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20121398
2

Strand: Financial Mathematics ........................................................................................................ 4
Strand: Data and Statistics .............................................................................................................. 5
Strand: Measurement ..................................................................................................................... 9
Strand: Probability ......................................................................................................................... 10
Strand: Algebra and Modelling ...................................................................................................... 11
Focus Study: Mathematics and Communication............................................................................ 13
Focus Study: Mathematics and Driving ......................................................................................... 24
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.
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Preliminary Mathematics General Course Support Material
The following online resources could be used to support the teaching and learning of this topic.
Average Australian salary
Award finder
Budget planner
Household budget management
Pay rates calculator
Personal finance
Youth Allowance rates http://content.mycareer.com.au/salary-centre www.fairwork.gov.au/awards/award-finder/pages/default.aspx https://www.moneysmart.gov.au/tools-and-resources/calculatorsand-tools/budget-planner www.youthcentral.vic.gov.au/Housing+&+Accommodation/Setting
+up+house/Managing+a+household+budget/ www.fairwork.gov.au/pay/pay-rates-calculator/pages/default.aspx http://australia.gov.au/topics/economy-money-and-tax/personalfinance www.centrelink.gov.au/internet/internet.nsf/payments/ya_rates.htm
The following online resources could be used to support the teaching and learning of this topic.
Compound interest calculator
Dividend yield calculator
Financial calculators
Housing appreciation calculator
Share price appreciation calculator www.moneysmart.gov.au/tools-and-resources/calculators-andtools/compound-interest-calculator www.calculatorpro.com/calculator/dividend-yield-calculator/ www.miniwebtool.com/financial-calculators/ www.miniwebtool.com/housing-appreciation-calculator/ www.mbaware.com/share-appreciation.html
The following online resources could be used to support the teaching and learning of this topic.
Comprehensive tax calculator
Income tax rates
Individual non-business tax calculator
Medicare levy calculator
Work out your tax http://calculators.ato.gov.au/scripts/axos/axos.asp?CONTEXT=&
KBS=ctax2012.xr4&go=ok www.ato.gov.au/individuals/content.aspx?doc=/content/12333.htm
&mnu=42904&mfp=001/002 www.ato.gov.au/scripts/taxcalc/calc_standard_hire.aspx
http://calculators.ato.gov.au/scripts/axos/axos.asp?CONTEXT=&
KBS=Medicare12.xr4&go=ok www.ato.gov.au/individuals/entry.aspx?menuid=42513
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Preliminary Mathematics General Course Support Material
The following online resources could be used to support the teaching and learning of this topic.
These resources are generally applicable for use across the Strand, but particularly in relation to DS1.
Australian Bureau of Statistics
Centers for Disease Control and Prevention www.abs.gov.au/ www.cdc.gov/nchs/fastats/default.htm
Data sets (links) www.statsci.org/datasets.html
Gallup – particularly Wellbeing and World www.gallup.com/home.aspx
www.healthstats.nsw.gov.au/ Health statistics for NSW
(includes data and graphs)
Statistical language and terminology www.abs.gov.au/websitedbs/a3121120.nsf/89a5 f3d8684682b6ca256de4002c809b/cd21f4a6258
496aaca257949000f6938!OpenDocument
United Nations Department of Economic and Social Affairs, Population Division
The World Factbook www.un.org/esa/population/unpop.htm
https://www.cia.gov/library/publications/theworld-factbook/index.html
www.who.int/research/en/ World Health Organization (WHO) – health and environmental issues
World Values Survey www.worldvaluessurvey.org/ See note (1) below
The following online resources could be used to support the teaching and learning of this topic.
These resources are generally applicable for use across the Strand, but particularly in relation to DS2.
