CALLAGHAN COLLEGE JESMOND SENIOR CAMPUS
Empowering Young Men and Women to Succeed
HSC ASSESSMENT TASK
STANDARD MATHEMATICS
Module/s Mathematics and Driving
Task No
Weighting
Allocated marks
Due Date
Time allowed (if applicable)
Teacher/s
1
20%
88
Week 9 – Friday 13th December
Take home assignment
Mr Wright, Mrs Gambrill, Mr Hayes, Mrs Matheson, Mrs Plunkett, Mr
Roop
Outcomes:
 MS2-12-5 makes informed decisions about financial situations, including annuities and loan
repayments
 MS2-12-6 solves problems by representing the relationships between changing quantities in
algebraic and graphical forms
 MS2-12-9 chooses and uses appropriate technology effectively in a range of contexts, and
applies critical thinking to recognise appropriate times and methods for such use
 MS2-12-10 uses mathematical argument and reasoning to evaluate conclusions, communicating
a position clearly to others and justifying a response
General Instructions:





Write using black pen
Draw diagrams using pencil
Show all relevant working in questions involving calculations
NESA approved calculators may be used
In class time will be given with access to computers and the internet
Total Marks: 88
The student uses mathematical argument and reasoning to find the cost of purchasing a new car, paying a
personal loan and determining the stamp duty which is to be paid on this purchase. They will also be required to
define insurance terms, calculate the cost of insurance, find the depreciation of the car and then plot these results.
The student will also calculate the cost of fuel required for a journey, calculations involving stopping distance of
the car and also estimate Blood Alcohol Content for several scenarios.
1
2
Section A: Purchasing a new car.
Choose a new car to buy and record the details below. (Price cannot exceed $30 000)
(……/7)
Make: Suzuki
Model: Swift GLX Turbo
Engine Size: 998 cc
Tare/Kerb Weight: 945 kg
Fuel Consumption (City): 7.1L / 100km
Fuel Consumption (Highway): 3.1L / 100km
(If combined fuel consumption add 2 for City and subtract 2 for Highway)
Price: $ 22,990
A deposit of 15% will be paid on the new car and the balance financed with the Newcastle Permanent personal car
loan at 8.41%p.a flat interest.
Personal Loans
Comparison
Rate (12/11/19)
Secured Loan
8.41% p.a.
Calculate your monthly repayment
showing all working.
on your car loan,
Deposit (15%): 15% x 22,990 = 3,448.50
For example: You have already saved $2 000.
(..…/2)
Principal (Loan Amount):
Principal = Car market Value - Deposit
22,990 – 3,448.50 = 19,541.50
(..…/1)
Length of Loan (years): 3 Years
Choose between 2 to 5 years
Interest on the loan: (Use the formula 𝐼 = 𝑃𝑟𝑛)
(P = principal, r = rate of interest, n = number of years)
19,541.50 x 8.41% x 3 = $4,930.32
(..…/2)
Total to be repaid:
19,541.50 + 4,930.32 = $24,471.82
Amount Repaid = Interest + Principal
Monthly Repayment:
Monthly repayment = Amount repaid ÷ number of months
24,471.82 / 36 = $679.77
(..…/1)
(..…/2)
Section A
3
Total ......../15
Section B: Other costs of buying a new car.
Registration.
All vehicles attract a registration fee of $67 and light vehicles up to 4.5 tonnes Gross Vehicle Mass (GVM) attract
vehicle tax based on the tare (unladen) weight of the vehicle.
ServiceNSW website: 13/11/2019
Cost of registration: $67 + $215 = $ 282
(..…/1)
Number Plates
General issue number plates (Yellow) are $44 choose to customise your number plates by going to
http://www.myplates.com.au/index.html
Cost of Number plates: $344
(..…/1)
Special Plates Annual Fee (If Applicable): $109
4
Stamp Duty
Stamp duty is collected by Roads and Maritime Services on behalf of the Office of State Revenue when registration
is issued to a different person or corporation. Stamp duty is based on the market value of the vehicle or the price
you paid, whichever is greater.
Stamp duty is calculated at:
• 3% of the market value up to $45,000
• $1350 plus 5% of the vehicle’s value over $45,000.
Calculate your stamp duty below showing all working:
Stamp Duty: 3% x $22,990 = $689.70
(..…/2)
Dealer Delivery Charge
Delivery Charges is a cost designed to cover the incidentals of getting the car prepared for delivery to the customer
i.e. cleaning, petrol.
Most dealers quote from $1495 to $1695 but some try to charge up to $3000.
If the delivery charge is unknown choose a delivery charge within the range mentioned above.
Cost of delivery charge: $1,595
(..…/1)
Insurance
5
Define the following car insurances: (www.moneysmart.gov.au – search car insurance)
Compulsory third party:
Third party property:
(Green Slip) If involved in an accident it covers death or injury.
Territories have different ruling.
(.…/8)
Different States and
Covers the any repair costs of property damage your car causes. So policies cover you if
you are in an accident caused by another driver if they are uninsured.
Third party, fire and theft: Limited cover for damage to your own car caused by theft or fire but covers damage to
other people’s property
Comprehensive:
Includes fire, theft and an accident your car is involved. Covers damage to your own car and
other people’s property
Using the websites www.aami.com.au or www.nrma.com.au or any other Insurance provider, obtain a quote for
your Compulsory Third Party Insurance (CTP) and Comprehensive Car Insurance. (Must be your age 17 or 18).
YOU MUST INCLUDE A HARD COPY OF THE INSURANCE QUOTES.
Name of Insurer of Compulsory Third Party Insurance:
Cost of Annual Insurance:
AAMI
$ 285.80
(..…/1)
Name of Insurer of Comprehensive Car Insurance Company:
Cost of Annual Insurance:
(..…/2)
$ 1,583.34
AAMI
