Mathematics
General
Stage 6 Syllabus
HSC Mathematics General 1 Course
Support Material
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2
Contents
Support material for HSC Mathematics General 1 Strands and Focus Studies
Strand: Financial Mathematics ........................................................................................................ 4
Strand: Data and Statistics.............................................................................................................. 7
Strand: Measurement ..................................................................................................................... 9
Strand: Probability......................................................................................................................... 10
Strand: Algebra and Modelling ...................................................................................................... 11
Focus Study: Mathematics and Design ......................................................................................... 12
Focus Study: Mathematics and Household Finance...................................................................... 16
Focus Study: Mathematics and the Human Body .......................................................................... 18
Focus Study: Mathematics and Personal Resource Usage ........................................................... 23
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HSC Mathematics General 1 Course Support Material
Strand: Financial Mathematics
FM4CEC 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.
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HSC Mathematics General 1 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 1 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’.

Questions involving calculations for credit card accounts should be carefully constructed
to ensure that students have sufficient information to perform the calculations.

In the HSC Mathematics General 1 course:
– simple interest is to be assumed for all interest calculations, with interest calculated on
the daily outstanding account balance for each transaction and applied at the end of the
statement period
– the same interest rate is to be assumed to apply for all transaction types
– the daily interest rate is to be found by dividing the annual percentage interest rate by 365
– students are expected to carry out calculations, including calculations of simple interest for
one billing cycle, 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
– students are not expected to carry out calculations involving balance transfers, although
this could be considered for some students if appropriate.
Teachers should refer to the ‘Considerations’ section of FM4CEC on page 133 of the Mathematics
General Stage 6 Syllabus for further information about expectations regarding credit card
calculations in the HSC Mathematics General 1 course.
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HSC Mathematics General 1 Course Support Material
Strand: Data and Statistics
DS4CEC Distributions
The following online resource could be used to support the teaching and learning of this topic.
Applets to create and/or investigate
statistical displays
www.shodor.org/interactivate/activities/
(select ‘Statistics’ for a list of applicable applets)
DS5CEC Interpreting sets of data
The following online resources could be used to support the teaching and learning of this topic.
Scootle resources – enter the following
reference numbers into the Scootle
search function:
 L3513 Box plot/histogram: select
the histogram option – automatically
generates a histogram and calculates
mean and median as data values
are entered
 L5905 Graph investigator: reaction time
 L10338 Graph investigator: reaction
time (ESL)
 L5906 Graph investigator: hand
preference
 L10339 Graph investigator: hand
preference (ESL)
 L5912 Stem-and-leaf plots: an
introduction – focuses on back-to-back
stem-and-leaf plots
www.scootle.edu.au/ec/p/home
 M009386 Back-to-back stem-and-leaf
plot of sex vs concentration time –
uses CensusAtSchool data
DS6CEC Working with statistics
The following online resources could be used to support the teaching and learning of this topic.
Reversal Paradox
http://repository.upenn.edu/cgi/viewcontent.cgi?article=1014&
context=wharton_research_scholars
Simpson’s Paradox
http://en.wikipedia.org/wiki/Simpson%27s_paradox#cite_note-12
Refer also to page 5 of the Preliminary Mathematics General course support material for links to
resources relating to Data and Statistics.
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HSC Mathematics General 1 Course Support Material
For the teacher
The Reversal Paradox is also known as Simpson’s Paradox, the Amalgamation Paradox
or the Yule–Simpson Effect. The Reversal Paradox applies where the statistical relationship
between two variables is reversed in situations where, rather than considering the relevant
data in subgroups, the data of the subgroups is combined and viewed as a whole.
Reversal Paradox example: Kidney stone treatment study
The following example of the Reversal Paradox is adapted from Wikipedia and is based on
a real-life study of the success of two different kidney stone treatments (Treatment A and
Treatment B).
The table below shows the success rates and the numbers of treatments for cases involving
small kidney stones and for cases involving large kidney stones.
Treatment A
Treatment B
Small stones
Group 1
93% (81/87)
Group 2
87% (234/270)
Large stones
Group 3
73% (192/263)
Group 4
69% (55/80)
Both
78% (273/350)
83% (289/350)
The paradoxical conclusion is that Treatment A is more effective when used on small stones
and also when used on large stones, yet Treatment B is more effective when considering
both sizes at the same time. In this example, the ‘lurking variable’ or ‘confounding variable’
of the stone size was not known to be important until it was decided to include its effects.
Determining which treatment is better requires considering the inequality between two
fractions (successes/total) in the table. The reversal of the inequality between the fractions
(Simpson's Paradox) becomes evident because two effects occur together:
1.
