Embed Size (px)
Citation preview
WORKSHEET General 2 MathematicsTopic Areas:FOCUS STUDIES
Mathematics and Driving Costs to Purchase / Insurance Depreciation / Running costs Safety: D=ST & BAC
Teacher: PETER HARGRAVESSource: HSC exam questionsExam Equivalent Time: 58.5 minutesWorked Solutions: IncludedNote: Each question has designated marks. Use this information as both a guide to the question's difficultyand as a timing indicator, whereby each mark should equate to 1.5 minutes of working (examination) time.
Questions
1. FS Driving, 2UG 2014 HSC 9 MC
A car is bought for . It will depreciate at per annum.
Using the declining balance method, what will be the salvage value of the car after years, tothe nearest dollar?
(A)
(B)
(C)
(D)
$19 990 18%
3
$8968
$9195
$11 022
$16 392
2. FS Driving, 2012 HSC 16 MC
A machine was bought for .
Which graph best represents the salvage value of the machine over years using thedeclining balance method of depreciation?
3. FS Driving, 2012 HSC 15 MC
The time taken to complete a journey varies inversely with the speed of a car. A car takes hours to complete a journey when travelling at .
How long would the same journey take if the car were travelling at ?
(A)
(B)
(C)
(D)
$25000
10
6 60 km/h
100 km/h
36 minutes
1 hour and 40 minutes
3 hours and 6 minutes
3 hours and 36 minutes
4. FS Driving, 2010 HSC 11 MC
Which of the following graphs shows the lowest rate of depreciation over the given timeperiod?
5. FS Driving, HSC supplement MC
The blood alcohol content ( ) of a male's blood is given by the formula;
, where
is the number of standard drinks consumed,
is the number of hours drinking and
is the person's mass in kgs.
Calculate the of a male who consumed standard drinks in hours and weighs , correct to 2 decimal places.
(A)
(B)
(C)
(D)
BAC
BA =Cmale10N − 7.5H
6.8M
N
H
M
BAC 4 3.568kgs
1.03
0.03
0.04
0.01
6. FS Driving, 2UG 2014 HSC 22 MC
Heather’s car uses fuel at the rate of for longdistance driving and for shortdistance driving.
She used the car to make a journey of , which included of shortdistance driving.
Approximately how much fuel did Heather’s car use on the journey?
(A)
(B)
(C)
(D)
7. FS Driving, 2011 HSC 21 MC
A train departs from Town at 3.00 pm to travel to Town . Its average speed for thejourney is , and it arrives at 5.00 pm. A second train departs from Town at3.10 pm and arrives at Town at 4.30 pm.
What is the average speed of the second train?
(A)
(B)
(C)
(D)
6.6 L per 100 km8.9 L per 100 km
560 km 65 km
37 L
38 L
48 L
50 L
A B90 km/h A
B
135 km/h
150 km/h
216 km/h
240 km/h
Alex wishes to take out comprehensive insurance for the car for months. Thecost of comprehensive insurance is calculated using the following:
Stamp Duty for this car is calculated at for every , or part thereof, of thesale price.
Calculate the Stamp Duty payable. (1 mark)
Alex borrows the total amount to be paid for the car including Stamp Duty andtransfer of registration. Interest on the loan is charged at a flat rate of perannum. The loan is to be repaid in equal monthly instalments over years.
Calculate Alex’s monthly repayments. (4 marks)
Find the total amount that Alex will need to pay for comprehensive insurance. (3marks)
Alex has decided he will take out the comprehensive car insurance rather than theless expensive noncompulsory thirdparty car insurance.
What extra cover is provided by the comprehensive car insurance? (1 mark)
8. FS Driving, 2UG 2014 HSC 27a
Alex is buying a used car which has a sale price of . In addition to the sale price thereare the following costs:
(i)
(ii)
(iii)
(iv)
9. FS Driving, 2012 HSC 26b
Jim buys a photocopier for .
Its value is depreciated using the declining balance method at the rate of per annum.
What is its value at the end of years? (2 marks)
$13 380
$3 $100
7.5%3
12
$22 000
15%
3
10. FS Driving, 2013 HSC 28e
Zheng has purchased a computer for for his company. He wants to compare twodifferent methods of depreciation over two years for the computer.
Method 1: Straightline with depreciation per annum.
