Year 10 Cambridge Maths Textbook - Stage 5.1/5.2/5.3 PDF

10 YEAR CambridgeMATHS NSW STAGE 5.1 / 5.2 / 5.3...

10 YEAR CambridgeMATHS NSW STAGE 5.1 / 5.2 / 5.3 SECOND EDITION STUART PALMER, DAVID GREENWOOD SARA WOOLLEY, JENNY GOODMAN JENNIFER VAUGHAN ISBN 978-1-108-46847-3 © Palmer et al. 2019 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party. Updated August 2021  University Printing House, Cambridge CB2 8BS, United Kingdom One Liberty Plaza, 20th Floor, New York, NY 10006, USA 477 Williamstown Road, Port Melbourne, VIC 3207, Australia 314–321, 3rd Floor, Plot 3, Splendor Forum, Jasola District Centre, New Delhi – 110025, India 103 Penang Road, #05–06/07, Visioncrest Commercial, Singapore 238467 Cambridge University Press is part of the University of Cambridge. It furthers the University’s mission by disseminating knowledge in the pursuit of education, learning and research at the highest international levels of excellence. www.cambridge.org Information on this title: www.cambridge.org/9781108468473 © Stuart Palmer, David Greenwood, Sara Woolley, Jenny Goodman, Jennifer Vaughan, 2014, 2019 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2014 Second Edition 2019 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 Cover designed by Sardine Design Text designed by Loupe Studio Typeset by diacriTech Printed in China by C & C Offset Printing Co. Ltd. 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Updated August 2021 9781108468473pre_pi-xix.indd Page ii 12/08/21 11:07 AM  iii Table of Contents About the authors ix Introduction and guide to this book x Overview of the digital resources xv Acknowledgements xix 1 Measurement 2 Measurement and Geometry Pre-test 4 Numbers of any Magnitude (S5.1) 1A Converting units of measurement 5 Area and Surface Area 1B Accuracy of measuring instruments 10 (S5.1, S5.2, S5.3) 1C Pythagoras’ theorem in three-dimensional problems 14 Volume (S5.2, S5.3) 1D Area of triangles, quadrilaterals, circles and sectors REVISION 21 MA5.1–9MG, MA5.1–8MG, 1E Surface area of prisms and cylinders 29 MA5.2–11MG, MA5.3–13MG, 1F Surface area of pyramids and cones 35 MA5.2–12MG, MA5.3–14MG 1G Volume of prisms and cylinders 40 1H Volume of pyramids and cones 46 1I Volume and surface area of spheres 50 Investigation 56 Puzzles and challenges 59 Review: Chapter summary 60 Multiple-choice questions 61 Short-answer questions 62 Extended-response questions 65 2 Indices and surds 66 Number and Algebra Pre-test 68 Indices (S5.1, S5.2) 2A Rational numbers and irrational numbers 69 Surds and Indices (S5.3§) 2B Adding and subtracting surds 76 MA5.1–5NA, MA5.2–7NA 2C Multiplying and dividing surds 80 MA5.3–6NA 2D Binomial products 84 2E Rationalising the denominator 88 2F Review of index laws REVISION 92 2G Negative indices REVISION 96 2H Scientific notation REVISION 101 2I Fractional indices 104 2J Exponential equations 109 2K Exponential growth and decay FRINGE 113 Investigation 119 Puzzles and challenges 121 ISBN 978-1-108-46847-3 © Palmer et al. 2019 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party. Updated August 2021 iv Review: Chapter summary 122 Multiple-choice questions 123 Short-answer questions 123 Extended-response questions 125 3 Probability 126 Statistics and Probability Pre-test 128 Probability (S5.1, S5.2) 3A Review of probability REVISION 129 MA5.1–13SP, MA5.2–17SP 3B Formal notation for Venn diagrams and two-way 134 tables EXTENSION 3C Mutually exclusive events and non-mutually exclusive 141 events EXTENSION 3D Formal notation for conditional probability EXTENSION 146 3E Using arrays for two-step experiments 151 3F Using tree diagrams 157 3G Dependent events and independent events EXTENSION 165 Investigation 170 Puzzles and challenges 172 Review: Chapter summary 173 Multiple-choice questions 174 Short-answer questions 175 Extended-response questions 177 4 Single variable and bivariate statistics 