General Mathematics
Unit 3 Examination
Student name:
Unit 3 Examination (69 marks)
Question 1 (2 marks) SF
Describe the associations shown in the scatterplots below in terms of direction and strength.
a.
b.
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General Mathematics
Unit 3 Examination
Question 2 (2 marks) SF
Suppose the variance of X is 1.7, the variance of Y is 8.8, and the covariance of X and Y is 1.7.
Find the value of r, the correlation between X and Y.
Question 3 (4 marks) SF
55 students were interviewed about what sport they played at their school. Of the 22 Year 11 students interviewed,
10 played soccer, while 12 Year 12 students played AFL. 21 students played neither sport, with 9 of those being
from year 11.
Complete the two-way frequency table below, using year levels as the explanatory variable.
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General Mathematics
Unit 3 Examination
Question 4 (4 marks) SF
A town has its highest temperature in February measured every year.
Year
2013
2014
2015
2016
2017
2018
2019
2020
Temperature (C )
30.3
31.0
35.7
36.7
36.2
36.5
39.7
40.5
a. Construct a time series plot to display this data using the table above.
b. Describe the trend of the time series.
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General Mathematics
Unit 3 Examination
Question 5 (6 marks) SF
The value of the Australian dollars in Great British Pounds (exchange rate) over 6 days is given below.
Day
1
2
3
4
5
6
Exchange rate
0.5517
0.5518
0.5518
0.5521
0.5532
0.5506
a. Calculate the three-mean smoothing averages of this data.
b. Plot the three-mean smoothing values on the graph below.
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General Mathematics
Unit 3 Examination
Question 6 (3 marks) SF
$75000 is borrowed at a simple interest rate of 8.6% per annum.
a. Determine the amount of interest charged each year.
b. Write down an expression for the amount owed at the end of nth year.
c. Calculate how much is owed after 5 years.
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General Mathematics
Unit 3 Examination
Question 7 (5 marks) SF
A geometric sequence is described by the recurrence relation t1
4 and tn 1 3tn .
a. Write the rule for the nth term of this sequence.
b. Plot the first five terms of this geometric sequence. Use tn as the y-axis and n as the x-axis.
c. Describe what trend is shown by this graph.
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General Mathematics
Unit 3 Examination
Question 8 (4 marks) SF
The Kenyan capital city of Nairobi has longitude 37 E , while the Queensland city of Rockhampton has longitude
151 E longitude.
a. Calculate the time difference between the two places (ignore time zones and daylight saving).
b. What time is it in Nairobi when it is 9:30 am in Rockhampton? (Ignore time zones and daylight saving.)
Question 9 (3 marks) SF
Port Douglas has latitude 16.48 S and longitude 145.47 E. Find the distance, correct to the nearest kilometre, of
Port Douglas to
a. the equator
b. the south pole
c. the north pole
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General Mathematics
Unit 3 Examination
Question 10 (2 marks) SF , (3 marks) CF
A marketing campaign for a clothing company models its sales (in thousands of dollars) using a linear model:
sales
10
5.5advertising
a. Identify the explanatory and response variables.
b. Interpret the slope and intercept in terms of the variables in the question.
c. If the company invests $3500 into advertising, calculate the sales predicted by the model.
d. The actual sales from the above investment resulted in $22 500. Determine the residual value.
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General Mathematics
Unit 3 Examination
Question 11 (4 marks) SF , (4 marks) CF
Eighty-eight people in a town were surveyed about whether they used a streaming service to listen to music. The
results are displayed in the two-way frequency table below.
Age group
Age 18-45
Age 46-70
Total
Uses a
Yes
28
15
43
streaming service
No
12
33
45
Total
40
48
88
a. Calculate the percentage of people in the Age 18-45 bracket who use a streaming service to listen to music.
b. Of those people who don’t use a streaming service, calculate the percentage of those who are in the 46-70 age
bracket.
c. Determine whether there is an association between age and use of a streaming service. Write a brief report
quoting appropriate percentages.
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General Mathematics
Unit 3 Examination
Question 12 (7 marks) CF
You are offered a job with a starting salary of $30 250 per year, with yearly pay rises of $500.
a. Write down a rule for determining your salary, sn , at the start of each year you work on the job.
b. What would your salary be:
i. at the start of the fourth year on the job?
ii. at the start of the seventh year on the job?
c. At this rate, how many years would you have to be on the job to have a salary of $65 000 per year?
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General Mathematics
Unit 3 Examination
Question 13 (9 marks) CU
The table below shows the quarterly sales of a denim jeans company in 2018, along with three of the quarterly
seasonal indices.
Jeans sales
Quarter 1
Quarter 2
Quarter 3
Quarter 4
2018
1102
1438
3923
2543
Seasonal index
0.49
0.64
1.74
Determine the equation of a least squares line which could be used to model the sales after deseasonalising the
data, and use this to predict sales for first quarter of 2019.
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General Mathematics
Unit 3 Examination
Question 14 (7 marks) CU
Six years ago, a motorcycle was bought for $18 500. Two methods for determining its future value are listed below:
Model A: Flat-rate depreciation at 13% per annum.
Model B: Reducing-balance depreciation at 18% per annum.
On the same axes, sketch a graph of the value of the motorcycle against the number of years for both the flat-rate
and reducing-balance models.
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General Mathematics
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Unit 3 Examination
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General Mathematics
Unit 3 Examination
Examination marks summary
Simple Familiar ( SF )
Complex Familiar ( CF )
1
2
2
2
3
4
4
4
5
6
6
3
7
5
8
4
9
3
10
2
3
11
4
4
12
Complex Unfamiliar ( CU )
7
13
9
14
7
Total
39
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14
16
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