The sizes of the groups, which are combined when the lurking variable is ignored, are
very different. Doctors tend to give the severe cases (large stones) the better treatment
(Treatment A), and the milder cases (small stones) the inferior treatment (Treatment B).
Therefore, the totals are dominated by Group 2 and Group 3, and not by the two much
smaller groups, Group 1 and Group 4.
2.
The lurking variable has a large effect on the ratios, ie the success rate is more strongly
influenced by the severity of the case than by the choice of treatment. Therefore, the
group of patients with large stones using Treatment A (Group 3) does worse than the
group with small stones, even if the latter was using the inferior Treatment B (Group 2).
Source: Adapted from Wikipedia, ‘Simpson’s Paradox’, http://en.wikipedia.org/wiki/Simpson%27s_paradox, citing
CR Charig, DR Webb, SR Payne and JE Wickham (1986) ‘Comparison of treatment of renal calculi by open surgery,
percutaneous nephrolithotomy, and extracorporeal shockwave lithotripsy’, Br Med J (Clin Res Ed) 292:879.
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HSC Mathematics General 1 Course Support Material
Strand: Measurement
MM4CEC 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
Refer also to page 9 of the Preliminary Mathematics General course support material for links to
resources relating to Measurement.
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HSC Mathematics General 1 Course Support Material
Strand: Probability
PB2CEC Multistage events and applications of probability
The following online resources could be used to support the teaching and learning of this topic.
Dice rolling simulator (two dice) with
histogram comparing experimental
results to theoretical results
https://www.math.duke.edu//education/postcalc/
probability/dice/index.html
Probability simulations
(coin, spinner and others)
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.
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HSC Mathematics General 1 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.
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HSC Mathematics General 1 Course Support Material
Focus Study: Mathematics and Design
FSDe1CEC Scale drawings and house plans
The following online resources could be used to support the teaching and learning of this topic.
Building plan examples and free software
www.edrawsoft.com/Building-Plan-Examples.php
Drawing and scale diagram tool
(for floor plans, for example)
www.gliffy.com/
Floor plan examples and free software
www.edrawsoft.com/floorplan.php
Floor plan symbols explained
www.floorplansfirst.com/symbols.cfm
Floor plans of properties for sale
www.realestate.com.au/buy
www.domain.com.au/
From Concept to Construction (video
about mathematics used by engineers)
www.mathscareers.org.uk/viewitem.cfm?cit_id=383234
Graph paper generator
(includes a variety of styles)
http://incompetech.com/graphpaper/
Graph paper generator
(includes isometric paper)
http://illuminations.nctm.org/ActivityDetail.aspx?ID=205
(select ‘Graph Paper’)
Home plan examples and free software
www.edrawsoft.com/homeplan.php
Homestyler
(drag-and-drop floor plan design tool)
www.homestyler.com/designer
Math by Design
(interactive design of local amenities)
http://mathbydesign.thinkport.org/
(select either ‘Flossville Town Park’ or
Windjammer Environmental Center’)
http://mathbydesign.thinkport.org/educator_resources/mathin
action.aspx
Math in Action (videos)
Sample floor plan with features explained
www.homedesigndirectory.com.au/articles/plans/LargeFloorPlan
2.html
Sample house plan with dimensions
(opens in Microsoft Word)
https://www.dlsweb.rmit.edu.au/toolbox/electrotech/toolbox1204/
resources/04diagrams/02architectural/03floor_plan.htm
Sample house plans with dimensions
www.maddisonconstructions.com.au/newhome_example_plans.
html
Teacher package: ‘Maths and art’
http://plus.maths.org/content/teacher-package-maths-andart#design
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HSC Mathematics General 1 Course Support Material
FSDe2CEC Design
The following online resources could be used to support the teaching and learning of this topic.