178 Statistics and Probability Pre-test 180 Single Variable Data Analysis 4A Collecting, using and misusing statistical data 181 (S5.1, S5.2, S5.3) 4B Review of data displays REVISION 186 Bivariate Data Analysis (S5.2, S5.3) 4C Summary statistics 194 MA5.1–12SP, MA5.2–15SP, 4D Box plots 199 MA5.3–18SP, MA5.2–16SP, 4E Standard deviation 204 MA5.3–19SP 4F Displaying and analysing time-series data 210 4G Bivariate data and scatter plots 215 4H Line of best fi t by eye 221 4I Linear regression with technology 228 Investigation 232 Puzzles and challenges 234 Review: Chapter summary 235 Multiple-choice questions 236 Short-answer questions 237 Extended-response questions 239 ISBN 978-1-108-46847-3 © Palmer et al. 2019 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party. Updated August 2021  v 5 Expressions, equations and linear relationships 240 Number and Algebra Pre-test 242 Algebraic Techniques (S5.2, S5.3§) 5A Review of algebra REVISION 243 Linear Relationships 5B Algebraic fractions REVISION 249 (S5.1, S5.2, S5.3§) 5C Solving linear equations REVISION 254 Equations (S5.1, S5.2§, S5.3§) 5D Linear inequalities 259 MA5.2–6NA, MA5.3–5NA, 5E Graphing straight lines 263 MA5.2–8NA, MA5.3–7NA, 5F Finding the equation of a line 271 MA5.1–6NA, MA5.2–9NA, 5G Using formulas for distance and midpoint 277 MA5.3–8NA 5H Parallel lines and perpendicular lines 282 5I Solving simultaneous equations using substitution 288 5J Solving simultaneous equations using elimination 293 5K Further applications of simultaneous equations 297 5L Regions on the Cartesian plane EXTENSION 300 Investigation 307 Puzzles and challenges 310 Review: Chapter summary 311 Multiple-choice questions 312 Short-answer questions 314 Extended-response questions 317 Semester review 1 318 6 Geometrical figures and circle geometry 328 Measurement and Geometry Pre-test 330 Properties of Geometrical Figures 6A Review of geometry REVISION 331 (S5.1, S5.2, S5.3$) 6B Congruent triangles REVISION 342 Circle Geometry (S5.3#) 6C Using congruence to investigate quadrilaterals 349 MA5.1–11MG, MA5.2–14MG, 6D Similar figures 355 MA5.3–16MG, MA5.3–17MG 6E Proving and applying similar triangles 360 6F Circle terminology and chord properties 367 6G Angle properties of circles 374 6H Further angle properties of circles 381 6I Theorems involving tangents 386 6J Intersecting chords, secants and tangents 391 Investigation 395 Puzzles and challenges 397 Review: Chapter summary 398 Multiple-choice questions 399 Short-answer questions 400 Extended-response questions 402 ISBN 978-1-108-46847-3 © Palmer et al. 2019 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party. Updated August 2021 vi 7 Trigonometry 404 Measurement and Geometry Pre-test 406 Right–angled Triangles 7A Trigonometric ratios 407 (Trigonometry) (S5.1, 5.2◊) 7B Finding unknown angles 414 Trigonometry and Pythagoras’ 7C Applications in two dimensions 419 Theorem (S5.1, S5.2, S5.3$) 7D Directions and bearings 424 MA5.1–10MG, MA5.2–13MG, 7E Applications in three dimensions 430 MA5.3–15MG 7F Obtuse angles and exact values 435 7G The sine rule 442 7H The cosine rule 447 7I Area of a triangle 451 7J The four quadrants 455 7K Graphs of trigonometric functions 462 Investigation 470 Puzzles and challenges 472 Review: Chapter summary 473 Multiple-choice questions 474 Short-answer questions 475 Extended-response questions 477 8 Quadratic expressions and quadratic equations 478 Number and Algebra Pre-test 480 Algebraic Techniques (S5.2, S5.3§) 8A Expanding expressions REVISION 481 Equations (S5.2, S5.3§) 8B Factorising expressions 486 MA5.2–6NA, MA5.3–5NA, 8C Factorising monic quadratic trinomials 490 MA5.2–8NA, MA5.3–7NA 8D Factorising non-monic quadratic trinomials 494 8E Factorising by completing the square 498 8F Solving quadratic equations by factorising 502 8G Using quadratic equations to solve problems 507 8H Solving quadratic equations by