Financial Mathematics
A real estate agent sells a house for $400 000. From the selling price he earns $10 000
for his services.
Which term is used to describe the money he earns?
(A) Commission
(B) Income tax
(C) Royalty
(D) Superannuation
Commission
⇒A
A high school has 100 students in each year group, Year 7 to Year 12. A survey is to be conducted to determine the average number of text messages sent per month by students at the school.
Which of the following would provide the most representative sample for this survey?
(A) All Year 7 students
(B) All physics students in Year 11 and 12
(C) 20 students chosen at random from each year group
(D) 120 students chosen at random from the school roll
The best sample would have an equal amount
of people in each year randomly selected.
⇒ C
Perth in Western Australia is 8 hours ahead of Coordinated Universal Time (UTC). Cape Town in South Africa is 2 hours ahead of UTC.
What is the time in Cape Town when it is 1 pm in Perth?
(A) 3 am
(B) 7 am
(C) 7 pm
(D) 11 pm
Perth is 6 hrs ahead of Cape Town
∴ 1pm in Perth = 7 am in Cape Town
⇒B
Kate is comparing two different models of car. Car A uses fuel at the rate of 9 L/100 km. Car B uses 3.5 L/100 km.
Suppose Kate plans on driving 8000 km in the next year.
How much less fuel will she use driving car B instead of car A?
A. 280 L
B. 440 L
C. 720 L
D. 1000 L
Fuel used by car A
=8000100×9
=720 L
Fuel used by car B
=8000100×3.5
=280 L
∴ Fuel saved using car B
=720–280
=440 L
⇒ B
The heights of Year 12 girls are normally distributed with a mean of 165 cm and a standard deviation of 5.5 cm.
What is the z-score for a height of 154 cm?
A. −2
B. −0.5
C. 0.5
D. 2
z-score=x–μσ =154–165 5.5 =−2
⇒A
Tom earns a weekly wage of $1025. He also receives an additional allowance of $87.50 per day when handling toxic substances.
What is Tom’s income in a fortnight in which he handles toxic substances on 5 separate days?
A. $1112.50
B. $1462.50
C. $2225.00
D. $2487.50
Fortnightly wage=2×1025 =$2050Allowances=5×87.50 =$437.50
∴ Income=2050+437.50 =$2487.50
⇒D
On a school report, a student’s record of completing homework is graded using the following codes.
C = consistently
U = usually
S = sometimes
R = rarely
N = never
What type of data is this?
(A) Categorical, ordinal
(B) Categorical, nominal
(C) Numerical, continuous
(D) Numerical, discrete
The data has been grouped into categories and
because each category can be ranked, it is ordinal.
⇒A
Kim lives in Perth. He wants to watch an ice hockey game being played in Toronto starting at 10.00 pm on Wednesday.
Toronto is 13 hours behind Perth.
What is the time in Perth when the game starts?
(A) 9.00 am on Wednesday
(B) 7.40 pm on Wednesday
(C) 12.20 am on Thursday
(D) 11.00 am on Thursday
∴ Time in Perth
= 10 pm (Wed) + 13 hours
= 11 am on Thursday
⇒ D
The driving distance from Alex's home to his work is 20 km. He drives to and from work five times each week. His car uses fuel at the rate of 8 L/100 km.
How much fuel does he use driving to and from work each week?
Total distance travelled each week
=5×2×20
=200 km
∴ Total fuel used
=200100×8 L
=16 L
⇒ A
The weights of 10 000 newborn babies in NSW are normally distributed. These weights have a mean of 3.1 kg and a standard deviation of 0.35 kg.
How many of these newborn babies have a weight between 2.75 kg and 4.15 kg?
(A) 4985
(B) 6570
(C) 8370
(D) 8385
Find z-scores of 2.75 and 4.15 kg
z (2.75)=x–μ5=2.75–3.10.35=−1z (4.15)=4.15–3.10.35=3
68% between z=–1 and 1
⇒34% between z=–1 and 0
99.7% between z=–3 and 3
⇒49.85% between z=0 and 3
∴% with z-scores between –1 and 3
=34+49.85
= 83.85%
∴ # Babies between 2.75 kg and 4.15 kg
=83.85%×10 000
=8385
⇒ D
Polly borrowed $11 000. She repaid the loan in full at the end of two years with a lump sum of $12 000.
What annual simple interest rate was she charged?
(A) 4.17%
(B) 4.55%
(C) 8.33%
(D) 9.09%
Total interest paid=12 000−11 000=$1000
I=Prn1000=11000×r×2r=1000/22 000 =4.55%
⇒ B
The July sales prices for properties in a suburb were:
$552 000, $595 000, $607 000, $607 000, $682 000, and $685 000.
On 1 August, another property in the same suburb was sold for over one million dollars.
If the property had been sold in July, what effect would it have had on the mean and median sale prices for July?
(A) Both the mean and median would have changed.
(B) Neither the mean nor the median would have changed.
(C) The mean would have changed and the median would have stayed the same.
(D) The mean would have stayed the same and the median would have changed.
Mean increases because new house is sold above
the existing average.