(..…/1)
6
Calculating Total Initial Costs for Purchasing Your New Car.
Complete the table below recording all initial costs.
(....../2)
Deposit
$ 3,448.50
First Monthly Payment
$ 679.77
Registration
$ 282.00
Number Plates (inc. Annual fee)
$ 453.00
Stamp Duty
$ 689.70
Delivery Charge
$ 1,595
Compulsory Third Party Insurance
$ 285.80
Comprehensive Car Insurance
$ 1,583.34
Calculate Total Initial Costs: $9,017.11
(..../2)
Section B
Total ......../17
7
Section C: Car Depreciation.
Unless you pick a vintage car you are burning money as soon as you drive your new wheels out of the dealer’s yard.
Your car has become a second hand model, and you’ve already lost the dealer delivery charges and registration
costs.
Depending on their size, cars depreciate on average by around 14% a year for the first three years, and about 7%
after that.
Note: These figures were obtained from Choice Magazine website in 2016.
http://www.choice.com.au/reviews-and-tests/transport/cars/buying/car-depreciation.aspx
Complete the depreciation table below using the depreciation rates quoted for the next 5 years for your new car.
(1 mark for each correct row)
(…../6)
Year
Value at Beginning Of Year
1
$ 22,990
2
Depreciation for the Year
Value at the end of the Year
$ 3.218.60
(14%)
$ 19,771.40
$ 19,771.40
$ 2,768
(14%)
$ 17,003.40
3
$ 17,003.40
$ 2,380.48
(14%)
$ 14,622.92
4
$ 14,622.92
$ 1,023.60
(7%)
$ 13,599.32
5
$ 13,599.32
$ 951.95
(7%)
$ 12,647.37
$ 10,342.63
(56%)
Total Depreciation
8
Using your table to graph the salvage value against the age in years.
Continue the graph to 8 years
6 Years
$12,647.37 x 93% = $11,762.05
7 Years
$11,762.05 x 93% = $10,938.71
8 Years
$10,938.71 x 93% = $10,173.00
(…../3)
(…../3)
Section C
Year
Start
1
2
3
4
5
6
7
8
Price
22,990.00
19,771.40
17,003.40
14,622.92
13,592.32
12,647.37
11,762.05
10,938.71
10,173.00
Total ......../12
9
Section D: Running Costs
The running costs covered here are fuel costs, which depend on the price of fuel and the
fuel consumption. A motor vehicle’s fuel consumption is the number of litres of fuel it
uses to travel 100 kilometres.
The cost of fuel for a journey can be calculated from the price of fuel ($/L) multiplied by
the amount of fuel used (L). Fuel prices can be found in your local area from websites
such as the one shown below.
State which type of petrol your chosen car uses (e.g. ULP, diesel) Premium Unleaded (E10)
(…../1)
Find the price of your chosen petrol from three different local petrol stations.
Petrol Station: BP Wallsend –
Price: 159.9
103 Newcastle Road, Wallsend 2287
Petrol Station: 7-11 Lambton -
Price: 154.9
24 Croudace Road, Lambton 2299
Petrol Station: Caltex Elermore Vale -
Price: 157.9
(…../1)
52 Cardiff Road, Elermore Vale 2287
Find the average price of petrol from the three different petrol stations
(…../1)
157.4
Write below your car’s fuel consumption that you recorded on page 2.
City: 7.1 L / 100 km
Highway:
10
3.1 L / 100 km
Answer the following questions using the information written on the previous page and show all working.
1
(a) How many litres of petrol will your car use on a trip of 155 km from Newcastle to Sydney on the
highway?
(…../2)
3.1L/100km
3.1/100 = 0.031
0.031 x 155 = 4.805
= 4.805
(b) How much will the petrol cost for the trip from Newcastle to Sydney using the daily average fuel price?
(…../2)
157.4 x 4.805 = $7.56
2
The approximate distance from Jesmond to Newcastle is 9 kilometres.
(a) How many litres of petrol will your car use travelling to and from Newcastle five days a week?
(…../2)
7.1L/100km
7.1/100 = 0.071
0.071 x 90 = 6.39
= 6.39
(b) How much will the petrol cost for the five days return journey?
(…../2)
157.4 x 6.39 = $ 10.06
3
If in one year you travelled 8000 km per year in the city and 10 000 km per year in the country. The average
cost of petrol is $1.48 per litre in the city and 10 cents higher in the country.
(a) Determine the cost of petrol to drive in the city for the year.
$1.48
8000km
7.1 x 80 = 568
(…../2)
7.1L/100km
568 x $1.48 = $840.64
$840.64
(b) Determine the cost of petrol to drive in the country for the year.
$1.58
10 000km
3.1 x 100 = 310
(…../2)
3.1L/100km
310 x $1.58 = $489.80
$489.80
(c) What is the total cost of petrol for one year?
(…../1)
$840.64 + $489.80 = $1,330.44
Section D
Total ......../16
11
Section E: Safety
1.
S=
D
T
D = ST
D
S
T = time taken
S= average speed
D = distance travelled
b) Exercise: Calculate the average speed when
154km is travelled in 2h 30 min.
(…../2)
(note 2h 30 min = 2.5h)
T=
a) Example: Calculate the average speed when
185km is travelled in 4h.
Solution:
Solution:
D
T
185
=
4
= 46.25 km/h
S = D/T
= 154 / 2.5
= 61.6
S=
c) Example: Find the time taken to travel 435km at
an average speed of 115km/h.
Write your answer in hours and minutes.
d) Exercise: Find the time taken to travel 36m at
an average speed of 16m/h.
(…../2)
Write your answer in hours and minutes.
Solution:
Solution:
T = D/S
= 36 / 16
= 2.25 h
= 2h 15min
D
T=
S
460
T=
115
= 3.75 h
= 3h 45 min
e) Example: Find the distance travelled at 45km/h
for 3h and 20 minutes.
f) Exercise: Find the distance travelled at 81km/h
for 1h and 40 minutes.
(…../2)
Solution:
Solution:
D = ST
D =SxT
= 81 x 1 40/60
= 135km
20
= 45 × 3
60
= 150km
Note: You can also use the degrees/minutes/seconds button on your calculator
12
2.The reaction-time distance is the distance travelled in the time it takes the driver to react to a situation; that
is, to realise there is a problem and move their foot to the brake. The usual reaction time, for drivers
unaffected by alcohol, drugs or fatigue has been found to be about 2.5 s.


