SCSA Mathematics Applications Time series analysis

5 sample questions with marking guides and sample answers · Avg. score: 51.6%

Q6
2024
QCAA
Paper 1
1 mark
Q6
1 mark

The table shows the maximum daily temperature (°C) for a week.

MonTueWedThuFriSatSun
24.425.224.625.225.625.725.9

If the simple 5-point moving average for Wednesday is 25.0 °C, what is the simple 5-point moving average (°C) for Friday?

A

25.4

B

25.5

C

25.6

D

26.0

Q13
2024
QCAA
Paper 1
1 mark
Q13
1 mark

The table shows time series data for a company's quarterly sales.

Quarter1234
Sales ($)2700360045007200
Seasonal index0.60.81.0

Determine the seasonally adjusted sales ($) for the fourth quarter.

A

4500

B

6000

C

8640

D

11 520

Q25
2024
QCAA
Paper 1
5 marks
Q25

The table shows Darwin’s actual rainfall (mm) each season for two years.

 20222023
Autumn410390
Winter3020
Spring205150
Summer11351100
Q25a
3 marks

Calculate the seasonal index for each season in Darwin.

Q25b
2 marks

This table shows Hobart’s actual rainfall (mm) each season for 2023 and the long-term seasonal indices.

 AutumnWinterSpringSummer
2023 rainfall (mm)130145155132
Seasonal index0.921.021.120.94

Deseasonalise the Hobart rainfall data to identify the 2023 season with the highest seasonally adjusted rainfall.

Q2
2023
QCAA
Paper 2
4 marks
Q2
4 marks

Buffalo fly bites cause skin wounds on cattle. The table shows the average number of skin wounds per animal in a herd for two years.

 AutumnWinterSpringSummer
202128528195460
202227622170392

Deseasonalise the data.

Q18
2021
QCAA
Paper 1
4 marks
Q18

The table shows the profit made each year (in thousands of dollars) by a small business.

YearProfit ($'000s)
201542.1
201636.9
201748.4
201852.3
201956.1
202059.8
Q18a
2 marks

Use a mathematical model to determine the equation of the least-squares line to fit this data.

Q18b
2 marks

Use the least-squares line to forecast the profit in 2021, to the nearest hundred dollars.

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000s) |\\n|---|---|\\n| 2015 | 42.1 |\\n| 2016 | 36.9 |\\n| 2017 | 48.4 |\\n| 2018 | 52.3 |\\n| 2019 | 56.1 |\\n| 2020 | 59.8 |\"}],\"parts\":[{\"partLabel\":\"a\",\"questionText\":\"Use a mathematical model to determine the equation of the least-squares line to fit this data.\",\"marks\":2,\"questionType\":\"short_answer\",\"mcOptions\":null,\"rubric\":{\"sampleAnswer\":\"Let $x =$ the number of years since 2014\\nLet $y =$ the business's annual profit (in \\\\

SCSA Mathematics Applications Time series analysis

5 sample questions with marking guides and sample answers · Avg. score: 51.6%

Q6
2024
QCAA
Paper 1
1 mark
Q6
1 mark

The table shows the maximum daily temperature (°C) for a week.

MonTueWedThuFriSatSun
24.425.224.625.225.625.725.9

If the simple 5-point moving average for Wednesday is 25.0 °C, what is the simple 5-point moving average (°C) for Friday?

A

25.4

B

25.5

C

25.6

D

26.0

Q13
2024
QCAA
Paper 1
1 mark
Q13
1 mark

The table shows time series data for a company's quarterly sales.

Quarter1234
Sales ($)2700360045007200
Seasonal index0.60.81.0

Determine the seasonally adjusted sales ($) for the fourth quarter.

A

4500

B

6000

C

8640

D

11 520

Q25
2024
QCAA
Paper 1
5 marks
Q25

The table shows Darwin’s actual rainfall (mm) each season for two years.

 20222023
Autumn410390
Winter3020
Spring205150
Summer11351100
Q25a
3 marks

Calculate the seasonal index for each season in Darwin.

Q25b
2 marks

This table shows Hobart’s actual rainfall (mm) each season for 2023 and the long-term seasonal indices.

 AutumnWinterSpringSummer
2023 rainfall (mm)130145155132
Seasonal index0.921.021.120.94

Deseasonalise the Hobart rainfall data to identify the 2023 season with the highest seasonally adjusted rainfall.

Q2
2023
QCAA
Paper 2
4 marks
Q2
4 marks

Buffalo fly bites cause skin wounds on cattle. The table shows the average number of skin wounds per animal in a herd for two years.