completing the square 510 8I Solving quadratic equations with the quadratic formula 514 Investigation 519 Puzzles and challenges 521 Review: Chapter summary 522 Multiple-choice questions 523 Short-answer questions 524 Extended-response questions 525 ISBN 978-1-108-46847-3 © Palmer et al. 2019 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party. Updated August 2021  vii 9 Non-linear relationships, functions and their graphs 526 Number and Algebra Pre-test 528 Non–linear Relationships 9A Exploring parabolas 529 (S5.1, S5.2, S5.3§) 9B Sketching parabolas using transformations 538 Functions and Other Graphs (S5.3#) 9C Sketching parabolas using factorisation 544 Ratios and Rates (S5.2, S5.3) 9D Sketching parabolas by completing the square 550 MA5.1–7NA, MA5.2–10NA, 9E Sketching parabolas using the quadratic formula and 555 MA5.3–9NA, MA5.2–5NA, the discriminant MA5.3–4NA, MA5.3–12NA 9F Applications of parabolas 560 9G Lines and parabolas 565 9H Functions and their notation 573 9I Graphs of circles 580 9J Exponential functions and their graphs 586 9K Hyperbolic functions and their graphs 591 9L Cubic equations, functions and graphs 598 9M Further transformations of graphs 606 9N Using graphs to describe change 612 9O Literal equations and restrictions on variables 622 9P Inverse functions 627 Investigation 635 Puzzles and challenges 637 Review: Chapter summary 638 Multiple-choice questions 640 Short-answer questions 642 Extended-response questions 645 10 Logarithms and polynomials 646 Number and Algebra Pre-test 648 Logarithms (S5.3#) 10A Introducing logarithms 649 Polynomials (S5.3#) 10B Logarithmic graphs 653 MA5.3–10NA, MA5.3–11NA 10C Laws of logarithms 664 10D Solving equations using logarithms 668 10E Polynomials 671 10F Expanding and simplifying polynomials 675 10G Dividing polynomials 678 10H Remainder theorem and factor theorem 681 10I Factorising polynomials to find zeros 684 10J Graphs of polynomials 687 ISBN 978-1-108-46847-3 © Palmer et al. 2019 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party. Updated August 2021 viii Investigation 692 Puzzles and challenges 693 Review: Chapter summary 694 Multiple-choice questions 695 Short-answer questions 695 Extended-response questions 697 Semester review 2 698 Answers 710 Index 841 ISBN 978-1-108-46847-3 © Palmer et al. 2019 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party. Updated August 2021  ix About the authors Stuart Palmer was born and educated in NSW. He is a high school mathematics teacher with more than 25 years’ experience teaching students from all walks of life in a variety of schools. He has been a head of department in two schools and is now an educational consultant who conducts professional development workshops for teachers all over NSW and beyond. He also works with pre-service teachers at The University of Sydney. David Greenwood is the Head of Mathematics at Trinity Grammar School in Melbourne and has over 20 years’ experience teaching mathematics from Years 7 to 12. He has run workshops within Australia and overseas regarding the implementation of the Australian Curriculum and the use of technology for the teaching of mathematics. He has written more than 30 mathematics titles and has a particular interest in the sequencing of curriculum content and working with the Australian Curriculum proficiency strands. Sara Woolley was born and educated in Tasmania. She completed an Honours degree in Mathematics at the University of Tasmania before completing her education training at the University of Melbourne. She has taught mathematics in Victoria from Years 7 to 12 since 2006, has written more than 10 mathematics titles and specialises in lesson design and differentiation. Jenny Goodman has worked for over 20 years in comprehensive State and selective high schools in NSW and has a keen interest in teaching students of differing ability levels. She was