Histograms – demonstrations of varying the bin width (class-interval size) www.shodor.org/interactivate/activities/Histogram/ http://demonstrations.wolfram.com/EffectsOfBinWi dthAndHeightInAHistogram/ http://onlinestatbook.com/stat_sim/histogram/index.
html
Histograms – general information
Histograms – interpreting http://en.wikipedia.org/wiki/Histogram http://quarknet.fnal.gov/toolkits/new/histograms.
html
Statistical displays – applets to create and/or investigate displays www.shodor.org/interactivate/activities/
(select ‘Statistics’ for a list of applicable applets)
(1) World Values Survey
The World Values Survey collects data about the cultural and political views of societies around the world. This data is available from the website through steps (a) to (g) on the following pages.
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Preliminary Mathematics General Course Support Material
(a) Select ‘Online Data Analysis’ from the ‘Site Shortcuts’ menu.
© World Values Survey, reproduced with permission.
(b) Select ‘Begin analysis’.
© World Values Survey, reproduced with permission.
(c) Select a data set, eg
‘WVS 2005–2008’.
© World Values Survey, reproduced with permission.
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Preliminary Mathematics General Course Support Material
(d) Select countries to compare, then ‘Confirm selection’.
© World Values Survey, reproduced with permission.
(e) Choose a variable, eg
‘Important in life: Friends’.
© World Values Survey, reproduced with permission.
(f) Select ‘Cross-tabs’.
© World Values Survey, reproduced with permission.
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Preliminary Mathematics General Course Support Material
(g) View the cross-tabular analysis presented.
© World Values Survey, reproduced with permission.
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Preliminary Mathematics General Course Support Material
The following online resources could be used to support the teaching and learning of this topic.
These resources are generally applicable for use across the Strand, but particularly in relation to MM1.
Google search
(eg search for ‘6000 m to km’)
Online unit conversions www.google.com.au/intl/en/help/features.html
#calculator www.unitconversion.org/
See note (1) below
The following online resources could be used to support the teaching and learning of this topic.
These resources are generally applicable for use across the Strand, but particularly in relation to MM2.
GeoGebra – multiplatform dynamic geometry, algebra, graphing, statistics and calculus package www.geogebra.org/cms/
Microsoft Word drawing tools
SketchUp – using 3D models to explore, explain and present ideas http://office.microsoft.com/en-au/word/ www.sketchup.com/
(1) Unit conversion can be carried out using the Google search page, as in the example below.
Google and the Google logo are registered trademarks of Google Inc., used with permission.
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Preliminary Mathematics General Course Support Material
The following online resources could be used to support the teaching and learning of this topic.
Coin flipping simulator (one coin) http://nlvm.usu.edu/en/nav/frames_asid_305_g_4_t_5.html?from
=category_g_4_t_5.html
Coin flipping simulator (one or more coins) www.mathsonline.co.uk/nonmembers/resource/prob/coins.html
Dice rolling simulator (one or more dice)
Dice rolling simulator with histogram
(one or more dice) www.random.org/dice/
Applet.html
www.stat.ucla.edu/~dinov/courses_students.dir/Applets.dir/Dice www.mathsonline.co.uk/nonmembers/resource/prob/index.html
Probability simulations
(coin, spinner and others)
Random number generator
Spinner creator www.random.org/ http://illuminations.nctm.org/ActivityDetail.aspx?ID=205
(select ‘Spinners’ tab)
Spinner simulator (adjustable spinner) http://nlvm.usu.edu/en/nav/frames_asid_186_g_4_t_5.html?open
=activities&from=category_g_4_t_5.html
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Preliminary Mathematics General Course Support Material
Emphasis should be placed on formulae from vocational and other practical contexts – including, but not limited to, formulae that students will encounter in other topics.
Students should be aware that formulae used in vocational contexts may use more than one letter to represent a single variable.
(1) The cutting speed CS of a drill bit with diameter D is the product of the circumference