Method 2: Declining balance with depreciation per annum.
Which method gives the greatest depreciation over the two years? Justify your answer withsuitable calculations. (3 marks)
11. FS Driving, 2UG 2008 HSC 27c
A plasma TV depreciated in value by per annum. Two years after it was purchased it haddepreciated to a value of , using the declining balance method.
What was the purchase price of the plasma TV? (2 marks)
12. FS Driving, 2UG 2014 HSC 27b
Xuso is comparing the costs of two different ways of travelling to university.
Xuso’s motorcycle uses one litre of fuel for every travelled. The cost of fuel is and the distance from her home to the university car park is . The cost of
travelling by bus is for single trips.
Which way of travelling is cheaper and by how much? Support your answer with calculations. (2 marks)
13. FS Driving, 2UG 2014 HSC 29b
What is the maximum number of standard drinks that a male weighing can consumeover hours in order to maintain a blood alcohol content (BAC) of less than ? (3 marks)
$5000
$1250
35%
15%$2023
17 km$1.67/L 34 km
$36.40 10
84 kg4 0.05
Find the gradient of the line shown in the graph. (1 mark)
What does the value of the gradient represent in this situation? (1 mark)
Write down the equation of the line shown in the graph. (1 mark)
Find all the values of that are not suitable for Norman to use when calculating thesalvage value of his tractor. Explain why these values are not suitable. (2 marks)
Pat used the declining balance formula for calculating the salvage value of hertractor. The depreciation rate that she used was per annum.
What did Pat calculate the salvage value of her tractor to be after years? (2marks)Using Pat’s method for depreciation, describe what happens to the salvage value ofher tractor for all values of greater than . (1 mark)
14. FS Driving, 2011 HSC 28b
Norman and Pat each bought the same type of tractor for at the same time. Thevalue of their tractors depreciated over time.
The salvage value , in dollars, of each tractor, is its depreciated value after years.
Norman drew a graph to represent the salvage value of his tractor.
(i)
(ii)
(iii)
(iv)
(v)
(vi)
$60 000
S n
n
20%
14
n 15
Find the amount that the computer would depreciate each year to be worth nothingafter years, if the straight line method of depreciation is used. (1 mark)Explain why the computer would never be worth nothing if the declining balancemethod of depreciation is used, with per annum rate of depreciation. Usesuitable calculations to support your answer. (2 marks)
15. FS Driving, 2009 HSC 24e
Jay bought a computer for . His friend Julie said that all computers are worth nothing(i.e. the value is ) after years.
(i)
(ii)
Copyright © 200914 The State of New South Wales (Board of Studies, Teaching and Educational Standards NSW)
$3600$0 3
3
30%
Worked Solutions
1. FS Driving, 2UG 2014 HSC 9 MC
2. FS Driving, 2012 HSC 16 MC
3. FS Driving, 2012 HSC 15 MC
S = V0(1 − r)n
= 19 990(1 − )18100
3
= 19 990(0.82)3
= $11 021.85⇒ C
B and D represent straight line depreciation
C incorrectly has no salvage value after 10 years
⇒ A
T =D
S
Since T = 6 when S = 60
6 =D
60D = 360 km
Need to find T when S = 100 and D = 360
T =360100
= 3.6 hours
= 3 hrs 36 minutes⇒ D
4. FS Driving, 2010 HSC 11 MC
5. FS Driving, HSC supplement MC
6. FS Driving, 2UG 2014 HSC 22 MC
The lowest rate of depreciation will occur when
an item retains value for the longest time.
⇒ D
BACmale =(10 × 4) − (7.5 × 3.5)
(6.8 × 68)
=13.75462.4
= 0.0297...⇒ B
Fuel used in short distance
= × 8.9 L = 5.785 L65100
Fuel used in long distance
= × 6.6 L = 32.67 L495100
Total Fuel = 5.785 + 32.67
= 38.455 L⇒ B
♦ Mean mark 49%
♦♦♦ Mean mark 12%IMPORTANT: "or part thereof .."in the question requiresstudents to round up to 134 toget the right multiple of $3 fortheir calculation.