awarded the Jones medal for education at Sydney University and the Bourke prize for Mathematics. She has written for Cambridge NSW and was involved in the Spectrum and Spectrum Gold series. Jennifer Vaughan has taught secondary mathematics for over 30 years in NSW, WA, Queensland and New Zealand and has tutored and lectured in mathematics at Queensland University of Technology. She is passionate about providing students of all ability levels with opportunities to understand and to have success in using mathematics. She has taught special needs students and has had extensive experience in developing resources that make mathematical concepts more accessible; hence, facilitating student confidence, achievement and an enjoyment of math ISBN 978-1-108-46847-3 © Palmer et al. 2019 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party. Updated August 2021 x Introduction and guide to this book The second edition of this popular resource features a new interactive digital platform powered by Cambridge HOTmaths, together with improvements and updates to the textbook, and additional online resources such as video demonstrations of all the worked examples, Desmos-based interactives, carefully chosen HOTmaths resources including widgets and walkthroughs, and worked solutions for all exercises, with access controlled by the teacher. The Interactive Textbook also includes the ability for students to complete textbook work, including full working-out online, where they can self-assess their own work and alert teachers to particularly difficult questions. Teachers can see all student work, the questions that students have ‘red-flagged’, as well as a range of reports. As with the first edition, the complete resource is structured on detailed teaching programs for teaching the NSW Syllabus, now found in the Online Teaching Suite. The chapter and section structure has been retained, and remains based on a logical teaching and learning sequence for the syllabus topic concerned, so that chapter sections can be used as ready-prepared lessons. Exercises have questions graded by level of difficulty and are grouped according to the Working Mathematically components of the NSW Syllabus, with enrichment questions at the end. Working programs for three ability levels (Building Progressing and Mastering) have been subtly embedded inside the exercises to facilitate the management of differentiated learning and reporting on students’ achievement (see page x for more information on the Working Programs). In the second edition, the Understanding and Fluency components have been combined, as have Problem-Solving and Reasoning. This has allowed us to better order questions according to difficulty and better reflect the interrelated nature of the Working Mathematically components, as described in the NSW Syllabus. Topics are aligned exactly to the NSW Syllabus, as indicated at the start of each chapter and in the teaching program, except for topics marked as: REVISION — prerequisite knowledge EXTENSION — goes beyond the Syllabus FRINGE — topics treated in a way that lies at the edge of the Syllabus requirements, but which provide variety and stimulus. See the Stage 5 books for their additional curriculum linkage. The parallel CambridgeMATHS Gold series for Years 7–10 provides resources for students working at Stages 3, 4, and 5.1. The two series have a content structure designed to make the teaching of mixed ability classes smoother. ISBN 978-1-108-46847-3 © Palmer et al. 2019 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party. Updated August 2021  xi Guide to the working programs It is not expected that any student would do every question in an exercise. The print and online versions contain working programs that are subtly embedded in every exercise. The suggested working programs provide three pathways through each book to allow differentiation for