Mathematics
General
Stage 6 Syllabus
HSC Mathematics General 2 Course
Support Material
© 2013 Board of Studies NSW for and on behalf of the Crown in right of the State of New South Wales.
This document contains Material prepared by the Board of Studies NSW for and on behalf of the State of
New South Wales. The Material is protected by Crown copyright.
All rights reserved. No part of the Material may be reproduced in Australia or in any other country by any process,
electronic or otherwise, in any material form or transmitted to any other person or stored electronically in any form
without the prior written permission of the Board of Studies NSW, except as permitted by the Copyright Act 1968.
School students in NSW and teachers in schools in NSW may copy reasonable portions of the Material for the
purposes of bona fide research or study.
When you access the Material you agree:

to use the Material for information purposes only 

to reproduce a single copy for personal bona fide study use only and not to reproduce any major extract or the
entire Material without the prior permission of the Board of Studies NSW 

to acknowledge that the Material is provided by the Board of Studies NSW 

not to make any charge for providing the Material or any part of the Material to another person or in any way
make commercial use of the Material without the prior written consent of the Board of Studies NSW and payment
of the appropriate copyright fee 

to include this copyright notice in any copy made 

not to modify the Material or any part of the Material without the express prior written permission of the
Board of Studies NSW. 
The Material may contain third-party copyright materials such as photos, diagrams, quotations, cartoons and artworks.
These materials are protected by Australian and international copyright laws and may not be reproduced or transmitted
in any format without the copyright owner’s specific permission. Unauthorised reproduction, transmission or commercial
use of such copyright materials may result in prosecution. 
The Board of Studies has made all reasonable attempts to locate owners of third-party copyright material and
invites anyone from whom permission has not been sought to contact the Copyright Officer, ph (02) 9367 8289,
fax (02) 9279 1482.

Published by
Board of Studies NSW
GPO Box 5300
Sydney NSW 2001
Australia 
Tel: (02) 9367 8111
Fax: (02) 9367 8484
Internet: www.boardofstudies.nsw.edu.au
20121459
2
Contents
Support material for HSC Mathematics General 2 Strands and Focus Studies
Strand: Financial Mathematics .......................................................................................................... 4
Strand: Data and Statistics ................................................................................................................ 8
Strand: Measurement ...................................................................................................................... 11
Strand: Probability ........................................................................................................................... 12
Strand: Algebra and Modelling ........................................................................................................ 13
Focus Study: Mathematics and Health ............................................................................................ 14
Focus Study: Mathematics and Resources ..................................................................................... 23
Note
The sample student exercises (labelled ‘For the student’) included in this document are
not intended to indicate the scope of questions that may be asked in relation to the relevant
Strand or Focus Study in the Mathematics General 2 HSC examination.
3
HSC Mathematics General 2 Course Support Material
Strand: Financial Mathematics
FM4 Credit and borrowing
The following online resources could be used to support the teaching and learning of this topic.
Credit card calculator
(calculate the total amount that will be
paid if only the minimum repayment is
made each month)
https://www.moneysmart.gov.au/tools-andresources/calculators-and-tools/credit-card-calculator
Credit card fees and charges explained
www.stgeorge.com.au/assets/stg/downloads/accounts_and_
cards/sgb_cc_fee_charges_0612.pdf
Credit card interest explained
(includes exemplar statements covering
a three-month period)
www.nab.com.au/vgnmedia/downld/Facts_about_credit_card
_interest_40014A0308.pdf
Credit card interest and fees explained
(includes credit card statement explained)
www.commbank.com.au/personal/apply-online/downloadprinted-forms/ADB3181-a-question-of-interest.pdf
Credit card interest-free periods explained
www.creditcardfinder.com.au/what-does-55-days-interest-freereally-mean.html
Credit card jargon buster
www.commbank.com.au/personal/credit-cards/credit-cardjargon-buster/
Credit card statements explained
www.creditcardfinder.com.au/understanding-credit-cardstatement-features.html
www.anz.com.au/personal/credit-cards/calculators-tools/how-toread-your-statement/
www.citibank.com.au/global_docs/statement_demo/
http://learn.nab.com.au/how-to-read-your-credit-card-statement/
Credit cards (includes videos)
https://www.moneysmart.gov.au/borrowing-and-credit/creditcards
Credit cards and store cards facts sheet
https://www.moneysmart.gov.au/media/283208/cfs-credit-cardsand-store-cards.pdf
For the teacher
Credit cards

The conditions and calculations of interest, fees, balances and payments for credit card
accounts vary depending on the type of card and the issuer.

By law, all Australian credit card issuers are required to provide those who apply for a credit
card with a ‘key facts sheet’ containing information on the:
–
minimum repayment (including how it will be calculated)
–
interest rate that applies to purchases and to cash advances
–
interest rate that applies to balance transfers (and for how long)
–
promotional interest rate (if any)
–
length of the interest-free period (if any)
–
annual and late payment fees (if any).
Search the websites of credit card issuers to locate the key facts sheets for particular
credit cards.
4
HSC Mathematics General 2 Course Support Material
Terminology used in credit card statements
Term
Meaning
Notes
annual fee or
monthly fee
A fee charged by the issuer for
maintenance of the account.
Annual fees are the most common
fees on credit card accounts. They
usually range from $0 to $300, but
they can be higher.
available credit
The total amount of money
available within the credit limit
for purchases/cash advances.
balance transfer
The act of transferring the balance
from an existing credit card account
to a different credit card account.
Balances transferred to a new card
often attract a significantly lower
interest rate for an introductory period.
After the introductory period expires,
any remaining balance usually
attracts the standard interest rate
for purchases, although in some
cases it attracts the interest rate
for cash advances.
cash advance
Cash withdrawn from a credit card
account.
Transactions considered to be
cash advances by most credit card
issuers include:
 withdrawing cash at an ATM or at
a branch
 ‘taking cash out’ when making
a purchase at a store
 using a credit card to gamble, either
online or at a casino
 using a credit card to buy foreign
currency.
cash advance fee
A fee charged by the issuer
when the cardholder takes out
a ‘cash advance’.
Cash advance fees are usually the
greater of a specified:
 percentage of the cash advance
(usually between 1% and 3%)
or
 amount between $2 and $5.
closing balance
The amount owing at the end of the
particular statement cycle.
credit limit
The maximum amount of money that
the issuer will allow the cardholder to
spend using the credit card account.
interest-free period or
interest-free days
The maximum number of days for
which a transaction will not incur
interest charges, provided that the
previous ‘closing balance’ is paid
in full by the ‘payment due date’.
The actual number of interest-free
days applicable to a particular
transaction depends on when the
date of the purchase occurs in the
statement cycle.
5
Any interest-free period usually applies
to purchases only (not cash advances)
and is typically between 40 and
55 days. A transaction on the first
day of the statement cycle will have
the maximum number of interest-free
days. For an account with a 55-day
interest-free period on purchases and
a 30-day statement cycle, a purchase
on day 10 of the statement cycle will
have 45 interest-free days (ie the
remaining 20 days of the statement
cycle plus the 25 days to make the
full payment).
HSC Mathematics General 2 Course Support Material
Term
Meaning
Notes
interest rate
The annual interest rate or the daily
interest rate that applies for a specified
type of transaction.
The interest rate that applies to cash
advances is usually higher than the
interest rate that applies to purchases.
late payment fee
A penalty fee charged by the issuer
when the cardholder does not pay
at least the ‘minimum repayment’
by the ‘payment due date’.
Late payment fees are typically
between $10 and $50.
minimum repayment,
minimum amount due or
minimum payment due
The amount the issuer requires the
cardholder to pay by the due date.
The minimum repayment is usually the
greater of a specified:
 percentage of the cash advance
(usually between 2% and 5%)
or
 amount between $10 and $30.
opening balance or
prior month balance
The amount owing at the start
of the particular statement period
(ie the closing balance on the
previous statement).
overdue amount or
outstanding balance
The amount overdue if the minimum
repayment for the previous statement
period was not made.
payment due date
The date by which at least the
minimum amount due is to be paid.
statement cycle or
statement period
The period of time that the particular
statement covers.
The statement period is usually
30 days and may be expressed
in terms of a ‘statement start date’
and a ‘statement end date’.
transactions or
transaction details
An itemised list of all transactions,
including purchases, cash advances,
interest, fees and repayments.
The transaction list usually includes
details of all purchases, cash
advances, payments and credits
during the statement period, including
the date, description and amount of
each transaction.

