QCAA General Mathematics Bivariate data analysis 2

5 sample questions with marking guides and sample answers

Q4
2021
QCAA
Paper 1
1 mark
Q4
1 mark

A confounding variable is a variable that

A

can only take on a certain number of values.

B

remains constant throughout a statistical investigation.

C

is used to predict a difference in the response variable.

D

other than the explanatory variable, influences the response variable.

Q9
2020
QCAA
Paper 1
1 mark
Q9
1 mark

It is observed that as the number of ice blocks sold each month increases, the number of fans sold also increases. Which of these statements is therefore true?

A

There is a negative causation between the number of ice blocks sold and the number of fans sold each month.

B

There is a positive causation between the number of ice blocks sold and the number of fans sold each month.

C

There is a negative association between the number of ice blocks sold and the number of fans sold each month.

D

There is a positive association between the number of ice blocks sold and the number of fans sold each month.

Q19
2020
QCAA
Paper 1
4 marks
Q19

Data was collected relating the number of hours spent fishing and the total number of fish caught.
The linear model for this data was found to be y=2.3x+31.4y = 2.3x + 31.4, where xx is the number of hours spent fishing, and yy is the total number of fish caught.

Q19a
1 mark

Use the model to predict the number of fish caught if 12 hours were spent fishing.

Q19b
3 marks

The correlation coefficient for this data is 0.688 and the coefficient of determination is 0.473. Use each of these to describe the strength of the linear association between the two variables and decide if your prediction is valid.

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.

Q16
2022
QCAA
Paper 1
3 marks
Q16

The table shows the number of sales for a small business in their first six months of trading.

Time in months, ttNumber of sales, nn
186
2180
3160
4226
5240
6335
Q16a
1 mark

Use your calculator to determine the equation of the least-squares line.

Q16b
2 marks

Use the equation from Question 16a) to predict the number of sales in the 21st month.

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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 \\\\

QCAA General Mathematics Bivariate data analysis 2

5 sample questions with marking guides and sample answers

Q4
2021
QCAA
Paper 1
1 mark
Q4
1 mark

A confounding variable is a variable that

A

can only take on a certain number of values.

B

remains constant throughout a statistical investigation.

C

is used to predict a difference in the response variable.

D

other than the explanatory variable, influences the response variable.

Q9
2020
QCAA
Paper 1
1 mark
Q9
1 mark

It is observed that as the number of ice blocks sold each month increases, the number of fans sold also increases. Which of these statements is therefore true?

A

There is a negative causation between the number of ice blocks sold and the number of fans sold each month.

B

There is a positive causation between the number of ice blocks sold and the number of fans sold each month.

C

There is a negative association between the number of ice blocks sold and the number of fans sold each month.

D

There is a positive association between the number of ice blocks sold and the number of fans sold each month.

Q19
2020
QCAA
Paper 1
4 marks
Q19

Data was collected relating the number of hours spent fishing and the total number of fish caught.
The linear model for this data was found to be y=2.3x+31.4y = 2.3x + 31.4, where xx is the number of hours spent fishing, and yy is the total number of fish caught.

Q19a
1 mark

Use the model to predict the number of fish caught if 12 hours were spent fishing.

Q19b
3 marks

The correlation coefficient for this data is 0.688 and the coefficient of determination is 0.473. Use each of these to describe the strength of the linear association between the two variables and decide if your prediction is valid.

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.

Q16
2022
QCAA
Paper 1
3 marks
Q16

The table shows the number of sales for a small business in their first six months of trading.

Time in months, ttNumber of sales, nn
186
2180
3160
4226
5240
6335
Q16a
1 mark

Use your calculator to determine the equation of the least-squares line.

Q16b
2 marks

Use the equation from Question 16a) to predict the number of sales in the 21st month.

Frequently Asked Questions

How many QCAA General Mathematics questions cover Bivariate data analysis 2?
AusGrader has 99 QCAA General Mathematics questions on Bivariate data analysis 2, all with instant AI grading and detailed marking feedback.

Ready to practise QCAA General Mathematics?