Building, Progressing and Mastering students. Each exercise is structured in subsections that match the Working Mathematically strands, as well as Enrichment (Challenge). The questions suggested for each pathway are listed in three columns at the top of each Building Progressing Mastering subsection: UNDERSTANDING AND FLUENCY 1–3, 4, 5 3, 4–6 4–6 The left column (lightest-shaded colour) is the Building pathway PROBLEM-SOLVING AND REASONING 7, 8, 11 8–12 8–13 The middle column (medium-shaded colour) is the Progressing pathway ENRICHMENT — — 14 The right column (darkest-shaded colour) is the Mastering pathway. Gradients within exercises and question subgroups The working programs make use of the gradients that have been seamlessly integrated into the exercises. A gradient runs through the overall structure of each exercise, where there is an increasing level of mathematical sophistication required in the Problem-solving and Reasoning group of questions than in the Understanding and Fluency group, and within each group the first few questions are easier than the last. The right mix of questions Questions in the working programs are selected to give the most appropriate mix of types of questions for each learning pathway. Students going through the Building pathway will likely need more practice at Understanding and Fluency but should also attempt the easier Problem-Solving and Reasoning questions. Choosing a pathway There are a variety of ways of determining the appropriate pathway for students through the course. Schools and individual teachers should follow the method that works for them if the chapter pre-tests can be used as a diagnostic tool. For classes grouped according to ability, teachers may wish to set one of the Building, Progressing or Mastering pathways as the default setting for their entire class and then make individual alterations, depending on student need. For mixed-ability classes, teachers may wish to set a number of pathways within the one class, depending on previous performance and other factors. The nomenclature used to list questions is as follows: 3, 4: complete all parts of questions 3 and 4 1–4: complete all parts of questions 1, 2, 3 and 4 10(½): complete half of the parts from question 10 (a, c, e … or b, d, f, …) 2–4(½): complete half of the parts of questions 2, 3 and 4 4(½), 5: complete half of the parts of question 4 and all parts of question 5 ––: do not complete any of the questions in this section. ISBN 978-1-108-46847-3 © Palmer et al. 2019 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party. Updated August 2021 xii Guide to this book Features: NSW Syllabus: strands, substrands and content outcomes for chapter (see teaching program for more detail) Chapter introduction: use to set a context for students What you will learn: an overview 126 of chapter contents Chapter 4 Understanding fractions, decimals and percentages 1 In which diagram is one-third shaded? A B C D Pre-test: establishes prior knowledge Key ideas Pre-test (also available as an auto-marked quiz 452 Chapter 2 Which of the10 Measurement following and is not equivalent computation to one whole? of length, perimeter and area in the Interactive Textbook as well as A 2 B 6 C 1 D 12 2 6 4 12 a printable worksheet) 3 Which of the following is not equivalent to one-half? 2 3 5 5A D Describing probability 205 10 A Ancient measurement B systems thatCdeveloped from about 4 9 10 203000 bce include the Egyptian, 4 Find: Babylonian, Greek and Roman systems. The metric system is the commonly used system Topic introduction: use to relate the 5A− 1Describing a 1 today probability in many countries, b 1− 1 includingcAustralia. 1− 1 d 1− 1 4 2 3 5 topic to mathematics in the wider world 5 Find: Roman Often, system there are times when you may wish to describe how likely it is that an event will occur. For example,1 you may want to know how 1 likely it is that it will rain1 tomorrow, or how likely3it is that your a 3 − 1 foot = 12 inches b 2 − = 16 digits = c 410palms − d 6− sporting4 team will win this year’s premiership, 2 or how likely it2is that you will win a lottery. 