The terms ‘outstanding balance’ and ‘outstanding amount’ (where the adjective ‘outstanding’
is used to mean ‘unpaid’) may need to be explained explicitly, as some students may be
unfamiliar with this meaning of ‘outstanding’.

For the purpose of this course, students are:

–
expected to carry out calculations, including calculations of interest, for credit card
statements on which the ‘opening balance’ is $0 and also for credit card statements
on which the ‘opening balance’ is not $0
–
not expected to carry out calculations involving balance transfers, although this could
be considered for some students if appropriate.
Questions involving calculations for credit card accounts should be carefully constructed
to ensure that students have sufficient information to perform the calculations.
The following table outlines the information that should be specified when an activity involves
the calculation of interest on purchases and/or cash advances.
6
HSC Mathematics General 2 Course Support Material
Questions involving INTEREST
CALCULATIONS ON PURCHASES
on a credit card account should specify:
Questions involving INTEREST
CALCULATIONS ON CASH ADVANCES
on a credit card account should specify:
calculation
and
application
of interest
how often interest is calculated and/or
applied to the account (usually interest is
calculated daily on the outstanding balance,
taking into account any interest-free period,
and applied to the account at the end of the
statement period)
how often interest is calculated and/or
applied to the account (usually interest is
calculated daily from the date of the cash
advance and applied to the account at the
end of the statement period)
interest-free
days
the number of interest-free days, if any,
including whether or not the interest-free
period includes the date of purchase and/or
the date of payment
the number of interest-free days, if any,
including whether or not the interest-free
period includes the date of the cash advance
and/or the date of payment
opening
balance
the amount owing for purchases, if any, at
the start of the statement period (an opening
balance of $0 should be specified if the
closing balance of the previous statement
was paid in full by the due date)
the amount owing for cash advances,
if any, at the start of the statement period
rate of
interest
the rate of interest for purchases as
an annual and/or daily percentage
interest rate
the rate of interest for cash advance as an
annual and/or daily percentage interest rate
(usually the interest rate for cash advances
is higher than that for purchases)
type of
interest
whether simple or compound interest
is to be used for the calculation
(usually simple interest is used)
whether simple or compound interest
is to be used for the calculation
(usually simple interest is used)

When only an annual interest rate is specified, the daily interest rate is the annual percentage
rate divided by 365. In these situations, students do not need to determine the daily interest
rate as a decimal. Rather, they should show the daily interest rate in their working as the
division of the annual interest rate by 365. For example, to calculate the interest accrued
on a cash advance of $800 after 20 days at a simple interest rate of 16.8% pa, the calculation
can be written as:
16.8%
Interest  $800 
 20
365
0.168
 $800 
 20
365
 $7.364...
 $7.36