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}]}]}}]},{\"questionNumber\":16,\"year\":2022,\"paper\":1,\"authorName\":\"QCAA\",\"calculatorAllowed\":true,\"inlineStimulus\":[{\"part\":null,\"text\":\"The table shows the number of sales for a small business in their first six months of trading.\\n\\n| Time in months, $t$ | Number of sales, $n$ |\\n|---|---|\\n| 1 | 86 |\\n| 2 | 180 |\\n| 3 | 160 |\\n| 4 | 226 |\\n| 5 | 240 |\\n| 6 | 335 |\"}],\"parts\":[{\"partLabel\":\"a\",\"questionText\":\"Use your calculator to determine the equation of the least-squares line.\",\"marks\":1,\"questionType\":\"short_answer\",\"mcOptions\":null,\"rubric\":{\"sampleAnswer\":\"$n = 42.6t + 55.4$\",\"mcExplanations\":null,\"columns\":[{\"name\":\"Response\",\"isMarkingBands\":false,\"criteria\":[{\"descriptor\":\"Correctly determines the equation of the least-squares line\",\"marks\":1}]}]}},{\"partLabel\":\"b\",\"questionText\":\"Use the equation from Question 16a) to predict the number of sales in the 21st month.\",\"marks\":2,\"questionType\":\"short_answer\",\"mcOptions\":null,\"rubric\":{\"sampleAnswer\":\"Let $t = 21$\\n$n = 42.6(21) + 55.4$\\n$= 950$\\n\\nThe predicted number of sales is 950.\",\"mcExplanations\":null,\"columns\":[{\"name\":\"Response\",\"isMarkingBands\":false,\"criteria\":[{\"descriptor\":\"Substitutes into equation from Question 16a)\",\"marks\":1},{\"descriptor\":\"Predicts number of sales\",\"marks\":1}]}]}}]}]}")

QCAA General Mathematics Bivariate data analysis 2

5 sample questions with marking guides and sample answers

Q4
2021
QCAA
Paper 1
1 mark
Q4
1 mark

A confounding variable is a variable that

A

can only take on a certain number of values.

B

remains constant throughout a statistical investigation.

C

is used to predict a difference in the response variable.

D

other than the explanatory variable, influences the response variable.

Q9
2020
QCAA
Paper 1
1 mark
Q9
1 mark

It is observed that as the number of ice blocks sold each month increases, the number of fans sold also increases. Which of these statements is therefore true?

A

There is a negative causation between the number of ice blocks sold and the number of fans sold each month.

B

There is a positive causation between the number of ice blocks sold and the number of fans sold each month.

C

There is a negative association between the number of ice blocks sold and the number of fans sold each month.

D

There is a positive association between the number of ice blocks sold and the number of fans sold each month.

Q19
2020
QCAA
Paper 1
4 marks
Q19

Data was collected relating the number of hours spent fishing and the total number of fish caught.
The linear model for this data was found to be y=2.3x+31.4y = 2.3x + 31.4, where xx is the number of hours spent fishing, and yy is the total number of fish caught.

Q19a
1 mark

Use the model to predict the number of fish caught if 12 hours were spent fishing.

Q19b
3 marks

The correlation coefficient for this data is 0.688 and the coefficient of determination is 0.473. Use each of these to describe the strength of the linear association between the two variables and decide if your prediction is valid.

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.

Q16
2022
QCAA
Paper 1
3 marks
Q16

The table shows the number of sales for a small business in their first six months of trading.

Time in months, ttNumber of sales, nn
186
2180
3160
4226
5240
6335
Q16a
1 mark

Use your calculator to determine the equation of the least-squares line.

Q16b
2 marks

Use the equation from Question 16a) to predict the number of sales in the 21st month.

Frequently Asked Questions

How many QCAA General Mathematics questions cover Bivariate data analysis 2?
AusGrader has 99 QCAA General Mathematics questions on Bivariate data analysis 2, all with instant AI grading and detailed marking feedback.

Ready to practise QCAA General Mathematics?

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

Start Practising Free