Escher gallery of designs
www.mcescher.com/Gallery/gallery.htm
GeoGebra (freeware)
www.geogebra.org/cms/
Golden ratio (includes tessellations)
www.miqel.com/fractals_math_patterns/visual-math-phigolden.html
Golden ratio and beauty in art
http://library.thinkquest.org/trio/TTQ05063/phibeauty3.htm
Golden ratio calculator
http://goldenratiocalculator.com/
Golden ratio explained
http://en.wikipedia.org/wiki/Golden_ratio
www.goldennumber.net/
www.phiday.org/phi-golden-ratio/
Golden ratio – The Divine Proportion: Phi
(video)
www.youtube.com/watch?v=3sERcM9o25g
Golden Ratio − Universal Principles
of Design (video)
www.youtube.com/watch?v=jCUJzNsKGW4
Islamic tiling pattern
(photograph, with inquiry questions)
www.aamt.edu.au/digital-resources/R11271/index.html
Logos designed using the golden ratio
www.banskt.com/blog/golden-ratio-in-logo-designs/
Pyramid composed of glass tiles
(photograph, with inquiry questions)
www.aamt.edu.au/digital-resources/R11197/index.html
Tessellating garden design
(photograph, with inquiry questions)
www.aamt.edu.au/digital-resources/R11276/index.html
Tessellation creation (animation)
http://library.thinkquest.org/16661/escher.html
Tessellation creators
http://illuminations.nctm.org/ActivityDetail.aspx?ID=205
(select ‘Tessellations’ tab)
www.shodor.org/interactivate/activities/Tessellate/
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HSC Mathematics General 1 Course Support Material
For the student
Designs: golden or not?
(1) Research the ‘golden ratio’ (also known as the ‘golden proportion’, the number ‘phi’
and various other names) online (eg www.youtube.com/watch?v=3sERcM9o25g,
http://en.wikipedia.org/wiki/Golden_ratio, www.goldennumber.net/).
(2) What is the value of the golden ratio, correct to three decimal places?
(3) Consider your own bank card,
or the example shown here.
The same dimensions are used
for credit cards, loyalty cards,
driver licences, and so on.
Are the dimensions (length and
width) of the bank card in the
golden ratio?
CC-BY-SA-3.0-MIGRATED. Released under the
GNU Free Documentation Licence.
(4) Consider the logo of the BMW
car company. The design
includes an ‘outer’ circle and
an ‘inner’ circle.
Measure the radius of each circle
and determine whether or not the
circles were constructed using
the golden ratio.
© BMW AG RE. 97. L. 1491.
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HSC Mathematics General 1 Course Support Material
(5) Consider the logo of the BP oil and
gas company. The design includes
concentric circles (circles with the
same centre). These concentric circles
and two axes have been drawn on the
image at left.
Measure the diameter of each of the
circles and determine whether or not
the golden ratio has been used in the
design of the logo.
© BP Australia Pty Ltd, reproduced with permission.
(6) Consider the logo of the iCloud service
operated by Apple. It is composed of
four circles and a base line. The four
circles have been drawn on the image
at right in two pairs, one pink and one
blue. A red rectangle has been drawn
around the cloud to show the length
and width of the cloud.
Has the golden ratio been used in the
iCloud logo? If so, describe where it
has been applied.
© Apple Inc., registered in the US and other countries.
(7) Find a logo or other commonly used symbol with dimensions that are in the golden ratio.
Record a picture of your logo or symbol. Label the picture with the dimensions that you have
measured that are in the golden ratio. Write down the calculations that you did to determine
that the dimensions are in the golden ratio.
(8) Design a logo for a new car company called ‘Movus’ using simple shapes and the golden
ratio correct to one decimal place. You may use appropriate technology, or pencil and paper.
Grid paper may also be helpful.
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HSC Mathematics General 1 Course Support Material
Focus Study: Mathematics and Household Finance
FSHo1CEC Accommodation costs: buying and renting
The following online resources could be used to support the teaching and learning of this topic.
Buying a home
https://www.moneysmart.gov.au/tools-and-resources/lifeevents/buying-a-home
Buying a home – costs
www.anz.com.au/personal/home-loans/getting-started/costsbuying-home/
Buying into a strata scheme
www.fairtrading.nsw.gov.au/Tenants_and_home_owners/Buying
_property/Buying_into_a_strata_scheme.html
Buying property (includes three videos)
www.fairtrading.nsw.gov.au/Tenants_and_home_owners/Buying
_property.html
Home loans
https://www.moneysmart.gov.au/borrowing-and-credit/homeloans
Leaving home costs (includes renting,
sharing, setting up utilities, etc)
https://www.moneysmart.gov.au/tools-andresources/information-for/under-25s/leaving-home
Mortgage calculator
https://www.moneysmart.gov.au/tools-and-resources/calculatorsand-tools/mortgage-calculator
Mortgage calculator (shows amount
owing over time in a graph or table)
www.infochoice.com.au/calculators/home-loan-calculator/
(select ‘Yearly Breakdown’ tab for table)
Property buying cost calculators
(including additional costs)
www.yourmortgage.com.au/calculators/homecost/
http://service.commbank.com.au/personal/homeloans/calculators/additional-cost-calculator.aspx
www.ingdirect.com.au/home_loans/calculators/property_buying_
cost_calculator.htm
Renting a property
www.fairtrading.nsw.gov.au/Tenants_and_home_owners/Renting
_a_home.html
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HSC Mathematics General 1 Course Support Material
FSHo2CEC Costs of running a household, maintenance, and repairs
The following online resources could be used to support the teaching and learning of this topic.