Teachers should compare, using calculations, credit cards that don’t have an interest-free
period to those that do. It is recommended that teachers give examples spanning a three-month
period (ie three statements) with a manageable number of transactions.
FM5 Annuities and loan repayments
The following online resources could be used to support the teaching and learning of this topic.
Choosing a home loan
(includes sample key facts sheets)
https://www.moneysmart.gov.au/borrowing-and-credit/homeloans/choosing-a-home-loan
Home loan comparison calculator
www.mymoneycalculator.com.au/home-loan-comparisoncalculator/
Mortgage calculator
https://www.moneysmart.gov.au/tools-andresources/calculators-and-tools/mortgage-calculator
Mortgage calculator showing amount
owing over time in a graph or table
www.infochoice.com.au/calculators/home-loan-calculator/
(select ‘Yearly Breakdown’ tab for table)
Personal loan calculator
https://www.moneysmart.gov.au/tools-andresources/calculators-and-tools/personal-loan-calculator
7
HSC Mathematics General 2 Course Support Material
Strand: Data and Statistics
The following online resources could be used to support the teaching and learning of this Strand.
Applets to create and/or investigate
statistical displays
www.shodor.org/interactivate/activities/
(select ‘Statistics’ for a list of applicable applets)
Data sets
http://biostat.mc.vanderbilt.edu/twiki/bin/view/Main/DataSets?
CGISESSID=10713f6d891653ddcbb7ddbdd9cffb79
Links to useful websites and data sets
www.statsci.org/datasets.html
Pivot table tutorials
www.free-training-tutorial.com/animations/pivotTablefirstSteps.html
Pivot tables (article explaining
cross-tabulation, with examples)
www.custominsight.com/articles/crosstab-sample.asp
Pivot tables (Microsoft Office Help)
http://office.microsoft.com/en-us/excel-help/pivottable-reports101-HA001034632.aspx
Pivot tables in Excel
(video demonstrating cross-tabulation)
www.youtube.com/watch?v=kMeoFIdVRA4
Tutorials for a range of software
applications
www.atomiclearning.com/browse?page=tutorials
(to view the available tutorials, select the application,
version and platform)
Refer also to page 5 of the Preliminary Mathematics General course support material for links to
resources relating to Data and Statistics.
8
HSC Mathematics General 2 Course Support Material
For the student
Internet access and the use of social networking sites by Australian school students
Download and save the spreadsheet file for a random sample from the CensusAtSchool
website at www.cas.abs.gov.au/cgi-local/cassampler.pl using the default options, together
with the following:
Reference year: select the most recent year
Questions to display: select ‘All’
Sample size: select ‘200’
Use the ‘Variables List’ tab on the spreadsheet to identify what is referred to in each column of data.
(1) Use an online video tutorial or the ‘Help’ section of your spreadsheet application to
learn about the functionality and creation of pivot tables in spreadsheets, eg go to
www.atomiclearning.com/browse?page=tutorials and select your application, version
and platform to access available tutorials.
For your random sample, create a pivot table to analyse internet access from home
(‘InetAxs’) against the state or territory in which students live (‘WhreLive’). Your table
should look like the example below.
InetAxs
WhreLive
ACT
NSW
NT
Qld
SA
Tas
Vic
WA
Total
Broadband connection
Dial-up connection
Access by other means
Cannot access the
internet at home
Total
(a) What percentage of all students access the internet at home via a broadband connection?
(b) What percentage of all students access the internet at home via a dial-up connection?
(c) What percentage of all students access the internet at home by other means?
(d) What percentage of all students cannot access the internet at home?
(e) Compare your answers to (a), (b), (c) and (d) above with those obtained by other students
for other random samples. Discuss the reasons why different random samples may
generate different statistics for these measures.
(2) For your random sample, create another pivot table to analyse, by Year level (‘YrLevel’),
how many students use social networking sites on the internet (‘IntNtwrk’).
(a) What percentage of all students claim to use social networking sites ‘often’?
(b) Use the appropriate function of the spreadsheet to change the value field settings to show
the percentages of students for each Year level who claim to use social networking sites
‘never’, ‘rarely’, ‘sometimes’ and ‘often’.
(c) Examine the data and determine any suspected trends in relation to the use of social
networking in different Year levels. Compare your findings with those of other students
and write a few sentences to describe the use of social networking sites on the internet
among Australian school students.
9
HSC Mathematics General 2 Course Support Material
Who survived the Titanic disaster?
Download the spreadsheet of data about passengers on the Titanic at
http://biostat.mc.vanderbilt.edu/twiki/bin/view/Main/DataSets?CGISESSID=10713f6d891653ddcbb7
ddbdd9cffb79 (under the heading ‘Data for Titanic passengers’).
(1) For the Titanic data, create a pivot table to determine the number of passengers who survived,
by passenger class and sex. Your table should look like the example below.
Survivors
Passenger class
1
2
3
Total
Female
Male
Total
(2) How many passengers survived in total?
(3) How many females in second class survived?
(4) What percentage of females in second class survived?
(5) What percentage of female passengers survived?
(6) Calculate the probability of survival for passengers in each class.
(7) Which passenger class had the highest proportion of males who survived? Justify your answer
with appropriate calculations.
10
HSC Mathematics General 2 Course Support Material
Strand: Measurement
MM4 Further applications of area and volume
The following online resources could be used to support the teaching and learning of this topic.
Nets – interactive
www.learner.org/interactives/geometry/area_surface.html
Nets of prisms, pyramids, cylinders and
cones (create and print)
http://illuminations.nctm.org/ActivityDetail.aspx?ID=205
(select the ‘Nets’ tab)
Solids to nets – interactives
(made using GeoGebra)
http://mrskrummel.com/apps/Geometry/ch11_SurfaceArea.html
MM6 Spherical geometry
The following online resources could be used to support the teaching and learning of this topic.
Latitude and longitude
http://itouchmap.com/latlong.html
www.worldatlas.com/aatlas/imageg.htm
Time zones
www.timezonecheck.com/
www.timeanddate.com/worldclock/
www.worldtimezone.com/
Refer also to page 9 of the Preliminary Mathematics General course support material for links to
resources relating to Measurement.
11
HSC Mathematics General 2 Course Support Material
Strand: Probability
The following online resources could be used to support the teaching and learning of this Strand.
Dice rolling simulator (two dice) with
histogram comparing experimental results
to theoretical results
https://www.math.duke.edu//education/postcalc/
probability/dice/index.html
Monty Hall problem (stick or switch?)
http://nlvm.usu.edu/en/nav/frames_asid_117_g_
4_t_5.html
Probability simulations
(coin, spinner and other)
www.mathsonline.co.uk/nonmembers/resource/
prob/index.html
Probability tree diagram generator
http://kera.name/treediag/
Vehicle registration plates of the world
http://en.wikipedia.org/wiki/Vehicle_registration_
plate
See note (1)
below
Refer also to page 10 of the Preliminary Mathematics General course support material for links to
resources relating to Probability.
Note
(1) Go to ‘License plates by country or territory’ and select a country to obtain specific information
about that country’s vehicle registration plates.
12
HSC Mathematics General 2 Course Support Material
Strand: Algebra and Modelling
The following online resource could be used to support the teaching and learning of this Strand.
Algebraic modelling activities
www.thefutureschannel.com/algebra_real_world.php
Refer also to page 11 of the Preliminary Mathematics General course support material for links to
resources relating to Algebra and Modelling.
13
HSC Mathematics General 2 Course Support Material
Focus Study: Mathematics and Health
FSHe1 Body measurements
The following online resources could be used to support the teaching and learning of this topic.
Biometric data
http://biostat.mc.vanderbilt.edu/twiki/bin/view/Main/
DataSets?CGISESSID=10713f6d891653ddcbb7dd
bdd9cffb79
Body measurements
www.who.int/growthref/en/
CensusAtSchool random sampler
www.cas.abs.gov.au/cgi-local/cassampler.pl
Guessing correlations
http://istics.net/stat/correlations/
Height and ‘belly button’ height
compared
(video, view from 00:30 onwards)
http://teachertube.com/viewVideo.php?video_id=5163
8&title=ABS___CensusAtSchool___Using_CensusAt
School_in_the_classroom
Least-squares regression line
(applet)
http://illuminations.nctm.org/LessonDetail.aspx?ID=L49
1#applet
Linear regression
www.math.utah.edu/~hughes/Chapter_05.pdf
Linear regression (includes video)
http://stattrek.com/regression/linearregression.aspx?Tutorial=AP
Linear regression and body
measurements (PowerPoint)
www.google.com.au/url?sa=t&rct=j&q=&esrc=s&source
=web&cd=3&ved=0CC8QFjAC&url=http%3A%2F%2Fw
ww.cs.sunysb.edu%2F~mueller%2Fteaching%2Fvolum
eGraphicsSeminar%2Fch18Reg.ppt&ei=cMiUKK6LqeUiAemx4CgAg&usg=AFQjCNGmnxCkExOND
kCVBCkDNlt0Y76wxw&sig2=8waim-kJSlp289ofMJ1aPg
Regression by eye (applet)
www.ruf.rice.edu/~lane/stat_sim/reg_by_eye/index.html
Regression notes and examples
http://virtual.yosemite.cc.ca.us/jcurl/Math134%204%20
PDF%20Files/ch5-115-148.pdf
Relationships between quantitative
variables
http://sites.stat.psu.edu/~rho/stat462/Chap05MOS.PDF
Scatterplot, correlation and
line of best fit creator
http://nlvm.usu.edu/en/nav/frames_asid_144_g_4_t_5.
html?open=activities&from=category_g_4_t_5.html
See note (1)
below
Note
(1) The World Health Organization (WHO) website provides data on height, weight and body mass
index (BMI) by age.
14
HSC Mathematics General 2 Course Support Material
For the teacher
Anthropometry (from the Greek anthropos, meaning ‘man’, and metron, meaning ‘measure’)
is the measurement of human individuals. Many historical units of length were based on
body measurements. The ancient Egyptians used the ‘cubit’ and the ‘palm’ to measure length.
A cubit is the distance from the elbow to the tip of the middle finger when extended. A palm
is the distance across the knuckles at the base of the fingers when all four fingers are extended.
The ancient Egyptians equated one cubit to seven palms.
Students could investigate relationships between any or all of the following body measurements:

cubit – the distance from the elbow to the tip of the
middle finger when extended

fathom – the distance from fingertip to fingertip when
the arms are outstretched (armspan)

foot – the length of the foot from the back of the heel
to the tip of the longest toe

handspan – the distance from the tip of the outspread
little finger to the tip of the outspread thumb

height – the distance from the floor to the top of the
head when standing with bare feet flat on the ground

inch – the width of the thumb

navel (‘belly button’) height – the distance of the
‘belly button’ from the floor when standing with bare
feet flat on the ground

pace – the distance covered in one step (obtained
by dividing a distance walked, eg 10 metres, by the
number of ‘paces’ required to cover that distance)

palm – the distance across the knuckles at the base
of the fingers when all four fingers are extended.
The Metropolitan Museum of Art,
Rogers Fund, 1930 (30.4.137)
Image © The Metropolitan Museum of Art.
Source: www.metmuseum.org.
Teachers should be aware of the following:

Taking body measurements may be a sensitive issue for some students. Teachers should
adjust activities accordingly.

The ‘trendline’ created on charts in Microsoft Excel is the least-squares line of best fit.
15
HSC Mathematics General 2 Course Support Material
For the student
Can you predict a person’s height if you know their ‘belly button’ height?
(1) Download and save the spreadsheet file for a random sample from the CensusAtSchool
website at www.cas.abs.gov.au/cgi-local/cassampler.pl using the default options, together
with the following:
Reference year: select the most recent year
Questions to display: select ‘all’
Sample size: select ‘200’
(2) Use the ‘variables list’ worksheet to identify the columns of the data worksheet that relate
to height and belly button height. Remove all other columns from the spreadsheet.
(3) Watch the following video from 00:30 onwards:
http://teachertube.com/viewVideo.php?video_id=51638&title=ABS___CensusAtSchool___
Using_CensusAtSchool_in_the_classroom.
Use the video as a guide to construct a scatterplot to compare height with belly button
height for your sample. Ensure that the horizontal axis refers to belly button height.
Note: While you may have a different version of the spreadsheet, the functions used
in the video should be similar, though they may be found in a different manner.
(4) Use the process described in the video to identify and remove any outliers, including
through the use of conditional formatting.
(5) Use the process outlined in the video to create the line of best fit for your data. Why is it
reasonable to set the intercept value to 0 for this data? What effect does this have on the
equation of the line of best fit?
(6) Compare the equation of the line of best fit for your random sample with the lines of best
fit obtained by other students. What are the similarities and differences?
(7) Extension: The golden ratio
Research the ‘golden ratio’. What is it? Where does it occur in the natural environment?
Where has it been used in the built environment? Where has it been used in the arts?
Where is it found in the ‘ideal’ human body?
These online resources may be helpful:

Pythagoras: How to Measure Beauty − The Human Face (video, BBC Worldwide),
www.youtube.com/watch?v=mVVroi8q0Y0

Golden Ratio in Human Body (Golden Mean in Mankind) (video),
www.youtube.com/watch?v=085KSyQVb-U

the golden ratio, http://en.wikipedia.org/wiki/Golden_ratio

the golden ratio in the human body, http://merlib.org/node/1377.
16
HSC Mathematics General 2 Course Support Material
What relationships can be found between various body measurements?
Many historical units of length were based on body measurements, eg the ancient Egyptians used
the ‘cubit’ and the ‘palm’ to measure length. Some body measurements to investigate include:
cubit
fathom
foot
handspan
height
–
–
–
–
–
inch –
navel (‘belly button’) height –
pace –
palm –
the distance from the elbow to the tip of the middle finger when extended
the distance from fingertip to fingertip when the arms are outstretched (armspan)
the length of the foot from the back of the heel to the tip of the longest toe
the distance from the tip of the outspread little finger to the tip of the outspread thumb
the distance from the floor to the top of the head when standing with bare feet flat
on the ground
the width of the thumb
the distance of the ‘belly button’ from the floor when standing with bare feet flat
on the ground
the distance covered in one step (obtained by dividing a distance walked,
eg 10 metres, by the number of ‘paces’ required to cover that distance)
the distance across the knuckles at the base of the fingers when all four fingers
are extended
fathom
handspan
inch
palm
cubit
In the following activities, pairs of body measurements will be investigated to determine:

whether or not there is a correlation between a selected pair of body measurements