 
D ie
CS

 of the drill bit multiplied by the number of revolutions per minute
 
D

RPM .

RPM

,
(a) A drill bit has diameter 12.5 millimetres and revolves at the rate of 382 revolutions per minute to cut through cast iron. What is the cutting speed of the drill bit, correct to 2 significant figures?
(b) At this cutting speed, what is the maximum thickness of cast iron that can be drilled through in 1 second?
(2) A shopkeeper calculates the ‘display price’ of items to be sold in his shop as the cost price plus 35% ‘mark-up’. Write a formula that the shopkeeper could use to calculate the display price D in dollars, given the cost price C in dollars. Leave your answer in simplest form.
(3) The ‘root diameter’ R of a thread is equal to the ‘outside diameter’ D minus twice the sum of the ‘depth of the thread’ d and the ‘clearance’ c . Write a formula to calculate the root diameter in terms of D , d and c.
(4) The approximate length L of a ‘flat belt’ is equal to twice the distance between the centrelines of the two pulleys, c , plus 3.25 times the sum of the pulley diameters, D
1
and D
2
, divided by 2.
Write a formula for L.
Sample solutions
(1) (a)
(2)
(3)
(4)
(b)
CS
  
D

RPM
  
12.5

382

15 001.104...

Cutting speed

15 000 mm/min (correct to 2 significant figures)
Thickness drilled through in 1 second

