Oxford insight mathematics standard 2. [Year] 12

552 Pages·14.523 MB·English

by  Michael Fuller, Daniel Mansfield, John Ley

TITLE:LEY_IMS12SB_2_12145_CVR_02 FORMAT: 280MM X 217MM SPINE:21.7MM COLOURS USED: CMYK
OXFORD
INSIGHT
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IN STANDARD 2
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JOHN LEY
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MICHAEL FULLER
DANIEL MANSFIELD
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SFIELDFULLERLEY BARBCAORNAT MRIABRUINTAOKRISS

ANDREW HOLLAND
ISBN 978-0-19-031214-5
9 780190 312145
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OXFORD
INSIGHT
MATHEMATICS
STANDARD 2
12
JOHN LEY
MICHAEL FULLER
DANIEL MANSFIELD
ADDITIONAL RESOURCE
CONTRIBUTORS
BARBARA MARINAKIS
ANDREW HOLLAND
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1
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Published in Australia by
Oxford University Press
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© John Ley, Michael Fuller, Daniel Mansfield 2019
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First published 2019
Second Edition
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OXFORD UNIVERSITY PRESS
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CONTENTS
3 Rates and ratios 112
About the authors ...................................................v
Using Oxford Insight Mathematics Are you ready? ....................................................113
Standard 2 Year 12 ...............................................vi 3A Rates ..........................................................114
Top tips for study success .....................................vii 3B Heart rate ...................................................120
3C Fuel consumption rate ...............................124
3D Power and energy consumption rates .......130
1 Investments, depreciation and loans 2
3E Ratios .........................................................136
Are you ready? .......................................................3
3F Scale drawings ...........................................142
1A Comparing simple and compound interest
3G Building plans ............................................148
investments ...................................................4
3H Measurements of land using a scale .........156
1B The compound interest formula ..................10
Chapter review ....................................................166
1C Using a compounded value table .................18
1D Inflation and appreciated value ...................20
Chapters 1– 3 Cumulative review 174
1E Shares ..........................................................24
1F Declining- balance method of
depreciation .................................................30 4 Simultaneous linear equations 180
1G Reducing- balance loans ..............................36
Are you ready? ....................................................181
1H Credit cards ..................................................44
4A Graphs of the form y = mx + c ..................182
Chapter review ......................................................52
4B Linear models ............................................188
4C Identifying solutions to simultaneous
2 Non- right- angled trigonometry 58 linear equations .........................................192
4D Solving simultaneous linear equations
Are you ready? ......................................................59
graphically ..................................................196
2A Review of right- angled trigonometry ..........60
4E Break- even analysis ...................................200
2B Angles of elevation and depression .............68
Chapter Review ...................................................206
2C Bearings and navigational methods ............72
2D Area of a triangle .........................................82
2E Sine rule .......................................................84
2F Cosine rule ...................................................88
2G More problems involving trigonometry .......92
2H Compass radial surveys ...............................96
Chapter review ....................................................102
OXFORD UNIVERSITY PRESS Contents iii
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S 5 Bivariate data analysis 212 9 The normal distribution 378
T
N Are you ready? ....................................................213 Are you ready? ....................................................379
E 5A Bivariate scatterplots .................................214 9A Frequency distribution graphs ...................380
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5B Correlation .................................................218 9B The normal distribution .............................382
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O 5C Lines of best fit...........................................226 9C The standardised score ..............................386
C 5D Interpolation and extrapolation .................232 9D Properties of the normal distribution ........392
5E Statistical investigations ............................238 9E Probability and normal distributions .........398
Chapter review ....................................................242 Chapter review ....................................................406
6 Network concepts 250 10 Critical path analysis 414
Are you ready? ....................................................251 Are you ready? ....................................................415
6A Introduction to networks ............................252 10A Activity tables and charts ...........................416
6B Paths and cycles ........................................260 10B The earliest starting and finishing times ..428
6C Trees ...........................................................268 10C The latest finishing and starting times ......436
6D Minimum spanning trees ...........................274 10D The critical path .........................................444
6E The shortest path .......................................284 10E The maximum- flow minimum- cut
Chapter review ....................................................290 theorem ......................................................448
Chapter review ....................................................456
7 Annuities 300
Chapters 8– 10 Cumulative review 460
Are you ready? ....................................................301
7A Future and present value of an annuity .....302
Answers 464
7B Future value using a table .........................308
7C Present value using a table .......................312
7D Repaying loans ...........................................316 Glossary 536
7E Using technology to model annuities ........320
Chapter review ....................................................328
Index 539
Chapters 4– 7 Cumulative review 334
Acknowledgements 542
8 Non- linear relationships 340
Are you ready? ....................................................341
8A The parabola ..............................................342
8B Quadratic models .......................................348
8C The exponential graph ...............................358
8D Exponential models ...................................360
8E The rectangular hyperbola ........................366
8F Reciprocal models .....................................368
Chapter review ....................................................372
iv Oxford Insight Mathematics Standard 2 Year 12 OXFORD UNIVERSITY PRESS OXFORD UNIVERSITY PRESS
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JOHN LEY S
R
is a passionate and innovative mathematics educator. He has completed his PhD on mathematics
O
education while lecturing and tutoring at the University of Western Sydney. John has held an array
H
of teaching positions including Head of Mathematics, Assistant Principal, and Acting Principal.
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An experienced senior marker for the HSC, John was a member of the 2012–2014 assessment
U
committees, setting the HSC calculus course examinations. John is the lead author of the Oxford
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Insight Mathematics series for NSW.