4 Probability is the study 1 chance.= 6 palms of cubit Let’s start: an activity (which can often 6 Tom eats half a block of chocolate on Monday and half of the remaining block on Tuesday. How much is1 left chocolate pace for (double Wednesday?step) = 5 feet be done in groups) to start the lesson Let’s start: Likely 1 mile or unlikely? = 1000 paces 7 Find the next three terms in these number sequences. Try to1rank these 1 events from least likely to most likely. a 0,imperial , 1, 1 , __,system __, __ 2 your Compare 2 answers with other students in the class and b discuss 31 foot 1 2 any = differences. , , , __ , __, __ 12 inches (1 inch is about 2.5 cm) 3It 3will 31rain yardtomorrow. = 3 feet (1 yard is about 91.5 cm) 50 1Australia 3 4 will 2 Chapter 2 win therelationships Angle soccer World Cup. c , , 1 , __, = , rod __,16.5 __ feet 4Tails 4 4landing 4 uppermost when a 20-cent coin is tossed. 1 1 chain = 22 yards Key ideas: summarises the knowledge and d , , 1 1The 6The sun 3 king will rise , __, __, __ tomorrow. 2 of spades is at the top of a shuffled deck of 52 playing cards. 1When furlong = (or two rays 40lines) rodsmeet, an angle is formed at the intersection point Key ideas skills for the lesson A diamond card is at the bottom of a shuffled deck of 52 playing cards. 8 Copy and complete. 1 mile = 8 furlongs = 1760 yards (1 called the vertex. The two rays are called arms of the angle. mile is about 1.6 km) arm 1 1 1 1 3 3 3 3 3 vertex a + + = __ × b + + + = __ × 2This2topic 2 involves2the use of sophisticated terminology. 4 4 4 4 4 arm 5 metric5 system Key ideas 6 6 c × __ = named using three points, withdthe8 ÷ __ = A 6 angle isExample 6 Terminology 1Ancentimetre (cm) = 10 millimetres (mm) Defi 8nition or vertex as the middle point. A common type of 9 Find: chance 1notation metre(m) rolling is ∠ABC =or100 a fair 6 centimetres -sided ∠CBA die (cm). The measure of the A chance B experiment is an activity that a° 1 experiment 1 3 may produce a variety1of different results 4 = 1000 metres (m) a b a represents of $160 an unknowncnumber. C d 2 1 kilometre (km) of $15angle is a°, where of $1 which occur randomly. of $6 3 The example given Examples: solutions with 4 is a single-step experiment. 10 State whether each of the Lower-case following letters is true are often usedortofalse. represent the number of B explanations and descriptive titles to a 1 trials degrees in rolling a die 50 times of 16 = 16 ÷ 2 an unknown angle. b 16 1 When an experiment is performed one or of 16times, each occurrenceAis called aC = more 2 4 4 aid searches. Video demonstrations Example 1 Using measurement systems 3 trial. The 1 example given indicates D 50 trials c of 100 = 75 d one-tenth of a=single-step experiment. 4 100 of every example are included in the a Howmany feetlines These two outcome arearethere parallel. rolling a 5 inThis 1 mile, using is written the. Roman measuring system? AB || DC C An outcome is one of the possible results B b Howmany inches These two areperpendicular. lines are there in 3This yards, is written AB ⟂of using the CD.imperial a chance system? experiment. Interactive Textbook. equally likely rolling a 5 Equally likely outcomes are two or more outcomes rolling a 6 A results that have the same chance of D SOLU TI ON 9781108466172c04_p124-201.indd Page 126 E X P LAN ATI ON occurring. 