15 000

60

250 mm
D

D

C

0.35

C
C

0.35
C
( think D

1 C

0.35
C )
D

1.35
C
R

D

2
 
L

2 c

3.25

D
1

D
2
2

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Preliminary Mathematics General Course Support Material
Students will require access to appropriate technology to create graphs of functions and to observe the effect on the graph of a function when parameters are changed. The following online resources could be used to support the teaching and learning of this topic.
GraphSketch – software for sketching a broad range of functions http://graphsketch.com
WolframAlpha – ‘computational knowledge engine’ incorporating graphing tools www.wolframalpha.com/
See note (1) below
See note (2) below
(1) Using GraphSketch
© Andy Schmitz, reproduced with permission.
(2) Using WolframAlpha
Wolfram Alpha LLC, 2013, Wolfram|Alpha, www.wolframalpha.com/input/?i=plot+y%3Dx%5E2%2B3 (accessed 31 January 2013).
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Preliminary Mathematics General Course Support Material
The following online resources could be used to support the teaching and learning of this topic.
Compare mobile phone plans/carriers www.phonechoice.com.au/index.cfm?Section=Mobile www.whistleout.com.au/MobilePhones
Mobile phone bills
Mobile phone plans www.peopletelecom.com.au/pdf/PT_Sample Bill_-_Explainer.pdf
http://optus.custhelp.com/app/answers/detail/a_id/291 www.telstra.com.au/telstrabills/mobile/index.htm
www.three.com.au/cs/ContentServer?c=Page&pagename=3CA/
Page/3CAStatic&cid=1236150768678 http://virginmobile.custhelp.com/app/answers/detail/a_id/4318/~/ understanding-your-bill www.vodafone.com.au/help/account/billexplainer https://www.optus.com.au/shop/mobilephones/plans www.telstra.com.au/mobile-phones/mobile-plans/ www.three.com.au/ www.virginmobile.com.au/mobile-phone-plans/ www.virginmobile.com.au/mobile-phone-plans/
(1) The table below shows a sample prepaid mobile phone plan.
Cost Credit
STARTER PACKAGE
Data
Within the network
Calls Texts
$10
$10
(30-day expiry)
Not included
Add data package
RECHARGE PACKAGE
$25
10c per minute
(billed per
30 seconds) plus 25c call connection fee
$25
(45-day expiry)
Not included
Add data package
10c per minute
(billed per
30 seconds) plus 25c call connection fee
10c
10c
Outside the network
Calls Texts
12c per minute
(billed per
30 seconds) plus 27c call connection fee
12c per minute
(billed per
30 seconds) plus 27c call connection fee
10c
10c
(a) Calculate the cost of a 5-minute call to a mobile phone on a different network.
(b) Calculate the cost of a call lasting 5 minutes and 3 seconds to a mobile phone within the network.
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Preliminary Mathematics General Course Support Material
(2) The table below compares two mobile phone plans from Telstra.
© Telstra Corporation Limited, reproduced with permission.
Jake is on the Telstra mobile phone ‘$30 plan’ outlined in the table above.
(a) For the billing period 20 April to 19 May, Jake made standard voice and video calls and also sent text and MMS messages to the total value of $38. He had data costs (in Australia only) to the value of $4. How much would Jake have been charged for this billing period?
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Preliminary Mathematics General Course Support Material
(b) A section of Jake’s bill for the billing period 20 May to 19 June is shown below.
Messages
Date Time Type
20 May 02:17pm Mobile Originated SMS
21 May 03:08pm Mobile Originated MMS
21 May 08:23pm Mobile Originated SMS
22 May 11:57am Mobile Originated SMS
23 May 02:18pm Mobile Originated SMS
23 May 02:18pm Mobile Originated MMS
24 May 05:27pm Mobile Originated SMS
26 May 03:44pm Mobile Originated MMS
28 May 12:36pm Mobile Originated Video
29 May 04:01pm Mobile Originated SMS
31 May 05:50pm Mobile Originated SMS
31 May 07:48pm Mobile Originated Video
2 Jun 10:37am Mobile Originated MMS
4 Jun 03:09pm Mobile Originated SMS
5 Jun 11:49am Mobile Originated SMS
5 Jun 04:24pm Mobile Originated SMS
7 Jun 03:31pm Mobile Originated SMS
9 Jun 01:17pm Mobile Originated SMS
9 Jun 01:18pm Mobile Originated Video
11 Jun 02:25pm Mobile Originated SMS
11 Jun 05:52pm Mobile Originated MMS
12 Jun 12:29pm Mobile Originated SMS
13 Jun 09:10am Mobile Originated SMS
15 Jun 08:21am Mobile Originated SMS
15 Jun 03:38pm Mobile Originated MMS
16 Jun 02:15pm Mobile Originated SMS
18 Jun 09:19am Mobile Originated SMS
Data
Date Time Type Origin
26 May 05:15pm National to Telstra Mobiles Bathurst
4 Jun 01:03pm National to Telstra Mobiles Taree
Origin Number
Wollongong
Kiama
Kiama
Camden
Sydney
Sydney
Sydney
Bathurst
Mudgee
Dubbo
Coffs Harbour
Coffs Harbour
Taree
Taree
Gosford
Gosford
Sydney
Nowra
Nowra
Bega
0414xxxxxx
0400xxxxxx
0428xxxxxx
0428xxxxxx
0414xxxxxx
0400xxxxxx
0400xxxxxx
Merimbula 0428xxxxxx
Wagga Wagga 0414xxxxxx
Albury
Deniliquin
0400xxxxxx
0400xxxxxx
Hay
Mildura
Broken Hill
0414xxxxxx
0400xxxxxx
0428xxxxxx
0428xxxxxx
0404xxxxxx
0414xxxxxx
0414xxxxxx
0400xxxxxx
0448xxxxxx
0400xxxxxx
0414xxxxxx
0428xxxxxx
0428xxxxxx
0400xxxxxx
0400xxxxxx
0414xxxxxx
Amount in $ Subtotal in $
Subtotal
Less Discounts
Total
Calls
Date Time Type Origin Number
20 May 09:19am National to Telstra Mobiles Wollongong 0428xxxxxx
21 May 08:34pm National Video to Telstra Mobiles Kiama 0404xxxxxx
