i 2 j 5 4 a 13 b 26 c 13 5 a 9 b 6

1 4

1

2

b 13 c 0 d 13 e

3 4

5 1 1 3 a tossing a tail with a coin b winning a cricket match 4 a P(E) = 2 b P(Ẽ) = 2 c P(E) + P(Ẽ) = 1

Chapter 14 – Statistics

2 a Frequency: 9, 7, 9, 6, 8, 11; cumulative frequency 9, 16, 25, 31, 39, 50 b 6 c 5 d 50 e 25 f 31 g 34 50 h

10

Frequency (f)

8 6 4 2 6

7

8 Score (x)

9

10

Cumulative Frequency (f)

Page 157 1 a 5 b 9 c 26 d

40 30 20 10 1

2

3 Score (x)

4

5

6

Page 158 1 a census b census c sample 2 a sample b census c sample d sample e census f census 3 a census b sample c census d sample e census f sample Page 159 1 a chance b systematic c strata 2 a systematic b random c stratified 3 a systematic b stratified c stratified d systematic e random sample Page 160 1 a In a census the whole population is surveyed, whereas in a sample only part of the population is surveyed. b Categorical data is data that can be placed in categories or sorted by types. Categorical data cannot be measured. Numerical data has number values. Calculations can be made with numerical data. c Discrete data has specific number values and is usually collected by counting. Continuous data is found by measurement and does not have exact values. 2 a numerical b numerical c numerical d categorical e numerical f categorical g numerical h numerical 3 a discrete b continuous c discrete d discrete e continuous f discrete g continuous h continuous i discrete j continuous k continuous Page 161 1 a numerical, discrete b categorical c categorical d categorical e numerical, discrete f numerical, continuous g numerical, continuous h numerical, discrete i categorical j numerical, discrete k categorical l numerical, continuous m categorical n categorical o numerical, continuous 2 a systematic b stratified c random d systematic e systematic 3 The meeting may be an English teachers’ meeting, so the views of teachers in other faculties would not be obtained. 4 Year 7, 43; Year 8, 40; Year 9, 42; Year 10, 44; Year 11, 45; Year 12, 36

191



Answers

Page 162 1 a 5 b 8.8 c 66.5 d 9 e 5 f 20 g 2.625 h 8.2 i 6 2 a 5.9 b 3.9 c 15.3 d 45.9 3 a x f fx mean = 3.375 b x f fx mean = 1.95 c x f 1 5 5 0 11 0 6 3 2 8 16 1 13 13 7 5 3 6 18 2 14 28 8 6 4 9 36 3 12 36 9 7 5 12 60 4 10 40 10 4 Total 40 135 Total 60 117 Total 25

fx 18 35 48 63 40 204

mean = 8.16

4 a 3930 b 12.3 c 91% Page 163 1 a 15 b 7.5 c 76 d 28 e 116 f 63 2 a 5 b 9 c 3 d 52 e 8 f 5 and 6 3 a cumulative frequency: 3, 9, 17, 24, 29, 33; mode = 3 median = 3 b cumulative frequency: 12, 31, 49, 64, 74, 87; mode = 6 median = 7 c cumulative frequency: 8, 14, 21, 31, 36; mode = 19 median = 18 d cumulative frequency: 5, 12, 20, 34, 40 mode = 19 median = 18.5 Page 164 1 a i 95.5 ii 81 iii 96 b Barry was above the average but he did not do well, he was second lowest in the class. When data includes atypical scores, the median should be used as the measure of ‘the middle’. 2 Few houses would have identical prices so the mode is not used. If one or several very expensive homes were sold this would significantly increase the mean, the mean would no longer be a good indicator of the price of the majority of houses sold. The median would be unaffected by the few high prices. 3 a 16.7 b 14 c 16 d The shop owner would sell more of this size and so would need to stock more of the modal size. Page 165 1 a 14 b 11 c 18 d 35 e 23 f 64 g 14 h 17 i 9 j 32 k 22 l 46 2 a 5 b 9 3 a 44 b 44 4 a 38 b 77 Page 166 1 C 2 C 3 B 4 C 5 A 6 A 7 D 8 D 9 A Page 167 1 a It is not random because each student on the bus does not have an equal chance of being selected. 3

b He would need to survey every student. 2 a 15 b 15 c 14.9 d 7 e 8 3 a 75 b 180 4 a 27 b 132

Exam Papers

Page 168 1 D 2 C 3 A 4 B 5 C 6 B 7 B 8 D 9 C 10 C 11 B 12 C Page 169 1 37 216 2

x

y

–1

0

–5

–2

1

1

2

4

12

3 3.645 L 4 10ab 5 211 6 3000 7 760 kg 8 25 9 2 – 2a 10 24 cm

11 105 m 12 432 13 212 14 x = 45 15 120 cm3 16 950 m 17 90º 18 3b(2a – b + 4a2) 19 $7.90 20 312 2

3

Page 170 1 a i FD ii ∠EFD b 105 cm3 2 a 6a b 10x – 6 c 3(x – 8) 3 a 40 b 150 c 14 d b 7:51 pm c 11:25 pm 5 a x = 105 b x = 205 c x = 31 6 a

26 35

4 a 12:18 pm

b (-1,0)

y

y=x+1 x

Page 171 1 A 2 B 3 B 4 C 5 B 6 D 7 C 8 C 9 A 10 D 11 B 12 C

7

5

Page 172 1 1635 h 2 9.4 3 8(a – 1) 4 85º 5 288 mm2 6 34 cents 7 x = 2 8 2 20 9 6 10 5x – 6 11 6.43 12 18 cm 13 •