7. FS Driving, 2011 HSC 21 MC
8. FS Driving, 2UG 2014 HSC 27a
(i)
(ii)
1st train
Travels 2hrs at 90km/h
Distance = Speed × Time
= 90 × 2
= 180 km2nd train
Travels 180 km in 1hr 20min ( hrs)43
Speed =Distance
Time
= 180 ÷43
= 180 ×34
= 135 km/h⇒ A
= 133.8$13 380
100∴ Stamp duty = 134 × $3
= $402
Total loan = $13 380 + 30 + 402
= $13 812
Total interest (I) = Prn
= 13 812 × × 37.5100
= 3107.70
Total to repay = 3107.70 + 13 812
= 16 919.70
# Repayments = 3 × 12 = 36
16 919.70
♦ Mean mark 34%.
(iii)
(iv)
9. FS Driving, 2012 HSC 26b
∴ Monthly repayment =16 919.70
36= 469.9916...
= $470 (nearest dollar)
Base rate = $845FSL = 1 % × 845 = $8.45
Stamp = 5.5 % (845 + 8.45)
= 46.9397...
= $46.94 (nearest cent)
GST = 10 % (845 + 8.45)
= 85.345
= $85.35
∴ Total cost = 845 + 8.45 + 46.94 + 85.35
= $985.74
Comprehensive insurance covers Alex
for damage done to his own car as well.
S = V0(1 − r)n
= 22 000(1 − 0.15)3
= 22 000(0.85)3
= 13 510.75∴ After 3 years, it is worth $13 510.75
10. FS Driving, 2013 HSC 28e
11. FS Driving, 2UG 2008 HSC 27c
Depreciation over 2 years = 2 × 1250
= $2500
Method 2
Depreciation (Year 1) = 35 % × 5000
= $1750
Depreciation (Year 2) = 35 % × (5000 −1750)
= $1137.50
⇒ Depreciation over 2 years = 1750 + 1137.50
= $2887.50
∴ Method 2 gives the greater depreciation.
S = V0(1 − r)n
⇒ 2023 = V0(1 − 0.15)2
2023 = V0(0.85)2
V0 =2023
0.852
= 2800∴ The purchase price = $2800
12. FS Driving, 2UG 2014 HSC 27b
13. FS Driving, 2UG 2014 HSC 29b
Compare cost of a 1-way trip
Motorcycle
Fuel used = = 2 L3417
Cost = 2 × $1.67 = $3.34
Bus
Cost = = $3.6436.40
10Difference = $3.64 − 3.34 = $0.30
∴ Motorcycle is $0.30 cheaper
per 1-way trip
=BACmale10N − 7.5H
6.8M
Find N for BAC < 0.05
given H = 4 and M = 84
⇒10N − 7.5(4)
6.8(84)< 0.05
10N − 30 < 0.05(571.2)
10N < 28.56 + 30
< 58.56
N < 5.856
∴ Max number of drinks is 5.
♦♦♦ Mean mark 14%COMMENT: The intercepts ofboth axes provide points wherethe gradient can be quicklyfound.
♦ Mean mark 37%
♦♦ Mean mark 28%COMMENT: Using the generalform is quick herebecause you have the gradient(from part (i)) and the interceptis obviously .
♦♦♦ Mean mark 20%
♦♦♦ Mean mark 37%
14. FS Driving, 2011 HSC 28b
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Gradient =riserun
=−60 000
15= − 4000
The amount the tractor depreciates each year
y = mx + b
y60 000
We know S = − DnV0
∴ Equation is
S = 60 000 − 4000n
It is unsuitable to use
n < 0 because time must be positive
n > 15 because it has no more value after 15
years and therefore can't depreciate further.
Using S = where r = 20%, n = 14V0(1 − r)n
S = 60 000(1 − 0.2)14
= 60 000(0.8)14
= 2 638.8279...∴ After 14 years, the tractor is worth $2638.83
As n increases above 15 years, S decreases
but remains > 0.
♦ Mean mark 45%
15. FS Driving, 2009 HSC 24e
(i)
(ii)
Copyright © 2015 M2 Mathematics Pty Ltd (SmarterMaths.com.au)
S = − DnV0
0 = 3600 − D × 3
3D = 3600
D =3600
3= 1200
∴ Annual depreciation = $1200
Using S = V0(1 − r)n
where r = 30% and = 3600V0
S = 3600(1 − )30100
n
= 3600(0.7)n
Since > 0 for all n(0.7)n
⇒ Salvage value is always > 0