23 May 12:46pm National to Telstra Mobiles Sydney 0400xxxxxx
26 May 02:16pm National to Telstra Mobiles
28 May 08:38pm National to Telstra Mobiles
31 May 09:07pm National to Telstra Mobiles
Bathurst
Mudgee
0414xxxxxx
0428xxxxxx
Coffs Harbour 0400xxxxxx
4 Jun 10:43am National to Telstra Mobiles
5 Jun 01:47pm National to Telstra Mobiles
9 Jun 07:35pm National to Telstra Mobiles
11 Jun 09:19pm National to Telstra Mobiles
15 Jun 11:37am National to Telstra Mobiles
Taree
Gosford
Nowra
Merimbula
Hay
0414xxxxxx
0428xxxxxx
0400xxxxxx
0428xxxxxx
0414xxxxxx
Min:Sec Amount in $ Subtotal in $
03:23
06:02
00:35
03:45
12:18
20:48
01:58
05:27
04:33
09:26
04:47
Subtotal
Less Discounts
Total
Number
0414xxxxxx
0414xxxxxx
MB
1.2MB
0.9MB
Amount in $ Subtotal in $
Subtotal
Less Discounts
Total
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Preliminary Mathematics General Course Support Material
(i) Determine the charge for each of the messages that Jake sent during this billing period.
(ii) Using a spreadsheet or calculator, calculate the charge for each of the calls that
Jake made during the billing period.
(iii) Determine the subtotals and totals of the charges for both messages and calls.
Hint : ‘Discounts’ refers to the included monthly allowance for the item(s). If the subtotal amount is less than the included monthly allowance, then the discount is equal to the subtotal.
(iv) Calculate the charge for each item of data usage, and the subtotal and total for data usage.
(v) By how much did Jake exceed the amount of his monthly allowance for messages, calls and data?
(vi) Calculate the total amount that Jake would have paid for the billing period.
(c) Jake decided to recalculate his bill for the billing period 20 May to 19 June as though he had been on the $40 plan.
(i) Calculate the amounts, subtotals and totals for the billing period if Jake had been on the $40 plan.
(ii) How much more or less would Jake have had to pay if he had been on the $40 plan for the billing period?
(d) Jake considers that his phone usage for the billing period 20 May to 19 June is typical of his call, message and data usage for one month. Research various mobile phone plans.
Calculate the amount of Jake’s bill for the billing period 20 May to 19 June using these alternative plans and identify a plan that will save Jake money. Compare your findings to those of others in the class.
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Preliminary Mathematics General Course Support Material
The following online resources could be used to support the teaching and learning of this topic.
B it depth visualisation − interactive comparing 8 bits per pixel, 16 bits per pixel and 24 bits per pixel
Colour – 24-bit colour explained
Colour depth − n -bit colour explained
Computer monitors – how they work
Data representation fundamentals – bitmaps www.cambridgeincolour.com/tutorials/bit-depth.htm
http://printwiki.org/24-Bit_Color http://en.wikipedia.org/wiki/Color_depth http://computer.howstuffworks.com/monitor4.htm
http://en.wikibooks.org/wiki/A-level_Computing/AQA/Problem_
Solving,_Programming,_Data_Representation_and_Practical_
Exercise/Fundamentals_of_Data_Representation/Bitmaps
Digital Music Report 2012
Digital piracy
File transfer time – data transfer speed calculator iPods – do they really shuffle? www.ifpi.org/content/library/DMR2012.pdf
www.riaa.com/faq.php
www.t1shopper.com/tools/calculate/downloadcalculator.php www.mathscareers.org.uk/viewItem.cfm?cit_id=382943
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Preliminary Mathematics General Course Support Material
The table below summarises the units used to measure digital storage and data transfer. Students should be reminded to take care with the symbols for units and, in particular, the use of uppercase and lowercase letters.
Data storage Data transfer
Measure of
Conversion the size of data
(memory size, file size, capacity of digital device) the rate of transfer of data
(download speed, upload speed)
Measured in bits bytes
(b)
(B) kilobytes (kB) megabytes (MB) gigabytes (GB) terabytes (TB)
Note:
The symbol ‘b’ is used for ‘bit’; the symbol ‘B’ is used for ‘byte’. bits per second (bps) kilobits per second (kbps)
1 byte = 8 bits
1 kilobyte = 2 10 bytes = 1024 bytes
1 megabyte = 2 20 bytes = 1 048 576 bytes
1 gigabyte = 2 30 bytes = 1 073 741 824 bytes
1 terabyte = 2 40 bytes = 1 099 511 627 776 bytes
1 kilobit (kb) = 1000 bits (b)
Note:
The conversions involve powers of two, not powers of ten, even though the prefixes are those used for SI units. Students can use the powers of two
(expressed in index form) or, alternatively, they can use the following:
1 kilobyte = 1024 bytes
1 megabyte = 1024 kilobytes
1 gigabyte = 1024 megabytes
1 terabyte = 1024 gigabytes
Note:
The prefix ‘kilo’ represents the standard 10 3 when working with ‘bits’.
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Preliminary Mathematics General Course Support Material
The term ‘bit’ is a contraction of ‘ b inary dig it ’. A bit is the smallest unit of data storage − computers store all data/information using sequences of bits. A single bit can be used to represent two different things only. A binary digit is usually represented as a 1 or a 0. Therefore, to extend the number of unique things that can be represented, more bits need to be used.
Number of bits
1
2 n
3