the strength of the correlation, if one exists

an algebraic model for the relationship between a selected pair of body measurements
(ie a line of best fit).
(1) Work in small groups using a tape measure to obtain the body measurements listed in the
table below for each person in the group. Record all measurements in the table in centimetres
to the nearest centimetre, with the exception of the inch and palm, which should be measured
in centimetres to the nearest millimetre.
Body measurement (cm)
Student A
Student B
Student C
Student D
Sex (please circle M or F)
M/F
M/F
M/F
M/F
Cubit
Fathom (armspan)
Foot length
Handspan
Height
Inch
(to nearest 0.1 cm)
Navel (‘belly button’) height
Palm
(to nearest 0.1 cm)
17
HSC Mathematics General 2 Course Support Material
(2) Enter the data for each student into a spreadsheet (see below) so that all students in the
class have access to the body measurements of each member of the class. If students of
other classes are also participating in this investigation, combine the sets of data into one
spreadsheet. It is preferable to have as many data values as possible.
Spreadsheet for use by students
Spreadsheet for use by teachers/students (includes hidden formulae)
Spreadsheet for use by teachers (includes formulae displayed)
(3) Use the appropriate spreadsheet function to calculate the mean of each set of body
measurements.
Note: In Microsoft Excel, the mean function is =AVERAGE(array).
(4) Use the appropriate spreadsheet function to calculate the sample standard deviation of each
set of body measurements.
Note: In Microsoft Excel, the sample standard deviation function is =STDEV(array).
The population standard deviation is =STDEVP(array).
(5) Use the appropriate spreadsheet function to calculate the correlation coefficient for each pair
of body measurements. Correlation coefficients can be arranged in a table for easy reference
(see below).
Note: In Microsoft Excel, the correlation function is =CORREL(array1,array2). Try entering the
formula in each of the cells in the column for ‘Cubit’ using ‘absolute cell reference’ (by pressing
F4 after typing the cell reference or by manually entering $ symbols), then use ‘fill across’ to
save time, eg the formulae in cells C38, C39 and C40 above would be:
=CORREL($C$3:$C$32,C3:C32) and
=CORREL($D$3:$D$32,C3:C32) and
=CORREL($E$3:$E$32,C3:C32) respectively.
(a) Are any values in the table identical? Why? Describe any patterns that you notice
in the table.
(b) Which pair of body measurements is most strongly correlated?
(c) Which pair of body measurements is least strongly correlated?
18
HSC Mathematics General 2 Course Support Material
(6) For each pair of body measurements that has a correlation coefficient greater than 0.5,
determine the least-squares line of best fit using the following:
least-squares line of best fit: y  gradient  x  y-intercept
where r is the correlation coefficient (correct to 4 decimal places)
gradient  r 
standard deviation of y scores
standard deviation of x scores
y-intercept  y  gradient  x 
(7) Use the chart function of the spreadsheet application to create scatterplots that compare
each pair of body measurements, eg cubit with handspan, foot length with palm size, height
with foot length. Ensure that all scatterplots are labelled appropriately (heading and axes).
Note: To select cells in columns that are not adjacent, hold down the CTRL key while
selecting cells.
(8) Examine any outliers in each scatterplot and consider whether they should be removed.
An outlier should not be removed unless there is a strong reason to believe that it does
not belong in the set of data. For example, a navel height of 150 cm for a person of height
180 cm is not physically possible and must have been measured or recorded incorrectly,
so it should be removed from the set of data.
Record any outliers that you remove from the set of data and justify their removal with a reason.
(9) Match the appropriate correlation coefficient to each scatterplot.
Describe the relationship between the spread of data points on the scatterplot and the value
of the correlation coefficient for the pair of body measurements that is:
(a) most strongly correlated
(b) least strongly correlated.
(10) For each pair of body measurements that has a correlation coefficient greater than 0.5,
use the appropriate spreadsheet function to construct and display the equation of the
least-squares line of best fit on the scatterplot.
Note: The line of best fit may be known as the ‘trendline (linear)’ or similar. Non-linear
trendlines are beyond the scope of this course.
(11) Compare each of the least-squares lines of best fit that you determined in part (6) with those
calculated by the spreadsheet in part (10).
(12) Use the equation of the appropriate line of best fit to calculate expected values for particular
body measurements given another body measurement, eg calculate the expected handspan
for a person of height 154 cm.
(13) Extension: Body measurement comparison
Compare the body measurements of males and females. Are they different?
Sort the data values by sex, and repeat the activities using the data values for each sex
separately. Compare the correlation coefficients and equations of the lines of best fit for
males and females for each pair of body measurements.
19
HSC Mathematics General 2 Course Support Material
FSHe2 Medication
The following online resources could be used to support the teaching and learning of this topic.
Formulae for calculating drip rates
http://emsstaff.buncombecounty.org/inhousetraining/ivdriprates/
ivdriprates_overview1.htm
www.dosagehelp.com/iv_rate_drop.html
Formulae for calculating rates given
as volume/time
www.dosagehelp.com/iv_rate_ml.html
Medical calculations for nurses
www.rncalc.com/
Nursing formulae
http://nursing.flinders.edu.au/students/studyaids/drugcalculations
/flash/PDF%20files/iv_dropspermin.pdf
www.csu.edu.au/division/studserv/mystudies/maths/pdfs/medicationcalculationspart2.pdf
Prescription medicines explained
(includes sample medicine label)
www.nps.org.au/consumers/publications/medicines_talk/mt19/
whats_on_the_label
For the teacher
Medicine labels
Real-world medicine labels that indicate various ‘dosage strengths’ can be found by searching
Google Images using search terms such as:

‘medicine label tablets mg’

‘medicine label suspension mg’.
Medicine labels used should include both ‘over-the-counter’ and ‘prescription-only’ examples.
Dosage strength
‘Dosage strength’ refers to the strength of the active ingredient in the medication. Dosage strengths
may be expressed as:

mass per tablet or capsule, eg [medication name] 10 mg tablets (each tablet contains 10 mg
of the active ingredient)

mass per volume, eg:

[medication name] 6 mg/mL for oral suspension (each millilitre contains 6 mg of the
active ingredient)

[medication name] ampoules of strength 2 mg/0.2 mL for oral, intravenous (IV) or
intramuscular (IM) administration (for every 0.2 mL, there is 2 mg of the active ingredient).
Flow rate for IV infusions
The ‘flow rate’ for an intravenous (IV) infusion refers to the rate at which fluid is to be administered
to a patient and is measured in millilitres per hour (mL/h).
Drip rate for IV infusions
The ‘drip rate’ for an IV infusion is measured in the number of drops per minute (drops/min).
In order to calculate the drip rate, it is necessary to know the following: the volume (in millilitres)
to be administered, the number of drops delivered per millilitre, and the time (in minutes) over
which the fluid is to be administered. The number of drops delivered per millilitre depends on
the rate at which the ‘giving set’ operates. Typically, giving sets operate at 20 drops per millilitre
(‘macrodrip’) or 60 drops per millilitre (‘microdrip’). Drip rates should be expressed correct to the
nearest whole number.
20
HSC Mathematics General 2 Course Support Material
FSHe3 Life expectancy
The following online resources could be used to support the teaching and learning of this topic.
Gapminder desktop for offline use
www.gapminder.org/desktop/
Gapminder World –
‘Wealth & Health of Nations’
www.gapminder.org/
(click on ‘GAPMINDER WORLD’)
See note (1)
below
Gapminder World Guide
www.gapminder.org/GapminderMedia/wpuploads/tutorial/Gapminder_World_Guide.pdf
See note (2)
below
Life expectancy (PowerPoint)
www.gapminder.org/downloads/life-expectancy-ppt/
Life expectancy in the USA (forecasting
the effects of obesity and smoking)
www.economics.harvard.edu/faculty/cutler/files/ste
wart cutler rosen nejm.pdf
Life expectancy trends in Australia
www.aihw.gov.au/australian-trends-in-lifeexpectancy/
www.abs.gov.au/websitedbs/D3310114.nsf/home/h
ome?opendocument
(use the search function to find
‘life expectancy trends’)
Life tables
www.who.int/gho/mortality_burden_disease/life_
tables/en/index.html
The Seemingly Impossible Is Possible
(video)
www.gapminder.org/videos/hans-rosling-ted-talk2007-seemingly-impossible-is-possible/
Social indicators by country
http://unstats.un.org/unsd/demographic/products/
socind/
(click on ‘HEALTH’ to view downloadable
spreadsheets of data related to health)
Urbanisation data
www.un.org/esa/population/publications/WUP2005/
2005wup.htm
The World Factbook
https://www.cia.gov/library/publications/the-worldfactbook/rankorder/2102rank.html
21
HSC Mathematics General 2 Course Support Material
Notes
(1) Gapminder World – ‘Wealth & Health of Nations’
This resource can display comparisons between life expectancy and a range of variables,
including:

