Advanced Maths Predictions (2 Viewers)

[tywebb]

Here are another set of solutions for advanced, but this time by John Drake:

 

[jackmccowan]

I think Q15 is wrong, not sure why its 1/5?

It should be 5/18

 

[PCNQQn2]

I looked at the 3 sets of solutions posted for discrepancies, and also looked at mine.
* Q15: I got 5/18 for 15a and 3/5 for 15b, which is different to two sets of solutions posted. I have verified both with 500,000 trials in a spreadsheet.
* Q28c I agree with John Drake's answer: 2ln2-3/2+pi/4
* Q32c should be $931.54 (also verified with a spreadsheet)
* For Q24, my answer is (emphasis on with reference to the context given).

• there is a positive correlation (r>0), meaning that as the age of characters increases, so does the age of the actors
• r=0.4564 means a moderate strength of the correlation. i.e. if the equation of the line of best fit was used for interpolation, it wouldn't be too reliable. For example, for a character of age 15, the equation suggests an actor age of 20. But the graph shows there is a lot of variation for 15 year old characters (14 to 27 years)
• gradient of 1.85 means that on average, for every extra year of character age, actor age increases by 1.85 years
• extrapolation would not be reliable given there is not data for <14 and >17 years for character age, and the study was for teenage characters only.

 

[chilli 412]

I looked at the 3 sets of solutions posted for discrepancies, and also looked at mine.
* Q15: I got 5/18 for 15a and 3/5 for 15b, which is different to two sets of solutions posted. I have verified 5/18 with 100,000 trials in a spreadsheet.
* Q28c I agree with John Drake's answer: 2ln2-3/2+pi/4
* Q32c should be $931.54 (also verified with a spreadsheet)
* For Q24, my answer is (emphasis on with reference to the context given).

• there is a positive correlation (r>0), meaning that as the age of characters increases, so does the age of the actors
• r=0.4564 means a moderate strength of the correlation. i.e. if the equation of the line of best fit was used for interpolation, it wouldn't be too reliable. For example, for a character of age 15, the equation suggests an actor age of 20. But the graph shows there is a lot of variation for 15 year old characters (14 to 27 years)
• gradient of 1.85 means that on average, for every extra year of character age, actor age increases by 1.85 years
• extrapolation would not be reliable given there is not data for <14 and >17 years for character age, and the study was for teenage characters only.

 

[PCNQQn2]

Is it wrong to say that there is a positive skew in the data whereby there's a larger concentration of actors aged 14-15?

I don't think there is a point to be made based on skew.
Considering characters, there are 18 of them aged 14-15, and 15 of them aged 17-18.
Considering actors, there are fewer at both ends (below 18 yrs, and above 26 yrs), and more in the middle.

 

[tywebb]

Official exam is up: https://www.educationstandards.nsw..../2022/mathematics-advanced-2022-hsc-exam-pack

 

[tywebb]

Dymocks Tutoring solutions: https://www.dymockstutoring.edu.au/2022-exam-solutions/

 

[tywebb]

Matrix Education solutions: https://www.matrix.edu.au/2022-hsc-maths-advanced-exam-paper-solutions/

 

[tywebb]

itute solutions: https://www.itute.com/wp-content/uploads/2022-NSW-ESA-Mathematics-Advanced-Solutions.pdf