Budget planner
https://www.moneysmart.gov.au/tools-andresources/calculators-and-tools/budget-planner
(select either online or Excel version)
Do-it-yourself (DIY) calculators
(including for paint and flooring)
www.bunnings.com.au/learn-how-to-diy_online-diy-tools.aspx
Drawing and scale diagram online tool
(for floor plans, for example)
www.gliffy.com/
Energy 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+Home
page/yourAccountNav/Your+bill+explained/
www.originenergy.com.au/1374/Understanding-your-bill
www.redenergy.com.au/docs/BillExplainerQuarterlyBill.pdf
Energy retailers in NSW
www.myenergyoffers.nsw.gov.au/useful-information/energyretailers.aspx
Floor plan examples and free software
www.edrawsoft.com/floorplan.php
Graph paper generator
(includes a variety of styles)
http://incompetech.com/graphpaper/
Household budget facts sheet
https://www.moneysmart.gov.au/media/344193/householdbudgets.pdf
How to read your energy bills and track
your consumption
www.transport.wa.gov.au/mediaFiles/AT_LS_P_read_bills_track
_consumption.pdf
Insurance
https://www.moneysmart.gov.au/managing-my-money/insurance
Kitchen planning and designing
www.mitre10.com.au/Kitchens/Plan-And-Design-Your-Kitchen/
www.kitchenplanneronline.com/
Phone bills explained
http://optus.custhelp.com/app/answers/detail/a_id/291
www.telstra.com.au/telstrabills/index.htm
Sample energy bill
(with links to bill examples from
South Australia)
www.sa.gov.au/subject/Water,+energy+and+environment/Energy
/Energy+efficiency/Understanding+your+energy+use/Understand
+your+energy+bills
Spending habits of Australians by state
(infographic)
https://www.moneysmart.gov.au/managing-mymoney/budgeting/spending/australian-spending-habits
Spending money
https://www.moneysmart.gov.au/managing-mymoney/budgeting/spending
Strata levies
www.strataman.com.au/levies.html
Strata levies listed in advertisements
of properties for sale
www.realestate.com.au/buy
www.domain.com.au/
‘Your money’ brochure
(includes scenario and sample budget)
https://www.moneysmart.gov.au/media/142419/your-money.pdf
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HSC Mathematics General 1 Course Support Material
Focus Study: Mathematics and the Human Body
FSHu1CEC Blood
The following online resources could be used to support the teaching and learning of this topic.
Blood pressure
http://en.wikipedia.org/wiki/Blood_pressure
Blood pressure chart
www.bloodpressureuk.org/BloodPressureandyou/The
basics/Bloodpressurechart
Blood safety and availability
(includes world map of blood
donation rates)
www.who.int/mediacentre/factsheets/fs279/en/index.html
Blood type
http://en.wikipedia.org/wiki/Blood_type
Blood types (includes blood
compatability two-way table)
www.donateblood.com.au/about-blood/types
Heart rate
http://en.wikipedia.org/wiki/Heart_rate
Heart rate and exercise
(activities)
www.bioedonline.org/resources/files/tso_hc_07_s.pdf
www.k8science.org/resources/files/PowerPlay_s/03_PPre_s.pdf
http://illuminations.nctm.org/LessonDetail.aspx?ID=U74
Inheritance patterns of blood
types
www.transfusion.com.au/blood_basics/blood_groups/in
heritance_patterns
FSHu2CEC 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/DataS
ets?CGISESSID=10713f6d891653ddcbb7ddbdd9cffb79
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/
Least-squares regression line
(applet)
http://illuminations.nctm.org/LessonDetail.aspx?ID=L491#
applet
Linear regression and body
measurements (PowerPoint)
www.google.com.au/url?sa=t&rct=j&q=&esrc=s&sourc
e=web&cd=3&ved=0CC8QFjAC&url=http%3A%2F%2F
www.cs.sunysb.edu%2F~mueller%2Fteaching%2Fvolu
meGraphicsSeminar%2Fch18Reg.ppt&ei=cMiUKK6LqeUiAemx4CgAg&usg=AFQjCNGmnxCkExON
DkCVBCkDNlt0Y76wxw&sig2=8waimkJSlp289ofMJ1aPg
Regression by eye (applet)
www.ruf.rice.edu/~lane/stat_sim/reg_by_eye/index.html
Scatterplot, correlation and
line of best fit creator
http://nlvm.usu.edu/en/nav/frames_asid_144_g_4_t_5.ht
ml?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.