country of birth

population

income per person (gross domestic product (GDP) per capita)

tax revenue as a percentage of GDP

food supply per person per day

energy use per person

percentage of urbanisation

total health spending as a percentage of GDP

medical doctors per 100 people

children per woman (total fertility)

child mortality rate (children aged 0–5 dying per 1000 children born)

school enrolment.
The user can animate the graphs to show trends over time and can trace a particular country
during the animation.
(2) Gapminder World Guide
Free material from www.gapminder.org.
22
HSC Mathematics General 2 Course Support Material
Focus Study: Mathematics and Resources
FSRe1 Water availability and usage
The following online resources could be used to support the teaching and learning of this topic.
Fertiliser calculations
www.dpi.nsw.gov.au/__data/assets/pdf_file/0004/16
6153/fertiliser-calculations.pdf
‘Let’s have a school rainwater tank!’
(student activity)
www.rouswater.nsw.gov.au/cmst/rw010/res.asp?id=
745
Major dams in NSW (real-time data)
http://realtimedata.water.nsw.gov.au/water.stm?ppbm See note (1)
=STORAGE_SITE&da&3&dakm_url
below
Rainfall data
(Hunter Region catchments)
www.hunterwater.com.au/Water-and-Sewer/WaterSupply/Rainfall-Data.aspx
Rainfall in a catchment calculator
www.calctool.org/CALC/other/default/rainfall
Rainfall tables
www.bom.gov.au/jsp/watl/rainfall/pme.jsp
Water (Australian Government)
www.environment.gov.au/water/index.html
Water (NSW Government)
www.nsw.gov.au/water
Water availability and usage
(includes data for international
locations)
www.publish.csiro.au/?act=view_file&file_id=978064
3103283_Chapter_1.pdf
Water education resources
www.environment.gov.au/water/education/index.html
Water harvesting calculations
http://oasisdesign.net/water/rainharvesting/drylands
book/Appendix3Calculations.pdf
Water suppliers in NSW
www.ewon.com.au/index.cfm/suppliers/suppliers-innsw/water-suppliers/
Water tanks
www.watertankfactory.com.au/Water-Tank-Range.php
http://tankworld.com.au/
Water usage and conservation
www.abs.gov.au/AUSSTATS/abs@.nsf/DetailsPage/4
602.0.55.003Mar 2010?OpenDocument
www.abs.gov.au/ausstats/abs@.nsf/mf/4602.0.55.003
Water usage calculator
(generate a personal household
water usage report)
www.sawater.com.au/interactivehouse/
Water usage statistical indicators
(state and territory)
www.abs.gov.au/ausstats/abs@.nsf/Lookup/by+Subj
ect/1367.0~2011~Main+Features~Water+Use~6.37
Note
(1) For real-time data on major dams, follow steps (a) to (e) outlined on the following pages.
23
HSC Mathematics General 2 Course Support Material
(a) Hover over each dam on the map to obtain summary data.
Select ‘Real Time Data − Major Dams’ to obtain a list of dams.
© New South Wales Department of Trade and Investment, Regional Infrastructure and Services.
(b) Select the dam name, eg Burrendong Dam, to obtain detailed information.
© New South Wales Department of Trade and Investment, Regional Infrastructure and Services.
24
HSC Mathematics General 2 Course Support Material
(c) Obtain different images of the dam by selecting ‘Map’, ‘Satellite’, ‘Hybrid’ and ‘Terrain’
views. The Terrain view is shown below.
© New South Wales Department of Trade and Investment, Regional Infrastructure and Services.
(d) Some graphs may be pre-generated via the ‘Latest Values’ tab, eg the third graph for
Burrendong Dam compares water storage in consecutive years.
© New South Wales Department of Trade and Investment, Regional Infrastructure and Services.
25
HSC Mathematics General 2 Course Support Material
(e) Select the ‘Custom Outputs’ tab to generate a variety of graphs for a particular dam
and a particular period of time, eg ‘Rainfall’ and ‘Reservoir Volume in Storage’ during
‘Last year’ for Burrendong Dam.
© New South Wales Department of Trade and Investment, Regional Infrastructure and Services.
26
HSC Mathematics General 2 Course Support Material
FSRe2 Dams, land and catchment areas
The following online resources could be used to support the teaching and learning of this topic.
Capacity of a dam – Working
Mathematically in a rural context
www.wmrural.net/activities/dam/worksheet.pdf
Catchment Management Authorities (NSW)
www.cma.nsw.gov.au/
Catchment maps (NSW)
www.environment.nsw.gov.au/ieo/catchlist.htm
Dams and catchments (Hunter Region)
www.hunterwater.com.au/Water-and-Sewer/WaterSupply/Dams-and-Catchments.aspx
Formulae for calculating the volumes
of different dam types
www.dpi.vic.gov.au/agriculture/farming-management/soilwater/water/solutions/available/how-much-water-is-in-my-dam
www.agric.wa.gov.au/objtwr/imported_assets/content/fm/small/
nw47_measuring dams lr.pdf
Google Earth
www.google.com/earth/index.html
Google Maps
http://maps.google.com/
Grid-square method for finding area
ftp://ftp.fao.org/fi/CDrom/FAO_Training/FAO_Training/General/
x6707e/x6707e10.htm#133a
For the teacher
Methods for finding the area of irregular-shaped land, dams and catchments
Three methods for determining the area of irregular-shaped blocks of land, dams and catchments
are considered in the Mathematics General 2 course:

grid-square method (introduced in this topic)

polygon method (introduced in this topic)

Simpson’s rule (introduced in MM4).
Grid-square method for estimating area from a scaled map or plan
The grid-square method can be used to estimate the area of irregular-shaped blocks of land and
catchments from a scaled map or plan. Usually this method is used when the edges of the area
are not straight.
(1) Selection of overlay
Select a grid-square overlay of appropriate size and scale for the area to be measured,
eg a 16 cm by 16 cm grid-square overlay consisting of 5 mm by 5 mm squares. The smaller
the unit squares on the overlay, the more accurate the estimate of the area of the land or
catchment will be. For the purposes of this course, the smallest unit square to be considered
is 5 mm by 5 mm.
(2) Placement of overlay
Place the grid-square overlay securely over a map of the block of land or catchment to
be measured. If the overlay is not large enough to cover the entire area, trace around its
perimeter before moving it to an adjacent position and aligning one of its edges with the first
outline. Trace around the perimeter of the second placement and repeat until the entire area
is accounted for.
(3) Whole units
Count the number of whole units included in the block of land or catchment being measured.
Mark each whole unit with a dot as it is counted. Depending on the shape of the area, it may
27
HSC Mathematics General 2 Course Support Material
be possible to identify a rectangle consisting of a significant number of unit squares towards
the centre of the area being measured. The number of unit squares in this rectangle can then
be obtained by counting the squares along its length and breadth and multiplying.
(4) Partial units
Examine the unit squares around the edge of the block of land or catchment to be measured.
If more than one-half of any unit square is within the area, count it (and mark it) as a whole
square. If less than one-half of any unit square is within the area, ignore it.
(5) Total number of units
Add the number of ‘whole units’ to the number of ‘partial units’ to obtain the total number
of unit squares.
(6) Unit area
Align the overlay to the scale of the map or plan to determine the equivalent land length
of each unit square of the overlay. Use this measure to calculate the equivalent land area
of one unit square.
(7) Area of the land or catchment
Multiply the total number of units by the land area equivalent to one unit square to obtain the
total area of the block of land or catchment.
Polygon method for determining area using field measurements
The polygon method can be used to determine the area of a polygonal block of land or catchment
that can be broken into regular plane shapes. The dimensions of the regular plane shapes can be
field measurements obtained from:

a radial survey that allows the area to be broken into triangles (involves lengths and angles)

an offset survey that allows the area to be broken into triangles, rectangles and trapeziums

a scale map or plan that allows the area to be broken into triangles, rectangles and trapeziums.
(1) Draw a diagram
Draw a diagram of the area to be measured and break it up appropriately into plane shapes
according to the method by which the field measurements will be obtained. Labelling the
vertices of each plane shape may assist students in naming and accounting for each shape
in their calculations.
(2) Field measurements
Obtain all of the necessary field measurements and label them on the diagram.
(3) Area of the land or catchment
Calculate the area of each plane shape using appropriate formulae and add these partial areas
to determine the total area.
Simpson’s rule for determining area using field measurements
Simpson’s rule can be used to estimate the area of irregular-shaped blocks of land and catchments
using field measurements. Usually this method is used when the area is bounded by a curve and
three straight sections that are perpendicular to each other, eg a paddock bounded by three straight
fences and a river.
Simpson’s rule can also be used to estimate areas bounded entirely by irregular curves, by
defining a base line through the area and taking measurements of its width at n equally spaced
intervals/offsets (where n is an odd number such that n  3). In this course, students are expected
to be able to estimate an area by using one application of Simpson’s rule with three equally
spaced intervals (two strips) and also by using two applications of the rule with five equally
spaced intervals (four strips).
28
HSC Mathematics General 2 Course Support Material
For the student (FSRe1 and FSRe2)
How much could you save on your water bill with a rainwater tank?
(1) Use an online calculator (eg www.sawater.com.au/interactivehouse/) to estimate and record the
number of litres of water used by your household in one year.
Note: You may need the assistance of other household members to complete this part of
the activity.
(2) Research rainfall data for your region to obtain and record the mean annual rainfall.
(3) Use a real estate website to find a suitable house to represent your household in your region.
Determine the ‘footprint’ of the ‘drip line’ of the house using the dimensions shown on the floor
plan of the house, ie the roof area available for water harvesting.
Note: The pitch/slope of the roof does not matter, as it is the footprint of the drip line of the roof
that determines how much water can be harvested.
(4) Roofs typically lose 5–20% of the rainwater that falls on them. The reasons for this include
the type of roof surface, light rain events that may be completely absorbed by the roof
surface, and water that remains on the roof after a rain event (and is subsequently lost
through evaporation). What is a conservative estimate of the percentage of rain that you
can expect to collect from the roof of the selected house (ie a conservative estimate of
the ‘runoff coefficient’)?
(5) The net annual volume of rainwater that can be collected from a roof can be calculated using
the formula V  A  R  C, where V is the volume of water collected in cubic metres, A is the
area of the collection surface in square metres, R is the mean annual rainfall expressed in
metres, and C is the runoff coefficient expressed as a decimal. Use the formula to calculate
a conservative net annual volume of water that can be collected from the roof of your
selected house.
(6) Determine whether or not the estimated net annual volume of rainwater to be collected from the
roof of your selected house is enough to meet your household’s annual water usage. How much
extra water is needed, or how much excess water is left over?
(7) Research and calculate the cost of water for your annual household usage if you do not use any
collected rainwater. On average, how much could you save on water bills in one year by using
rainwater collected from the roof of your selected house?
(8) Using online sources, research rainwater tanks suitable for household use and select a tank
with a capacity large enough to hold your estimated annual collected rainwater.
(a) Record the manufacturer’s name and URL, and the name, dimensions, capacity and cost
of the tank as stated on the website.
(b) Draw a diagram of the tank and clearly label it with the stated dimensions.
(c) Calculate the volume of the tank using the stated dimensions and find its capacity in litres
based on these calculations.
(d) Compare the capacity that you calculated for the tank with the capacity stated by the
manufacturer and explain why the calculated capacity might be different from that stated.
(e) Determine the number of years required to completely recoup the cost of buying the
tank through savings made on your annual water bill if water pricing remains unchanged
(include recouping installation costs, if these can be estimated).
29
HSC Mathematics General 2 Course Support Material
What’s the scale?
The aerial photograph below shows an area of Port Macquarie in New South Wales, which includes
an Olympic-sized swimming pool (lower left).
Imagery © 2012 DigitalGlobe, GeoEye. Map data © 2012 Google, Whereis®, Sensis Pty Ltd.
(1) An Olympic-sized swimming pool is 50 metres in length. Use the pool as a reference point
to determine the scale of the image.
(2) Use the scale to find the actual length of Mowle Street (centre left).
(3) Find the perimeter and area of the car park on Owen Street (centre).
(4) The Port Macquarie Tennis Club (top right) has four square bowling greens and six tennis
courts. Find the total area of the four bowling greens in square metres.
(5) Compare your answers to parts (1), (2), (3) and (4) above with those of other class members.
Explain why there may be a range of answers.
(6) What is the error in measurement when measurements of the image are taken to the
nearest millimetre?
(7) Use the scale to determine the actual length to which the ‘error value’ of part (6) refers.
30
HSC Mathematics General 2 Course Support Material
Using scaled satellite images to find areas and perimeters
The satellite image below shows a section of Sydney Olympic Park. Note the scale of the image
shown in the lower left corner, which indicates the length on the image that represents an actual
distance of 200 metres.
Imagery © 2012 Cnes/Spot Image, DigitalGlobe, GeoEye, Sinclair Knight Merz. Map data © 2012 Google, Whereis®, Sensis Pty Ltd.
(1) Calculate the actual length of Olympic Boulevard from Kevin Coombs Avenue to
Dawn Fraser Avenue.
(2) The Brickpit (upper right) is viewed from an elevated circular walkway, as shown.
How far would you travel if you walked the entire length of the circular walkway?
(3) Find the area of the large rectangular factory at the corner of Hill Road and
Carter Street (lower left).
(4) ANZ Stadium consists of a large circular structure with four circular access ways.
Calculate the area of the footprint of ANZ Stadium.
Using interactive software to find lengths and perimeters on satellite images
Use interactive software, such as Google Earth, to obtain a satellite image of your local area.