0 1
00 01 10 11
000 100 010 001 110 101 011 111
Unique things that can be represented
Number of unique things
2

2 1
4

2 2
8


2
3
2 n
A pixel is the smallest element of a digital image. The term ‘pixel’ is a contraction of ‘ pic ture el ement’. Digital images are often described as being composed of n -bit colour, ie n bits per pixel. n -bit colour
( n bits per pixel)
Number of colours available per pixel
Example of image
(images should be viewed on a digital device)
2
1 
2 unique colours available 1-bit colour
2
2 
4 unique colours available 2-bit colour
2
4 
16 unique colours available 4-bit colour
2
8 
256 unique colours available 8-bit colour
24-bit colour
2
24 
16 777 216 unique colours available
(known as ‘true colour’ and widely used in 2013 for digital displays)
Images: Thegreenj. CC-BY-SA-3.0. Released under the GNU Free Documentation Licence.
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Preliminary Mathematics General Course Support Material
Pixels
A ‘pixel’ (‘ pic ture el ement’) is the smallest element of a digital image.
Bits
Computers use ‘bits’ (‘ b inary dig its ’) to record the colour of each pixel of a digital image. A bit is the smallest unit of data storage. A single bit can be used to represent two different things only.
On a computer, the information for one bit is usually stored as a 1 or a 0.
Storing digital images on a computer
The larger the number of pixels in an image, the larger the file size. The larger the number of bits required to record the colour of each pixel in an image, the larger the file size.
Digital images are often described as being composed of n -bit colour, ie n bits per pixel.
(1) 1-bit colour images
Consider an image of a tree that is composed of only two colours, eg green and white.
The colour of each pixel is shown in the diagram below.
(a) How many pixels make up the image?
Images created using a palette of only two colours are created using 1-bit colour, ie 1 bit per pixel.
If the computer uses ‘0’ to store a white pixel and ‘1’ to store a green pixel, then the image is stored as a map of the bits (a ‘bitmap’), as shown in the diagram below.
Each 0 and each 1 is a bit. Note that zeros are stored and contribute to the file size.
(b) How many bits make up the image?
(c) What is the file size (in bytes) for the image?
Use 1 byte = 8 bits.
0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
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Preliminary Mathematics General Course Support Material
(2) n -bit colour
The 1-bit colour image of the tree in part (1) above represents a poor-quality image composed of only two colours and requires only a very small file size.
Better-quality images can be created by allowing each pixel to display more than two colours and by including more pixels within the same area (by making them smaller).
Consider 2-bit colour, 3-bit colour, 4-bit colour, etc. The colour of each pixel can be stored using two bits, three bits, four bits, etc. Complete the ‘3-bit’ and ‘4-bit’ columns in the table below.
Number of bits per pixel
( n -bit colour)
Possible combinations of bits
1-bit 2-bit 3-bit 4-bit
0
1
00
01
10
11
 n -bit
Total number of unique colours that can be stored
2

[Expression (in terms of n ) for the total number of unique colours for n bits]
(a) Is there a relationship between the number of bits per pixel and the number of unique colours that can be stored? If so, describe the relationship.
(b) How many bits per pixel would be needed to store 256 unique colours?
(c) ‘Bit depth’ refers to the number of bits per pixel in a bitmapped image. In 2012, the bit depth typically used to store digital images was 24-bit colour. Determine the current typical bit depth used to store digital images and calculate the number of unique colours that can be stored.
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Preliminary Mathematics General Course Support Material
(3) 3-bit colour images
(a) How many unique colours are available for 3-bit colour?
(b) A more colourful image of a tree
(at right) can be created using
3-bit colour.
The computer references the
‘colour lookup table’ to determine which bit combination (‘bit combo’) is used for each colour and creates a bitmap for the image.
Using the colour lookup table, complete the fifth row of the bitmap below.
010 010 000 000 010 010 010 010 010 010
010 000 000 000 001 001 001 010 010 010
010 010 010 010 001 001 001 010 010 010
010 010 010 010 001 001 001 010 010 010
111 111 111 111 111 110 111 111 111 111
111 111 111 111 111 110 111 111 111 111
111 111 111 111 111 110 111 111 111 111
100 100 100 100 100 100 100 100 100 100
100 100 100 100 100 100 100 100 100 100
(i) How many bits make up this image?
(ii) What is the file size (in bytes) for the image?
Colour lookup table
Bit combo Colour
000
001 white green
010
100
011
101
110
111 light blue yellow red purple brown dark blue
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Preliminary Mathematics General Course Support Material
(4) 24-bit colour images
This image was taken using a mobile phone that stores images in 24-bit colour.
The image measures
2592