A driver affected by fatigue has a reaction time of 3.5 s.
A driver affected by alcohol has a reaction time of 4.5 s.
a) Example: Calculate the reaction-time distance for
a car travelling at 60 km/h. Assume a reaction time of
2.5 s.
b) Exercise: Calculate the reaction-time distance
for a car travelling at 80 km/h. Assume a reaction
time of 2.5 s.
(…../4)
Solution:
Firstly convert 60km/h to m/s
60×1000
60km/h = 60×60 m/s
2
= 16 m/s
3
Solution:
80×1000
80km/h = 60×60 m/s
= 22.22 m/s
Reaction-time distance 𝐷 = 𝑆𝑇
2
= 16 × 2.5
3
= 41.7 …
Therefore, the distance the car will travel before the
driver applies the brakes in reaction to a situation is
about 42 m.
D=SxT
= 22.22 x 2.5
= 55.56
Therefore, the distance the car will travel before
the driver applies the brakes in reaction to a
situation is about 55.56 m.
The braking distance is the distance the car travels after the brakes have been applied. This distance
depends on (the square of) the speed of the car.
For a car with good brakes and tyres, travelling in dry conditions on a good road, the relationship can be
approximated by the formula
𝑑 = 0.01𝑣 2,
where d is the braking distance in metres and v is the speed of the car in km/h.
For the same car travelling on a slippery road, the formula for braking distance becomes 𝑑 = 0.014𝑣 2
c) Example Calculate the braking distance for a car
travelling in
i)
dry conditions at 60 km/h.
ii)
slippery conditions at 60km/h.
d) Exercise: Calculate the braking distance for a
car travelling in
i)
dry conditions at 80 km/h.
(…../2)
ii)
slippery conditions at 80km/h. (…../2)
Solution:
Solution:
i)
𝑑 = 0.01𝑣 2
= 0.01 × 602
= 36m
ii)
𝑑 = 0.014𝑣 2
= 0.014 × 60
= 50.4m
i) D = 0.01v2
= 0.01 x 802
= 64m
ii) D = 0.014v2
= 0.014 x 802
= 89.6m
2
Section E
Total ......../14
13
Section F: Blood Alcohol Content
1. Research to find answers for the following
(…../2)
a) Write a definition for BAC.
(…../2)
b) How is BAC measured?
_______________________________________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
c)
(…../3)
List 6 factors that influence BAC.