•

14 1 L 15 35.83% 16 $43.30 17 0. 7 18 8 19 $99 20 5.9 kg • Page 173 1 a diameter b tangent c minor segment 2 a x = 36 b x = 8 c a = 20 3 a 10 b 11.5 c 6 d 12 4 66. 6 m 5 a x = 2.5 m b y = 2.5 cm 6 440 m 7 10 cm


5 2


Answers

Page 174 1 C 2 B 3 C 4 D 5 B 6 D 7 D 8 C 9 A 10 D 11 C 12 B 1 1 Page 175 1 0.2 2 $62.50 3 x = 10 4 37 2 % 5 5.5 km 6 7x + 8y 7 41.2 8 5x + 1 9 3m(3 – m) 10 150º 11 0.375 12 6 13 alternate angles 14 107 15 9 cm 16 x = 6 17 200 minutes 18 5 hours 19 $204.30 20 88.4 cm2 Page 176 1 a 90 cm2 b 80 cm2 c 461.8 cm2 2 600 cm3 3 a b 79 4 a –7, –5, –3, –1, 1, 3, 5 S A 24 16 39 b

c –1 d x = 4 5 a AC = AB, CM = BM, AM = AM b ∆ACM ≡ ∆ABM

y

x

y = 2x – 1

Page 177 1 C 2 B 3 C 4 C 5 C 6 B 7 B 8 D 9 C 10 C 11 D 12 C 7

21

1

Page 178 1 $684 2 12 3 3500 4 (1, 2) 5 25 6 1 7 408 m 8 150 m 9 3 10 1400 g 11 42° 12 8 h 20 min 13 962 cm2 14 2(4m – 5) 15 25 cm2 16 6 cm 17 –3x2 + 5x 18 132 cm 19 43.6 20 x = 59 Page 179 1 a x = 34 (angles in a straight line) b a = 52 (cointerior angles) c x = 31° (angle sum of a quadrilateral) 2 a 87.5 cm2 b 142.5 cm2 3 157 728 mm3 4 a AB = CD, AD = CB, BD = DB b ∠A = ∠C, ∠ABD = ∠CDB, ∠ADB = ∠CBD c ∆ABD ≡ ∆CDB Page 180 5 a 6 b 7 c 7 d 6.44 6 a y = 13.5 b a = 42 7 a x = 60 b x = 20 c x = 75

193



Notes



Topic Test Feedback Chart Percentage Score Your score x 100%) ( Marks available

Your Score (Part A + Part B)

Chapter Topic Test 1


+

=

2

Percentages

+

=

3


+

=

4

Indices

+

=

5

Rational numbers

+

=

6

Basic algebra

+

=

7


+

=

8


+

=

9

Circles

+

=

10


+

=

11

Equations

+

=

12


+

=

13

Probability

+

=

14

Statistics

+

=

27 27 27 27 27 27 27 23 25 27 27 25 27 20

x 100% =

%

x 100% =

%

x 100% =

%

x 100% =

%

x 100% =

%

x 100% =

%

x 100% =

%

x 100% =

%

x 100% =

%

x 100% =

%

x 100% =

%

x 100% =

%

x 100% =

%

x 100% =

%

Exam Paper Feedback Chart Exam Paper

Percentage Score Your score x 100%) ( Marks available

Your Score (Part A + Part B + Part C)

1

+

+

=

50

x 100% =

%

2

+

+

=

47

x 100% =

%

3

+

+

=

44

x 100% =

%

4

+

+

=

50

x 100% =

%



Get the Results You Want! Year 8 Mathematics Revision & Exam Workbook This book is suitable for students of all abilities studying Year 8 Mathematics. It has been specifically written to help students revise their work and succeed in all their class tests, half-yearly and yearly exams. 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 8 Australian Curriculum Mathematics course Over 170 pages of practice exercises Fourteen topic tests Four 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 Excel Essential Skills The Complete Fractions Workbook Year 7.

Your own checklist for Excel books for Year 8 students: Bookseller reference

Books

Level

3

English books:

978-1-74125-411-2

Excel Essential Skills Grammar and Punctuation Workbook

Years 7–8

978-1-74125-408-2

Excel Essential Skills Reading and Vocabulary Workbook

Years 7–8

978-1-74125-414-3

Excel Essential Skills Writing and Spelling Workbook

Years 7–8

978-1-74020-037-0

Excel Essential Skills English Workbook

Year 8

Mathematics books:

978-1-74020-040-3


Years 7– 8

978-1-74020-316-6

Excel Essential Skills Mathematics Extension Revision & Exam Workbook

Year 8

978-1-74125-435-8

Excel Essential Skills Problem Solving Workbook

Year 8

978-1-74125-474-7

Excel SmartStudy Mathematics

Year 8

978-1-74125-007-7

Excel Mathematics Study Guide

Year 8

978-1-74020-041-7


Years 8 –10

Science books:

978-1-74125-421-1

Excel SmartStudy Science

Year 8

978-1-74125-392-4

Excel Science Study Guide

Year 8

Year 8 Mathematics Revision & Exam Workbook AS Kalra

About the author

Excel E S S E N TI AL S KIL L S

Excel

YEAR

8

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


ISBN 978-1-74020-033-2

Visit our website for more information at www.pascalpress.com.au Our address is Pascal Press PO Box 250 Glebe NSW 2037 (02) 8585 4044

9781740200332_ESS Maths RandE WB Yr8 2015 spine 11mm.indd All Pages

9 781740 200332

AS Kalra 8/07/15 12:15 PM