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HSC Mathematics General 1 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.
19
HSC Mathematics General 1 Course Support Material
For the student
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)
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HSC Mathematics General 1 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?
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HSC Mathematics General 1 Course Support Material
(6) 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.
(7) 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.
(8) 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.
(9) 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.
(10) 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.
FSHu3CEC Lung capacity
The following online resources could be used to support the teaching and learning of this topic.
Lung volumes
http://en.wikipedia.org/wiki/Lung_volumes
Measuring lung capacity
(includes the use of balloons)
www.biologycorner.com/worksheets/lungcapacity.html
22
HSC Mathematics General 1 Course Support Material
Focus Study: Mathematics and Personal Resource Usage
FSPe1CEC Water usage and collection
The following online resources could be used to support the teaching and learning of this topic.
‘Let’s have a school rainwater tank!’
(student activity)
www.rouswater.nsw.gov.au/cmst/rw010/res.asp?id=745
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=9780643103283_
Chapter_1.pdf
Water education recources
www.environment.gov.au/water/education/index.html
Water harvesting calculations
http://oasisdesign.net/water/rainharvesting/drylandsbook/Append
ix3Calculations.pdf
Water saving ideas
www.waterforgood.sa.gov.au/using-water/saving-water/
Water suppliers in NSW
www.ewon.com.au/index.cfm/suppliers/suppliers-in-nsw/watersuppliers/
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/4602.0.55.0
03Mar 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+Subject/1367.0~
2011~Main+Features~Water+Use~6.37
For the teacher
Find information about your local water supplier. It is also worth exploring suppliers from other
areas, as they may have more data and information that you could use with your students.
23
HSC Mathematics General 1 Course Support Material
FSPe2CEC Electricity
The following online resources could be used to support the teaching and learning of this topic.
Energy ratings for different appliances
http://reg.energyrating.gov.au/comparator/product_types/
Energy Savings Scheme (ESS)
www.ess.nsw.gov.au/Home
Energy tools and calculators
www.aglsmarterliving.com.au/energy-efficiency-advice/energytools/
www.redenergy.com.au/billbenchmark/
Energy usage
www.yourhome.gov.au/technical/fs61.html
kW and kWh explained
www.energylens.com/articles/kw-and-kwh
Reading electricity meters
www.actewagl.com.au/Help-and-advice/How-to-read-yourmeters.aspx
Sample energy rating labels
www.energyrating.gov.au/programs/e3-program/energy-ratinglabelling/obtain/
Tips on buying energy-efficient appliances
www.livinggreener.gov.au/energy/energy-efficient-appliances
Understanding demand and consumption
www.think-energy.net/KWvsKWH.htm
Your power usage
www.savepower.nsw.gov.au/get-the-facts/your-powerusage.aspx
FSPe3CEC Sustainability and energy-efficient housing
The following online resources could be used to support the teaching and learning of this topic.
BASIX – Building Sustainability Index
www.basix.nsw.gov.au/information/index.jsp
Building an energy-efficient home
www.environment.nsw.gov.au/energy/home.htm
Designing an energy-efficient home
www.sa.gov.au/subject/Water,+energy+and+environment/Energy
/Energy+efficiency/Home+energy+efficiency/Designing+an+ener
gy+efficient+home
Ecological footprint (measure your
impact on the environment)
www.epa.vic.gov.au/ecologicalfootprint/globalfootprint/index.asp
Energy-efficient home renovator
www.synergy.net.au/at_home/energy_efficient_renovator.xhtml
Energy saving tips interactive
www.originenergy.com.au/calculator
Home energy audits
(includes heating and cooling,
lighting, and water heating)
www.sa.gov.au/subject/Water,+energy+and+environment/Energy
/Energy+efficiency/Understanding+your+energy+use/Check+your
+home+energy+use+-+home+energy+audit/Do+your+own+home
+energy+audit
Interactive energy-efficient house
www.sa.gov.au/subject/Water,+energy+and+environment/Energy
/Energy+efficiency/Home+energy+efficiency/Interactive+energy+
efficient+house
Water tanks and BASIX package
www.rainwatertanksdirect.com.au/
Your Home Technical Manual
(includes information about sustainable
design and practices)
www.yourhome.gov.au/technical/index.html
(select ‘Material Use’, ‘Energy Use’, ‘Water Use’, etc)
24
HSC Mathematics General 1 Course Support Material
For the student (FSPe1CEC and FSPe3CEC)
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).
25