1944 pixels.
© SXC.hu.
(a) What is the file size (in megabytes) for this image? Give your answer correct to
4 significant figures.
(b) The data transfer speed for the mobile phone used to take this image is 200 kbps
(ie 200 kilobits per second). How long would it take to send this image to a friend ’s mobile phone? Give your answer in minutes and seconds.
(5) Extension: File compression
(a) What does it mean to ‘compress’ a file?
(b) Why is file compression important?
(c) What different types of file compression are used?
Hint: Compare GIF (‘lossless’) and JPEG (‘lossy’) compression techniques.
(d) Recalculate the file size for the 3-bit image in part (3) above if it is compressed using the GIF technique. What is the difference in the time taken to send the compressed file compared to the original image?
(e) Recalculate the file size for the mobile phone image in part (4) above if it is compressed using the JPEG technique. What is the difference in the time taken to send the compressed file compared to the original image?
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Preliminary Mathematics General Course Support Material
The following online resources could be used to support the teaching and learning of this topic.
Car loan calculator
Car loan comparison
Car ownership – real costs
Car ownership costs in Australian cities
(article)
Car registration costs
Crash statistics
Crime report data tools
CTP facts sheets
CTP ‘green slip’ calculator
Personal loan calculator
(also suitable for car loans)
Stamp duty calculator
Stamp duty costs www.carloan.com.au/car-loan-calculator/ www.ratecity.com.au/car-loans www.mynrma.com.au/motoring/buy-sell/buying-advice/realcost.htm
http://virginmoney.com.au/car-insurance/news/Australias-carfriendliest-town/ www.rta.nsw.gov.au/registration/feesconcessions/registrationfees.
html www.rta.nsw.gov.au/roadsafety/downloads/accident_statistics_dl4.
html
(see Downloads: ‘Annual statistical statement’ for files indicating crash statistics by NSW local government area) www.bocsar.nsw.gov.au/lawlink/bocsar/ll_bocsar.nsf/pages/bocsar
_onlinequeries www.maa.nsw.gov.au/default.aspx?MenuID=425 http://prices.maa.nsw.gov.au/ https://www.moneysmart.gov.au/tools-and-resources/calculatorsand-tools/personal-loan-calculator https://www.apps05.osr.nsw.gov.au/erevenue/calculators/motorsi mple.php
www.rta.nsw.gov.au/registration/feesconcessions/stampduty.html
The following online resources could be used to support the teaching and learning of this topic.
Car costs calculator
Car depreciation calculator
Car ownership cost calculator
Car running costs
(table of costs for particular vehicles)
Distance travelled by road
Fuel calculator – green vehicle guide
Fuel consumption labels
Fuel efficiency
Fuel price monitoring www.mynrma.com.au/motoring/buy-sell/buyingadvice/car-operating-costs.htm www.free-online-calculator-use.com/cardepreciation-calculator.html
www.freightmetrics.com.au/CalculatorsRoad/Car
OwnershipCost/tabid/545/Default.aspx
www.racq.com.au/motoring/cars/car_economy/ vehicle_running_costs www.whereis.com/
(select ‘Get Directions’) www.greenvehicleguide.gov.au/GVGPublicUI/Fuel
Calculator.aspx
www.environment.gov.au/settlements/transport/ fuelguide/label.html
www.livinggreener.gov.au/travel/motortransport/buy-fuel-efficient-car www.mynrma.com.au/motoring/car-care/fuel.htm
See note (1) below
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Preliminary Mathematics General Course Support Material
(1) Whereis.com
The Whereis website provides online maps and directions for travel by vehicle (or on foot) between addresses within Australia. Directions from one address to another can be obtained by following steps (a) to (c) below.
(a) Select ‘Get Directions’.
(b)
Enter the two addresses and select ‘Get Directions’.
(c) View the set of directions, the distance to be travelled, and a map of the route.
Whereis® maps are printed with permission from Location Navigation Pty Ltd and subject to copyright.
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Preliminary Mathematics General Course Support Material
Candice is 24 years old, single and lives in Thirroul, New South Wales. She works full-time
(five days per week) at St George Private Hospital in Kogarah. Candice needs to purchase a car to travel to and from work and to use on weekends. She estimates that, on average, she drives 30 kilometres each weekend. Most of her driving is on the open road. The car will be parked in her driveway in Thirroul each night and in the hospital car park while she is at work.
Candice has saved $15 000 as a deposit, but will need to borrow the balance to purchase the car.
She plans to use the car as security for the loan and to repay the loan by making equal monthly repayments over five years.
