CambridgeMaths stage 6. Year 12, Mathematics standard 1

322 Pages·18.156 MB·English

by  Gregory K. Powers

1122
YEAR
MATHEMATICS
STANDARD 1
CambridgeMATHS
STAGE 6
GK POWERS
Mathematics Standard 1 ISBN 978-1-108-44806-2 © GK Powers 2019 Cambridge University Press
Cambridge Maths Stage 6 Photocopying is restricted under law and this material must not be transferred to another party.
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Mathematics Standard 1 ISBN 978-1-108-44806-2 © GK Powers 2019 Cambridge University Press
Cambridge Maths Stage 6 Photocopying is restricted under law and this material must not be transferred to another party.
Contents
About the author vi
Acknowledgements vi
Introduction vii
1 Rates 1 M4
1A Rates 2
1B The unitary method 5
1C Using rates to make comparisons 7
1D Speed as a rate 10
1E Distance–time graphs 13
1F Fuel consumption rate 16
1G Heart rate 19
1H Blood pressure 23
Chapter summary 27
Multiple-choice 28
Short-answer 29
2 Networks and paths 31 N1.1, N1.2
2A Networks 32
2B Travelling a network 37
2C Drawing a network diagram 42
2D Eulerian and Hamiltonian walks 47
2E Network problems 51
2F Minimal spanning trees 55
2G Shortest path 60
Chapter summary 65
Multiple-choice 66
Short-answer 67
iii
Mathematics Standard 1 ISBN 978-1-108-44806-2 © GK Powers 2019 Cambridge University Press
Cambridge Maths Stage 6 Photocopying is restricted under law and this material must not be transferred to another party.
3 Investments 69 F2
3A Simple interest 70
3B Simple interest graphs 74
3C Compound interest – Future value 77
3D Compound interest – Present value 82
3E Compound interest graphs 84
3F Appreciation and inflation 87
Chapter summary 91
Multiple-choice 92
Short-answer 93
4 Right-angled triangles 95 M3
4A Pythagoras’ theorem 96
4B Applying Pythagoras’ theorem 99
4C Trigonometric ratios 101
4D Using the calculator in trigonometry 106
4E Finding an unknown side 110
4F Finding an unknown angle 114
4G Solving practical problems 117
4H Angles of elevation and depression 121
4I Compass and true bearings 125
Chapter summary 129
Multiple-choice 130
Short-answer 131
5 Simultaneous linear equations 133 A3.1
5A Linear functions 134
5B Linear models 139
5C Simultaneous equations – graphically 143
5D Simultaneous equation models 147
5E Break-even analysis 150
Chapter summary 153
Multiple-choice 154
Short-answer 155
Practice Paper 1 157
iv
Mathematics Standard 1 ISBN 978-1-108-44806-2 © GK Powers 2019 Cambridge University Press
Cambridge Maths Stage 6 Photocopying is restricted under law and this material must not be transferred to another party.
v
6 Further statistical analysis 163 S3
6A Constructing a bivariate scatterplot 164
6B Using a bivariate scatterplot 168
6C Line of best fit 174
6D Interpolation and extrapolation 177
6E Statistical investigation 181
Chapter summary 185
Multiple-choice 186
Short-answer 187
7 Scale drawing 189 M5
7A Ratios 190
7B Dividing a quantity in a given ratio 193
7C Similarity and scale factors 196
7D Scale drawing 201
7E Plans and elevations 205
Chapter summary 213
Multiple-choice 214
Short-answer 215
8 Depreciation and loans 217 F3
8A Declining-balance depreciation 218
8B Reducing-balance loans 222
8C Credit cards 227
8D Credit card statements 230
8E Fees and charges for credit card usage 233
Chapter summary 235
Multiple-choice 236
Short-answer 237
9 Graphs of practical situations 239 A3.2
9A Graphs of exponential functions 240
9B Exponential models 243
9C Quadratic functions 246
9D Quadratic models 250
9E Graphs of reciprocal functions 253
9F Reciprocal models 256
9G Miscellaneous problems 260
Chapter summary 263
Multiple-choice 264
Short-answer 265
Practice Paper 2 267
2019 Higher School Certificate Examination
Mathematics Standard 1/2 Reference sheet 273
Glossary 275
Answers 285
v
Mathematics Standard 1 ISBN 978-1-108-44806-2 © GK Powers 2019 Cambridge University Press
Cambridge Maths Stage 6 Photocopying is restricted under law and this material must not be transferred to another party.
About the author
Greg Powers is currently the Head of Mathematics at Cabramatta High School
and the coordinator of the Mathematics Head Teacher Western Network. He is
an experienced classroom teacher, having taught for over 30 years in a range
of different schools. Greg has been a senior marker for the HSC, educational
consultant for the Metropolitan South West Region and presented at numerous
MANSW inservices. He has also enjoyed several curriculum roles with the
Department of Education and Training. Greg is an experienced author who has
written numerous texts on mathematics and technology.