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MICHAEL FULLER H
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was involved in Mathematics in NSW for many years, and was a key author on the Oxford Insight

Mathematics series. He held the position of Head of Mathematics at Killara High School in Sydney T
for 24 years. U
O
DR DANIEL MANSFIELD B
A
is an award-winning Lecturer in the School of Mathematics and Statistics at the University of New
South Wales (UNSW). In 2017, his research into ancient Babylonian trigonometry made headlines
around the world. Locally, Daniel is known for supporting secondary school mathematics teachers
and their students. His passion for mathematics is further endorsed by his students at UNSW, who
voted him the ‘Most Inspiring Lecturer in First Year’.
ANDREW HOLLAND
has 18 years’ experience teaching Mathematics to Secondary School students of varied levels of
ability. He previously taught at St Andrew’s Cathedral School and Shore School. He is now Head of
Mathematics at St Joseph’s College, Hunters Hill. Andrew previously authored a book on past HSC
examination questions for General Mathematics.
BARBARA MARINAKIS
has taught Mathematics to Secondary School and Tertiary Education students for 17 years and has
widespread experience with students of all levels of ability. She has held teaching positions at Sydney
Girls High School, Cranbrook School and is now teaching at Ascham School. Barbara has lectured
the Year 12 HSC preparation lectures for The School for Excellence and has lectured and tutored at
Australian Catholic University. She holds a Masters of Education from the University of NSW.
OXFORD OXFORD
INSIGHT INSIGHT
MATSHTEAMN1ADTJAOIH1RCN LDSEY OXFORD INSIGHT MATHEMATICS STANDARD 1 MSATTAHNEMD1AARTJO2IDHCN LS1EY
MICHAEL FULLER MICHAEL FULLER
DANIEL MANSFIELD
ADDBITAIRAONBCNADOARRNLAET WRMRE IAHBSROOUILNUTLAORAKRNCISDSE MANSFIELDFULLER LEY ADDBITAIRAONBCNADOARRNLAET WRMRE IAHBSROOUILNUTLAORAKRNCISDSE
OXFORD UNIVERSITY PRESS About the authors v
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Using Oxford Insight Mathematics Standard 2 Year 12
New South Wales’ most trusted Mathematics series has been updated for the new Mathematics
Standard Stage 6 syllabus. The new edition includes comprehensive exercise sets, carefully graded
exercises and worked examples embedded where students need them. Enhanced opportunities for
support and extension, as well as consolidation and practice are offered in reviews, cumulative reviews,
exam- style questions and integrated technology.
helpful resources are outlined
at the beginning of each unit
1A Comparing simple and EXERCISE 1A Comparing simple and compound interest
investments
compound interest
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  a P I  ==  P$5rn000, r  = 0.0 S6o7l, v ne   = 4 Cdiovnidvienrgt tbhye  1p0e0rc. enta Tghei ninkt/e Arepspt lrya te to a decimal by 3 C a c alc $ $u47la51t00e00 t haaett 10to3.0t%a3l1 pa%.ma .po oeuvrn edt rat o3y   byoeev aerrres p1 a9i dd aoyns a simple intere b dst lo $ $a55n72 o59f00: aatt 01.49%% pp.ear. omvoenr t1h7 o mveorn 1th5s m. onths
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44 Oxford Insight Mathematics Standard 2 Year 12 OXFORD UNIVERSITY PRESS OXFORD UNIVERSITY PRESS Chapter 1 Investments, depreciation and loans 5
01_LEY_IMS12SB2_12145_TXT_3pp.indd 4-5 8/3/18 12:29 AM
‘Working Mathematically’ syllabus
components clearly signposted
Student o book  a ssess
Oxford Insight Mathematics Standard 2 (Year 12) is supported
by a range of engaging and relevant digital resources via
o book a ssess.
Students receive:
> a complete digital version of the Student book with
notetaking and bookmarking functionality
> targeted instructional videos by a team of Australia’s most
experienced Mathematics Standard teachers designed to
help students prepare for assessment tasks and exams
> interactive auto- correcting multiple- choice quizzes
> access to teacher- assigned work including readings,
homework, tests and assignments.
Teacher o book  a ssess
In addition to the student resources, teachers also receive:
> detailed planning resources
> printable (and editable) class tests with exam- style questions and answers
> the ability to set up classes, set assignments, monitor progress and graph results, and to
view all available content and resources in one place.
vi Oxford Insight Mathematics Standard 2 Year 12 OXFORD UNIVERSITY PRESS
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Top tips for study success
Tip 1 – read key documents Tip 5 – know the structure of exams
The first step to success is to gather all key It’s important for you to become familiar with the
documents and read them carefully. format of the exam and the types of questions that
> Your most important tool is the syllabus. It sets out typically appear. In an exam you should also:
all of the information about the course, including > show your working when answering a question
what you are expected to learn and how you will be – even if a question is incorrect or left unfinished,
assessed. You can download a copy from the NESA you might still get some marks for your working
website. > keep an eye on the clock to make sure you have
> Keep all documents from your teacher relating to enough time to answer every question
assessment tasks and copies of any assessment > re- read questions so you know that you have
advice (e.g. marking criteria or assessment provided a complete and accurate answer.
rubrics). Understanding exactly what is required in
an assessment task is crucial. Tip 6 – understand key terms
Assessment tasks will likely include key terms. These
Tip 2 – study regularly
range in level of difficulty. Some, such as solve or find,
If you’re going to perform at your best, you need are simple to understand and master. Others, such as
to allocate time for regular periods of study and justify, are more challenging and will take practice to
revision. Studying regularly will help you to continually master. Below is a list of common key terms and an
reinforce new concepts and avoid the stress of last- explanation of what they mean.
minute cramming. During your study you might: 
> summarise theory and key examples in your
TERM DEFINITION
own words
> focus on topics you find difficult and work through examine something complex by
the relevant examples and questions analyse breaking it down into smaller parts and
show how they relate to one another
> test your understanding with revision questions,
practice papers and past exams. calculate work out an answer mathematically
classify categorise into groups
Tip 3 – manage your study time
change to a different form without
When studying, it helps to put some practical convert
changing the value
strategies in place to stay on track. Try the following
time management strategies. describe give a detailed account of the features
> Create a study timetable to set up periods of evaluate determine the value
regular study and revision around your school and
make something clear by describing the
personal schedule.
explain relationships between different aspects
> Use a diary, wall planner or calendar to record
and giving reasons
the dates of upcoming assessment tasks, tests or
exams and allow you to adequately prepare. represent an answer as a number,
express
figure, formula or symbol
> Make lists of daily, weekly or monthly goals.
It helps to keep the bigger picture in mind determine the value or answer to a
find
and breaks big tasks down into smaller, more problem.
manageable tasks, so that you gain a sense of
identify determine and state clearly
achievement.
justify present an argument providing evidence
Tip 4 – take care of yourself
solve work out the solution to a question
Looking after yourself during for HSC is important:
> eat a balanced diet and stay hydrated – try to avoid
too much caffeine and junk food
> get enough sleep and regular exercise
> make time for breaks from study – a walk to get
some fresh air will help you reset before the next
study session.
OXFORD UNIVERSITY PRESS Study tips vii
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1
1A 1 What is the result of 2000 × 0.05 × 3?
A 1200 B 30 000
C 2003.05 D 300
1A 2 What is 9.5% expressed as a decimal?
A 0.95 B 0.095
C 9.5  D 950
1A 3 Given that a = 3, b = 4 and c = 8, what is the
value of abc?
A 348 B 15
C 96 D 3.48
1A 4 Given that a = 2, b = 5 and c = 9, what is the
value of a(b + c)?
1A 5 What is 20% of 970?
A 19 400 B 194
C 1940 D 19.4
1A 6 What is 7.5% of $11 300?
A $84 750 B $847.50
C $1506.67 D $1.51
Investments,
1A 7 How much interest is earned if $1000 is put
into a simple interest account paying 5% p.a.
for 1 year?
depreciation
A $5000 B $50
C $500 D $1050
and loans 1A 8 $2000 is put into a simple interest account
paying 7% p.a. How much is in the account
after 1 year?
A $2070 B $14 000
The main mathematical ideas investigated are:
C $140 D $2140
▶ making compound interest calculations using the formula
▶ making compound interest calculations using a compounded
value table
▶ comparing different investment strategies
▶ calculating the price of goods following inflation
▶ calculating new salaries after increases in line with inflation
▶ calculating the appreciated value of items
▶ the mathematics of shares
▶ calculating the salvage value of an item using the declining-
balance method of depreciation
▶ calculating declining- balance loan repayments, including
the use of tables
▶ calculating payments, charges and balances on credit cards.
FINANCIAL MATHEMATICS
Licensed to PhoebeM SSiu- F, 4fr oInmv eBsettmhaennyt sC aonlledg Leo uanntsil 2022-01-01. OXFORD UNIVERSITY PRESS Chapter 1 Investments, depreciation and loans
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