28/03/18 3:39 PM The markings on this diagram show that AB = CD, AD = BC, A B sample= a 1 mile 1000 ∠BAD paces = ∠BCD {1, 4, 5,∠6} 2, 3,and ABC = ∠ ADC. There The sample spaceare 1000 is the paces set of all possiblein a Roman mile and 5 space = 5000 feet outcomes of an experiment. It is usually in a pace. written inside braces, as shown in the D C b 3 yards = 9 feet example. There are 3 feet in an imperial yard and 12 i event = 108 e.g. inches 1: rolling a 2 An eventinisaeither foot.one outcome or a e.g. 2: rolling an even number collection of outcomes. It is a subset of the sample space. Example 1 Naming objects ISBN 978-1-108-46847-3 Example © Palmer et al. 22019 Choosing Name these objects. metric lengths Cambridge University Press Photocopying is restricted under law and this material must not be transferred toa another party. b P c Updated P August 2021  12 Three construction engineers individually have plans to build the world’s next tallest tower. The 1 Titan Circletower is todown or write be 1.12 whichkmmass tall, the Gigan towerare measurements is to thebesame. 109 500 cm tall and the Bigan tower is to be a 1210 1 kg, m 100tall. g, Which 1000 g,tower 10 t will be the tallest? b 1000 mg, 10 kg, 1 g, 1000 t 13 Steel chain costs $8.20 per metre. How much does is cost to buy chain of the following lengths? 2 aFrom1 km options A to F, choose the mass b that 80 cm best matches the given object. c 50 mm xiii a human hair A 300 g 14 A house is 25 metres from a cliff above the sea. The cliff is eroding at a rate of 40 mm per year. How b 10-cent coin B 40 kg many years will pass before the house starts to fall into the sea? c bottle C 100 mg 15 Mount Everest d large book is moving with the 10A Indo-Australian DMeasurement plate at akgrate of systems of the past and present 1.5 453 about e large10 bag cm per year. How many years will it take toE move of sand 13 t 5 km? Exercise questions categorised by the f truck F 5g 16 A ream of 500 sheets of paper is 4 cm thick. How thick is 1 sheet of Exercise 10A FRINGE 3 paper, in millimetres? From options A to D, choose the temperature that best matches the description. working mathematically components UNDERSTANDING a AND FLUENCYof coffee temperature A1–815°C 17 A snail slithers 2 mm every 5 seconds. How long will it take to 4–9 5–9(½) b temperature of tap water B 50°C and enrichment slither 1 m? 1 Complete cthese number of temperature sentences. oven C −20°C a Roman 18 Copy d system this chart and temperature fill in the missing information. D 250°C in Antarctica km i 14 Convert to the units shown=in12brackets. inches = 16 = m palms Example references link exercise ii 1 a 2 t (kg) Example 16 = 1000 paces b 70 kg (g) ÷ 100 cm questions to worked examples. b imperial 460 system cChapter 2.4 g10(mg)Measurement and computation of length,d perimeter 2300 mgand (g)area × 10 i 1 foot e 4620= 12mg (g) f 21 600 kg (t) mm g 0.47 t (kg) ii 3 PROBLEM-SOLVING AND REASONING = 1 yard h 312 g 10–12, 18 (kg) 12–14, 18 15–19 Investigations: iii 19 Many tradespeople measure and communicate with millimetres, i 27 mg (g) timber beams = 1760 yards j 3 t (kg) even for long measurements like 10 Arrange these or pipes. Can you measurements fromexplain whytothis smallest might 4be the case? largest. c metric ksystem inquiry-based activities Puzzles and a 38kg 1 8 (g)540 mm, 0.5 m cm, l b 10.5 0.02gkm, (kg)25 m, 160 cm, 2100 mm i 1m cm =0.003 ENRICHMENT 210 000 cmmm km,kg20(t)m, 3.1 m, 142 nd 0.47 — km, 0.1 m, 1000 0.001 t (kg) — cm, 10 mm 20 84 Chapter 2 challenges Angle relationships 504 ii 1 cm = Very Chapter 10 Measurement and computation11 olong592 of length, Joe 000 amg 1.2(g) andperimeter widensshort lengths mand doorway mm area by 50 mm. What is the pnew0.08 widthkgof(g)the doorway, in centimetres? iii km = 1000 m 20 Three 12 When construction 1 metre is divided into individually engineers 1 million parts, have each parttoisbuild plans called micrometre thea world’s (µm). tower. next tallest At the The other Without measuring, state which2 line List thelonger: units end A of length oftower the to(e.g. B?spectrum, acubit), light from kmtoyear is smallest used to to largest, describe large commonly distances used 500 cmintall and in space. thethe Roman