 AutumnWinterSpringSummer
202128528195460
202227622170392

Deseasonalise the data.

Q18
2021
QCAA
Paper 1
4 marks
Q18

The table shows the profit made each year (in thousands of dollars) by a small business.

YearProfit ($'000s)
201542.1
201636.9
201748.4
201852.3
201956.1
202059.8
Q18a
2 marks

Use a mathematical model to determine the equation of the least-squares line to fit this data.

Q18b
2 marks

Use the least-squares line to forecast the profit in 2021, to the nearest hundred dollars.

Frequently Asked Questions

How many SCSA Mathematics Applications questions cover Time series analysis?
AusGrader has 63 SCSA Mathematics Applications questions on Time series analysis, all with instant AI grading and detailed marking feedback.

Ready to practise SCSA Mathematics Applications?

Get instant AI feedback on past exam questions, aligned to the syllabus

Start Practising Free
000s)\\n\\n$y = 4.286x + 34.267$\",\"mcExplanations\":null,\"columns\":[{\"name\":\"Response\",\"isMarkingBands\":false,\"criteria\":[{\"descriptor\":\"correctly defines the variables\",\"marks\":1},{\"descriptor\":\"correctly determines the equation of the least-squares line\",\"marks\":1}]}]}},{\"partLabel\":\"b\",\"questionText\":\"Use the least-squares line to forecast the profit in 2021, to the nearest hundred dollars.\",\"marks\":2,\"questionType\":\"short_answer\",\"mcOptions\":null,\"rubric\":{\"sampleAnswer\":\"For 2021, $x = 7$\\n$\\\\therefore y = 4.286 \\\\times 7 + 34.267$\\n$= 64.269$\\n\\nThe business will make \\\\$64 300.\",\"mcExplanations\":null,\"columns\":[{\"name\":\"Working\",\"isMarkingBands\":false,\"criteria\":[{\"descriptor\":\"correctly determines the $x$ value\",\"marks\":1},{\"descriptor\":\"determines profit\",\"marks\":1}]}]}}]}]}")

SCSA Mathematics Applications Time series analysis

5 sample questions with marking guides and sample answers · Avg. score: 51.6%

Q6
2024
QCAA
Paper 1
1 mark
Q6
1 mark

The table shows the maximum daily temperature (°C) for a week.

MonTueWedThuFriSatSun
24.425.224.625.225.625.725.9

If the simple 5-point moving average for Wednesday is 25.0 °C, what is the simple 5-point moving average (°C) for Friday?

A

25.4

B

25.5

C

25.6

D

26.0

Q13
2024
QCAA
Paper 1
1 mark
Q13
1 mark

The table shows time series data for a company's quarterly sales.

Quarter1234
Sales ($)2700360045007200
Seasonal index0.60.81.0

Determine the seasonally adjusted sales ($) for the fourth quarter.

A

4500

B

6000

C

8640

D

11 520

Q25
2024
QCAA
Paper 1
5 marks
Q25

The table shows Darwin’s actual rainfall (mm) each season for two years.

 20222023
Autumn410390
Winter3020
Spring205150
Summer11351100
Q25a
3 marks

Calculate the seasonal index for each season in Darwin.

Q25b
2 marks

This table shows Hobart’s actual rainfall (mm) each season for 2023 and the long-term seasonal indices.

 AutumnWinterSpringSummer
2023 rainfall (mm)130145155132
Seasonal index0.921.021.120.94

Deseasonalise the Hobart rainfall data to identify the 2023 season with the highest seasonally adjusted rainfall.

Q2
2023
QCAA
Paper 2
4 marks
Q2
4 marks

Buffalo fly bites cause skin wounds on cattle. The table shows the average number of skin wounds per animal in a herd for two years.

 AutumnWinterSpringSummer
202128528195460
202227622170392

Deseasonalise the data.

Q18
2021
QCAA
Paper 1
4 marks
Q18

The table shows the profit made each year (in thousands of dollars) by a small business.

YearProfit ($'000s)
201542.1
201636.9
201748.4
201852.3
201956.1
202059.8
Q18a
2 marks

Use a mathematical model to determine the equation of the least-squares line to fit this data.

Q18b
2 marks

Use the least-squares line to forecast the profit in 2021, to the nearest hundred dollars.

Frequently Asked Questions

How many SCSA Mathematics Applications questions cover Time series analysis?
AusGrader has 63 SCSA Mathematics Applications questions on Time series analysis, all with instant AI grading and detailed marking feedback.

Ready to practise SCSA Mathematics Applications?

Get instant AI feedback on past exam questions, aligned to the syllabus

Start Practising Free