____________________________

____________________________

____________________________

____________________________

____________________________

____________________________
14
2.
Jessica has a BAC of 0.075 and burns off alcohol at the rate of 0.015 per hour, the following table
shows her BAC decline over 5 hours.
Time
(hours)
BAC
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0.075
0.0675
0.06
0.0525
0.045
0.0375
0.03
0.0225
0.015
0.0075
0
Use the information provided in the table to graph Jessica’s BAC over time.
(…../3)
Time (hours)
i)
Jessica is on her P Plates and must wait til her BAC is Zero before driving – from the graph how
long does it take for her BAC to be zero?
_______________________________________________________________________________
___________________________________________________________________________(…../1)
15
ii)
Phillipa is at the same party and her body absorbs alcohol at the same rate, and is also on her P
Plates.
If her BAC is 0.09, can she legally drive at 6am after finishing drinking at 3am?
(Justify with suitable Mathematical Calculations)
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
__________________________________________________________________________(…../3)
Section F
Total ......../14
16
Marking Criteria
A
88-70
B
69-53
C
52-33
D
32-15
E
14-0
The student demonstrates extensive knowledge of content and understanding of course
concepts, and applies highly developed skills and processes in a wide variety of contexts. In
addition the student demonstrates creative and critical thinking skills using perceptive
analysis and evaluation. The student effectively communicates complex ideas and
information.
The student demonstrates thorough knowledge of content and understanding of course
concepts, and applies well-developed skills and processes in a variety of contexts. In
addition the student demonstrates creative and critical thinking skills using analysis and
evaluation. The student clearly communicates complex ideas and information.
The student demonstrates sound knowledge of content and understanding of course
concepts, and applies skills and processes in a range of familiar contexts. In addition the
student demonstrates skills in selecting and integrating information and communicates
relevant ideas in appropriate manner.
The student demonstrates basic knowledge of content and understanding of course concepts,
and applies skills and processes in some familiar contexts. In addition the student
demonstrates skills in selecting and using information and communicates ideas in a
descriptive manner.
The student demonstrates an elementary knowledge of content and understanding of course
concepts, and applies some skills and processes with guidance. In addition the student
demonstrates elementary skills in recounting information and communicating ideas.
*****Please note full marks will not be awarded if no appropriate working has been shown.
17