Following some research, Candice has determined that she will buy either:
 a used Mazda3 SP25 (2009 model) 4-cylinder, 2.5-litre, 5-speed automatic hatchback or
 a used Nissan Dualis Ti (2011 model) 4-cylinder, 2-litre, 6-speed automatic all-wheel-drive wagon.
Candice has never been involved in an ‘at-fault’ collision, has no demerit points on her driver licence, and has accumulated the maximum no-claim bonus by being a nominated driver on her parents’ GIO comprehensive car insurance for the seven years that she has been driving.
She intends to take out comprehensive insurance on her car.
Create a report to assist Candice with her decision. Ensure that you record:
 the results of any relevant internet research, eg printouts or screenshots of information obtained via websites and online calculators
 any calculations and findings in a suitable format as you work through the steps outlined below, eg using a spreadsheet (or table) and text where necessary.
(1) Purchase costs
(a) Use a car-sales website to determine a realistic price for each of the two cars. Note the make, model, year of production, odometer reading and asking price for each car.
(b) Calculate the stamp duty (motor vehicle duty) that Candice would need to pay on the purchase of each car.
(c) Find the cost of transferring the registration of each car from the previous owner to Candice.
(d) Research car loans online and select three applicable reducing-balance secured car loans
(including at least one from a bank) that Candice could apply for in order to buy her car.
(e) Use an online loan repayment calculator to determine the amount of each monthly repayment for each of the selected car loans for each car.
(f) Calculate the total amount of interest paid over the term of each selected car loan for each car if Candice is to make only the minimum monthly repayment.
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Preliminary Mathematics General Course Support Material
(2) Insurance costs
(a) Research the features and costs of compulsory third-party (CTP) car insurance for each of the two cars, given the location of Candice’s residence and her intended vehicle usage, her age and her driving history. Select and record the features and cost of suitable CTP insurance for each car. Justify your selection of CTP insurance by referring to cost and/or features.
(b) Research the features of comprehensive car insurance for each car. As a residential address is required, ask your teacher to assist you in obtaining a quote for comprehensive car insurance for each car.
(3) Running costs
(a) Use a website that provides travel directions by road to determine the distance that Candice will cover in travelling to and from work.
(b) Calculate Candice’s anticipated annual distance travelled, including travel to and from work and on weekends. (Consider her weekly distance travelled while on annual leave to be the same as that for working weeks.)
(c) Use a car specifications website to determine the average fuel consumption of each of the cars. Use this measure to calculate how much fuel each car would require annually.
(d) Research the current average price of fuel in Sydney. Use this figure to calculate the approximate annual cost of fuel for each car. (Ensure that you consider the appropriate type of fuel for each car.)
(e) Research an average cost per kilometre for tyre wear for each car. Use these figures to calculate the annual cost of tyre wear for each car.
(f) Research the average cost per kilometre for servicing and repairs for each car. Use these figures to calculate the annual cost of servicing and repairs for each car.
(4) Recommendation
Which car would you recommend to Candice once the costs of purchase and ownership have been taken into account? Justify your answer.
The following online resources could be used to support the teaching and learning of this topic.
Reaction time simulator
Safer driving
Speeding www.phy.ntnu.edu.tw/ntnujava/index.php?topic=137 www.nrmasaferdriving.com.au/driving-tips.htm
(click on the ‘SPEEDING’ tab, then select
‘BRAKING IN AN EMERGENCY’) www.rta.nsw.gov.au/roadsafety/speedandspeedcameras/index.html
http://rac.com.au/Advocacy/Roadsafety/~/media/Files/PDFs_10/Advocacy_factsheets/RAC_FactShe et_Speeding.ashx
Stopping distance
Stopping distances infographic
Stopping distances simulator
Vehicle and driver safety www.sdt.com.au/safedrive-directory-STOPPINGDISTANCE.htm
www.direct.gov.uk/prod_consum_dg/groups/dg_digitalassets/@ dg/@en/@motor/documents/digitalasset/dg_188029.pdf
www.stoppingdistances.org.uk/simulator/Stopping_Distances.html
(uses miles rather than kilometres) www.finance.gov.au/vehicle-leasing-and-fleetmanagement/vehicle-and-driver-safety.html
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