Acknowledgements
The author and publisher wish to thank the following sources for permission to reproduce material:
Cover: © Getty Images / Adie Bush, Cover
Images: © Getty Images / Dallas Stribley, Chapter 1 Opener / ChubarovY, 1A (1) / James F Dean, 1D (1) /
Westend61, 1A (2) / Image Source, 1B (1) / Dan Dunkley, 1C (1) / Jeffrey Davis, 1D (1) / Chris Ryan, 1D
(2) / artisteer, 1F (1) / Andrew Watson, 1F (2 ) / Guido Mieth, 1G (1) / StockFood, 1H (1) / Darren Rob,
Chapter 2 Opener / Busakorn PongParnit, 2A (1) / NicElNino, 2C (1) / Robert Daley, 2E (1) / point A to
point B, 2G (1) / Gary S Chapman, Chapter 3 Opener / Universal History Archive, Chapter 4 Opener /
Martina Birnbaum, 4B (1) / Sumeet Sonpatki, 4D (1) / Klaus Vedfelt, 4E (1) / Jason Jones Travel Photos,
4G (1) / Hillview 1 4G (2) / Constantinis, 4G (3) / C Caldicott, 4H (1) / T Grist, 4E (1) / pbomaert,
Chapter 5 Opener / S Edwards, 5B (1) / Maximillan Stock Ltd, 5B (2) / M BLann, 5D (1) / Hero Images,
5D (1) / Roy Scott, Chapter 6 Opener / R James Shakespeare, 6A (1) / T Barwick, 6C (1) / T Merton, 6D
(1) / Guy Burchell, 6E (1) / JGI, 6E (1) / O Burston, Chapter 7 Opener / antorti, 7A (1) / D Dalton, 7A (1) /
S Zhukova, 7B (1) / J Kasawa, 7C / Auscape, 7D / T Nguyen, 7D / pamspix, 7E / PaulMaguire, 7E /
Westend1, 7E / C Lathom – Sharp, Chapter 8 Opener / E Audras, 8A (1) / P Seaward, 8A (3) / Maskot, 8A
(2) / Silverstock, 8A (4) / artpartner-images, 8B (1) / T Barwick, 8B (1) / Hero images, 8B (2) / J Davis, 8C
(1) / P Dazeley, 8C (3) / B Karademir, 8E / jcarrol-images, Chapter 9 Opener / j Rotman, 9B / T Barwick,
9F / frankreporter, 9F / Santiago, Urquijo, 9B.
© NSW Government, Transport.nsw.gov.au, 2E (2).
Every effort has been made to trace and acknowledge copyright. The publisher apologises for any
accidental infringement and welcomes information that would redress this situation.
vi
Mathematics Standard 1 ISBN 978-1-108-44806-2 © GK Powers 2019 Cambridge University Press
Cambridge Maths Stage 6 Photocopying is restricted under law and this material must not be transferred to another party.
Introduction
CambridgeMATHS Mathematics Standard 1 Year 12 provides complete and close coverage of the
NSW Stage 6 Mathematics Standard 1 Year 12 syllabus to be implemented from 2018.
Now part of the CambridgeMATHS series, this resource is part of a continuum from Year 7 through to 12.
The series includes advice on pathways from Stage 5 to Stage 6. The Year 12 resource gives access
to selected previous years’ lessons for revision of prior knowledge.
The four components of Mathematics Standard 1 Year 12 – the print book, downloadable PDF textbook,
online Interactive Textbook and Online Teaching Resource – contain a huge range of resources available to
schools in a single package at a convenient low price. There are no extra subscriptions or per-student charges
to pay.
Interactive Textbook powered by the HOTmaths platform – included with the print book or
available separately (shown on the page opposite)
The Interactive Textbook is an online HTML version of the print textbook powered by the HOTmaths
platform, completely designed and reformatted for on-screen use, with easy navigation. Its features include:
1 All examples have video versions to encourage independent learning.
2 All exercises including chapter reviews have the option of being done interactively on line, using
workspaces and self-assessment tools. Students rate their level of confidence in answering the question
and can flag the ones that gave them difficulty. Working and answers, whether typed or handwritten,
and drawings, can be saved and submitted to the teacher electronically. Answers displayed on screen if
selected and worked solutions (if enabled by the teacher) open in pop-up windows.
3 Teachers can give feedback to students on their self-assessment and flagged answers.
4 The full suite of the HOTmaths learning management system and communication tools are included in
the platform, with similar interfaces and controls.
5 Worked solutions are included and can be enabled or disabled in the student accounts by the teacher.
6 Interactive widgets and activities based on embedded Desmos windows demonstrate key concepts
and enable students to visualise the mathematics.
7 Desmos scientific and graphics calculator windows are also included.
8 Revision of previous years’ material is included.
9 Every section in a chapter has a Quick Quiz of automatically marked multiple-choice questions for
students to test their progress.