(1) Use the appropriate tool, such as the ‘Ruler’ (‘Line’) tool in Google Earth, to determine the
length of selected local landmarks in metres.
(2) Use the appropriate tool, such as the ‘Ruler’ (‘Path’) tool in Google Earth, to plot a path
around selected local landmarks and determine their perimeters.
31
HSC Mathematics General 2 Course Support Material
Areas of paddocks and dams
The satellite image below shows land located at 30 7' 47.26"S, 149 37' 58.42"E, near
Narrabri in New South Wales. Note the scale of the image shown in the lower left corner.
Imagery © 2012 Cnes/Spot Image, DigitalGlobe, GeoEye. Map data © 2012 Google.
(1) Calculate the area in square metres of the trapezium-shaped dam outlined in red.
(2) A white 5 mm grid-square overlay has been placed over the dam at the top of the image.
Use the grid-square method to estimate the area of the dam in square metres.
(3) The property owners estimate that the two dams have an average depth of 1.5 metres.
Assuming that the dams are filled to capacity, estimate the total amount of water available
in them. Give your answer in megalitres, correct to 2 significant figures.
(4) Use two applications of Simpson’s rule (ie four strips) to estimate the area of the paddock
outlined in green. Give your answer in hectares, correct to 2 significant figures.
(5) Use the polygon method to estimate the area of the paddock outlined in blue. Give your answer
in hectares, correct to 2 significant figures.
(6) The property owners wish to fertilise the two paddocks (outlined in green and blue) with
20 kilograms of phosphorus per hectare. They intend to use single superphosphate, which
contains 8.8% phosphorus.
They find the following formula, which can be used to calculate the amount of fertiliser
(in this case, superphosphate) required to fertilise each hectare of land with a given amount
of nutrient (in this case, phosphorus):
Amount of fertiliser required amount of nutrient desired per hectare (in kilograms)
100
per hectare (in kilograms) 
% nutrient in fertiliser
How much fertiliser do the property owners need to fertilise the two paddocks as intended?
32
HSC Mathematics General 2 Course Support Material
Area of Lake Cargelligo
The satellite image below shows Lake Cargelligo in New South Wales. Water is channelled from
the Lachlan River to the lake, which stores water for irrigation purposes. The image was created
in 2012. Note the scale of the image shown in the lower left corner. A 5 mm grid-square overlay
has been placed over the image.
Imagery © 2012 Cnes/Spot Image, DigitalGlobe, GeoEye. Map data © 2012 Google, Whereis®, Sensis Pty Ltd.
(1) Use the grid-square method to estimate the surface area of the water in Lake Cargelligo and
its nearby smaller water-storage areas at the time the image was created.
(2) Research online the published surface area of Lake Cargelligo (eg find ‘Cargelligo Storage’
at http://realtimedata.water.nsw.gov.au/water.stm?ppbm=STORAGE_SITE&da&3&dakm_url)
and compare your estimate for the surface area of the lake with the published figure. Provide
at least two reasons why your estimate differs from the published figure by considering the
estimation method used and the creation of the image.
33
HSC Mathematics General 2 Course Support Material
The map below also shows Lake Cargelligo and indicates the boundaries of the lake and its
nearby smaller water-storage areas. Note the scale of the map shown in the lower left corner.
A 1 cm grid-square overlay has been placed over the image.
Map data © 2012 Google.
(3) Use this map and the grid-square method to estimate the surface area of Lake Cargelligo
and its nearby smaller water-storage areas when it is filled to capacity.
(4) Compare your estimate for the surface area of the lake with the published figure.
(5) Using online sources, research rainfall data for Lake Cargelligo and record the mean
rainfall for the month of January based on all data available since records commenced
to be kept.
(6) Assuming that Lake Cargelligo received the mean January rainfall in January of this year,
use the published surface area of Cargelligo Storage to calculate the amount of rainfall
(in megalitres, correct to 2 significant figures) that would be collected from the surface of
the lake and its smaller water-storage areas.
(7) Research the actual amount of rainfall received at Lake Cargelligo in January of this year.
How much more, or less, rainfall (in megalitres, correct to 2 significant figures) was collected
from the surface of the lake and its smaller water-storage areas this year?
34
HSC Mathematics General 2 Course Support Material
Area of Richmond River catchment
The map below shows the Richmond River catchment in northern New South Wales.
Note the scale of the map shown in the lower left corner. A 1 cm grid-square overlay
has been placed over the map.
© NSW Office of Environment and Heritage, reproduced with permission.
Use the grid-square method to estimate the surface area of the catchment. Give your answer
in square kilometres, correct to 2 significant figures.
35
HSC Mathematics General 2 Course Support Material
FSRe3 Energy and sustainability
The following online resources could be used to support the teaching and learning of this topic.
BASIX – Building Sustainability Index
https://www.basix.nsw.gov.au/information/index.jsp
Building an energy-efficient home
www.environment.nsw.gov.au/energy/home.htm
Demand and consumption explained
www.think-energy.net/KWvsKWH.htm
Electricity bills explained
www.agl.com.au/home/billing-and-payments/Pages/agl-billexplainers.aspx
www.energyaustralia.com.au/residential/account-tools/billspayments/understanding-your-bill/different-types-of-bill
www.integral.com.au/wps/wcm/connect/IE/NSW/NSW+Homepa
ge/yourAccountNav/Your+bill+explained/
www.originenergy.com.au/3549/Electricity-bill
www.redenergy.com.au/docs/BillExplainerQuarterlyBill.pdf
Electricity meter reading
www.actewagl.com.au/Help-and-advice/How-to-read-yourmeters.aspx
Electricity usage calculator
www.redenergy.com.au/billbenchmark/
Energy bill sample
www.sa.gov.au/subject/Water,+energy+and+environment/Energy/
Energy+efficiency/Understanding+your+energy+use/Understand+
your+energy+bills
Energy rating label samples
www.energyrating.gov.au/programs/e3-program/energy-ratinglabelling/obtain/
Energy ratings for different appliances
http://reg.energyrating.gov.au/comparator/product_types/
Energy Savings Scheme (ESS)
www.ess.nsw.gov.au/Home
Energy suppliers in NSW
www.myenergyoffers.nsw.gov.au/useful-information/energyretailers.aspx
Energy usage
www.yourhome.gov.au/technical/fs61.html
Energy usage calculator
www.aglsmarterliving.com.au/energy-efficiency-advice/energytools/
How to read your energy bills and
track your consumption
www.transport.wa.gov.au/mediaFiles/AT_LS_P_read_bills_track
_consumption.pdf
kW and kWh explained
www.energylens.com/articles/kw-and-kwh
Report – National Electricity Market
(includes production costs)
www.esaa.com.au/policy/national_electricity_market_reports_1_
1_1
Report – State of the Energy Market
www.aer.gov.au/node/455
Tips on buying energy-efficient appliances
www.livinggreener.gov.au/energy/energy-efficient-appliances
Water tanks and BASIX package
www.rainwatertanksdirect.com.au/
36