Initial median=607 000+607 0002=607 000
New median=607 000 (4th value in a list of 7)
⇒ C
The Coordinated Universal Time (UTC) of Auckland is +12 hours and the UTC of Chicago is −5 hours.
When the time in Chicago is 2 pm, Thursday, what is the time in Auckland?
Auckland is 17 hours ahead of Chicago.
2 pm Thursday + 17 hours
= 2 am Friday + 5 hours
= 7 am Friday
⇒D
Peta’s car uses fuel at the rate of 5.9 L /100 km for country driving and 7.3 L /100 km for city driving. On a trip, she drives 170 km in the country and 25 km in the city.
Calculate the amount of fuel she used on this trip.
Fuel used in country
=170×5.9100
=10.03 L
Fuel used in city
=25×7.3100
=1.825 L
∴ Total fuel used
=10.03+1.825
=11.855 L
A patient is to receive 1.8 L of pain killer medication by intravenous drip that will take 1.5 hours to administer.
Given 1 mL = 4 drops, calculate the amount of drops per minute the machine must be set on.
Total drops required=1800×4 =7200 dropsTime (in minutes)=1.5×60 =90 minutesDrops per minute=720090 =80
∴ The machine must be set to 80 drops per minute.
Zina opened an account to save for a new car. Six months after opening the account, she made first deposit of $1200 and continued depositing $1200 at the end of each six month period. Interest was paid at 3% per annum, compounded half-yearly.
How much was in Zina's account two years after first opening it?
Interest: 3% p.a ⇒ 1.5% per 6 months
After 2 years,
Value of 1st deposit=1200(1.015)3=1254.81
Value of 2nd deposit=1200(1.015)2=1236.27
Value of 3rd deposit=1200(1.015)=1218
Value of 4th deposit=1200
∴ Amount in account after 2 years
=1254.81+1236.27+1218+1200
=$4909.08
⇒A
The mean of a set of ten scores is 14. Another two scores are included and the new mean is 16.
What is the mean of the two additional scores?
(A) 4
(B) 16
(C) 18
(D) 26
If x⎯⎯ of 10 scores = 14
⇒Sum of 10 scores=10×14=140
With 2 additional scores, x⎯⎯=16
⇒Sum of 12 scores=12×16=192
∴ Value of 2 extra scores=192 –140 =52
∴ Mean of 2 extra scores=522=26
⇒ D
Cassie flew from London to Manila. Manila is 8 hours ahead of London.
Her plane left London at 9.30 am Monday (London time), stopped for 5 hours in Singapore and arrived in Manila at 4.00 pm Tuesday (Manila time).
What was the total flying time? (Ignore time zones.)
∴ Flight time= 9:30 (Mon) to 4:00 pm (Tues) − (stopover + time difference) =14.5+16–(5+8) =17.5 hours
The weight of a bundle of A4 paper (W kg) varies directly with the number of sheets (N) of A4 paper that the bundle contains.
This relationship is modelled by the formula W=kN, where k is a constant.
The weight of a bundle containing 500 sheets of A4 paper is 2.5 kilograms.
a. W=2.5 kg when N=500:
2.5=k×500∴ k=2.5500 =0.005
b. Find N when W=1.2 kg:
1.2=0.005×N∴N=1.20.005 =240 sheets
Every day, a 1200-watt microwave oven is used for 45 minutes at 40% power. Electricity is charged at $0.25 per kWh.
What is the cost of running this microwave oven for 180 days?
Daily usage=1200×4560×40% =360 watts
180 day usage=180×360 =64 800 watts =64.8 kW
∴ Cost over 180 days=64.8×0.25 =$16.20
Sam is the driver at fault in a car accident.
Which of the following is covered by Sam's compulsory third-party (CTP) insurance?
CTP insurance covers liability for death or injury
to other people, but does not cover property damage.
⇒B
Which of the following relationships would most likely show a negative correlation?
(A) The population of a town and the number of hospitals in that town.
(B) The hours spent training for a race and the time taken to complete the race.
(C) The price per litre of petrol and the number of people riding bicycles to work.
(D) The number of pets per household and the number of computers per household.
Increased hours training should reduce the
time to complete a race.
⇒ B
Bert is in Moscow, which is three hours behind of Coordinated Universal Time (UTC).
Karen is in Sydney, which is eleven hours ahead of UTC.
a. Bert is 14 hours behind Karen.
At 9 pm in Moscow:
Time in Sydney=9 pm + 14 hours =11 am Wednesday
b. Arrival time=8 am + 15 hours =11 pm Wednesday (Sydney time)
∴ Time in Moscow=11 pm less 14 hours =9 am Wednesday
The number of hours that it takes for a block of ice to melt varies inversely with the temperature. At 30°C it takes 8 hours for a block of ice to melt.
How long will it take the same size block of ice to melt at 12°C?
Time to melt (T)∝1Temp ⇒ T=kTemp
When T=8,Temp = 30
8=k30k=240
When Temp = 12:
T=24012 =20 hours
⇒ B
A scalene triangle has angles in the ratio 9 : 2 : 4.
In degrees, what is the size of its largest angle?
108°