10 Definitions pop up for key terms in the text, and are also provided in a dictionary.
11 Each chapter has a Study Guide – a concise summary in PowerPoint slides that can be used for
revision and preparation for assessment.
12 Literacy worksheets can be accessed via the Interactive Textbook, with answers in the Online
Teaching Suite, providing activities to help with mathematical terminology.
13 Spreadsheet files are provided for spreadsheet questions.
Downloadable PDF textbook (shown on the page opposite)
14 The convenience of a downloadable PDF textbook has been retained for times when users cannot go online.
vii
Mathematics Standard 1 ISBN 978-1-108-44806-2 © GK Powers 2019 Cambridge University Press
Cambridge Maths Stage 6 Photocopying is restricted under law and this material must not be transferred to another party.
INTERACTIVE TEXTBOOK POWERED BY THE HOTmaths PLATFORM
Numbers refer to the descriptions on the opposite page. HOTmaths platform features are updated regularly.
Screenshots show Standard 2 content, Standard 1 has the same features.
10 Pop-up definitions 9 Quick quizzes
5 Worked solutions
(if enabled by teacher)
7 Desmos
Submit calculator
Show working
windows
Show answers
Open working 6 Interactive
solution
1 Video Desmos
worked widgets
examples
2 Answers
displayed on
screen
12 Printable
Literacy
worksheet
2 Interactive
exercises with
typing/hand- 11 Study Guides
13 Spreadsheet
writing/drawing
entry showing question and 8 Revision of prior
working files 10 Dictionary knowledge
4 Tasks sent by teacher
PDF TEXTBOOK
DOWNLOADABLE
14 Included with
Search
Interactive Textbook
functions
Note-taking
viii
Mathematics Standard 1 ISBN 978-1-108-44806-2 © GK Powers 2019 Cambridge University Press
Cambridge Maths Stage 6 Photocopying is restricted under law and this material must not be transferred to another party.
ix
Online Teaching Suite powered by the HOTmaths platform (shown on the page opposite)
The Online Teaching Suite is automatically enabled with a teacher account and appears in the teacher’s
copy of the Interactive Textbook. All the assets and ersources are in one place for easy access. Many of
them are opened by clicking on icons in the pages of the Interactive Textbook. The features include:
15 Editable teaching programs with registers, a scope and sequence document and curriculum grid.
16 Topic test worksheets A and B – based on the knowledge, skills and understanding gained in each chapter,
and Revision Quiz worksheets provide HSC-standard questions for further revision for each topic, with
worked solutions. NESA requirements for problem-solving investigative tasks will also be addressed.
17 A HOTmaths-style test generator provides additional multiple-choice questions, as well as digital
versions of the multiple-choice questions in the test worksheets.
18 The HOTmaths learning management system with class and student reports and communication tools
is included.
19 Teacher’s lesson notes – pop-up text boxes containing lesson notes and additional examples that can be
used in class, also available as editable PowerPoint slides which can be given to students as tutorials.
Other features:
20 The textbook is divided into smaller manageable topics to assist teaching.
21 Syllabus topic focus and outcomes are listed at the beginning of each chapter.
22 Each section and exercise begins at the top of the page to make them easy to find and access.
23 Each exercise develops a student’s skills to work mathematically at their level.
24 Step-by-step worked examples with precise explanations (and video versions for most of them)
encourage independent learning, and are linked to exercises.
25 Important concepts are formatted in boxes for easy reference.
26 Spreadsheet activities are integrated throughout the text, with accompanying Excel files in the
Interactive Textbook.
27 Chapter reviews contain a chapter summary and multiple-choice and short-answer questions.
28 A comprehensive glossary and HSC Reference sheet are included.
29 There are two complete HSC practice papers.
ix
Mathematics Standard 1 ISBN 978-1-108-44806-2 © GK Powers 2019 Cambridge University Press
Cambridge Maths Stage 6 Photocopying is restricted under law and this material must not be transferred to another party.
ONLINE TEACHING SUITE POWERED BY THE HOTmaths PLATFORM
Numbers refer to the descriptions on the opposite page. HOTmaths platfrom features are updated regularly.
16 Printable
test and
19 Teacher’s quiz sheets
lesson notes
(Indicated by T icon in
teacher’s interactive 15 Teaching
textbook) programs
18 Class reports
17 Test 18 Student
generator results
Teacher’s copy
18 Tasks sent to
of Interactive
students
Textbook
PRINT TEXTBOOK
23 Exercises
20 Smaller 27 Chapter
manageable summary
topics
28 Glossary
to assist
teaching Answers
29 HSC
practice
Icons indicate
papers
digital assets
24 Step-by-
step worked 24 Questions
examples linked to
with precise examples
explanations
x
Mathematics Standard 1 ISBN 978-1-108-44806-2 © GK Powers 2019 Cambridge University Press
Cambridge Maths Stage 6 Photocopying is restricted under law and this material must not be transferred to another party.