91585 – Worked Solutions - 2025

QUESTION THREE

3.5 (AS 91577) – 2025 Answers

Quite often, there are different ways to solve a Mathematics problem.

These solutions/strategies show one possible way to solve them.

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Question 3 (a) i

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Question 3 (a) ii

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Question 2 (b) i

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Question 2 (b) ii

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Question 3 (c) i

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Question 3 (c) ii

Question 3 (a) i

(a) The School Sports Census data for ultimate frisbee and archery from 2005 to 2020 is summarised below.

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1. In which year did ultimate frisbee have the highest proportion of the total participants in these two sports?

Justify your answer by referring to the graph.

Question 3 (a) i

(a) The School Sports Census data for ultimate frisbee and archery from 2005 to 2020 is summarised below.

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1. In which year did ultimate frisbee have the highest proportion of the total participants in these two sports?

Justify your answer by referring to the graph.

Question 3 (a) i

(a) The School Sports Census data for ultimate frisbee and archery from 2005 to 2020 is summarised below.

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​

​

​

​

​

​

1. In which year did ultimate frisbee have the highest proportion of the total participants in these two sports?

Justify your answer by referring to the graph.

Question 3 (a) i

(a) The School Sports Census data for ultimate frisbee and archery from 2005 to 2020 is summarised below.

​

​

​

​

​

​

​

1. In which year did ultimate frisbee have the highest proportion of the total participants in these two sports?

Justify your answer by referring to the graph.

Question 3 (a) i

(a) The School Sports Census data for ultimate frisbee and archery from 2005 to 2020 is summarised below.

​

​

​

​

​

​

​

1. In which year did ultimate frisbee have the highest proportion of the total participants in these two sports?

Justify your answer by referring to the graph.

Question 3 (a) i

(a) The School Sports Census data for ultimate frisbee and archery from 2005 to 2020 is summarised below.

​

​

​

​

​

​

​

1. In which year did ultimate frisbee have the highest proportion of the total participants in these two sports?

Justify your answer by referring to the graph.

Question 3 (a) i

(a) The School Sports Census data for ultimate frisbee and archery from 2005 to 2020 is summarised below.

​

​

​

​

​

​

​

1. In which year did ultimate frisbee have the highest proportion of the total participants in these two sports?

Justify your answer by referring to the graph.

2020 had the highest proportion of ultimate frisbee participants

Question 3 (a) ii

(a) The School Sports Census data for ultimate frisbee and archery from 2005 to 2020 is summarised below.

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​

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1. dd
2. Explain why the probabilities calculated from this data might not correctly represent the probability of a student playing ultimate frisbee, compared to other sports, in those years.

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Question 3 (a) ii

(a) The School Sports Census data for ultimate frisbee and archery from 2005 to 2020 is summarised below.

​

​

​

​

​

​

​

1. dd
2. Explain why the probabilities calculated from this data might not correctly represent the probability of a student playing ultimate frisbee, compared to other sports, in those years.

​

Question 3 (a) ii

(a) The School Sports Census data for ultimate frisbee and archery from 2005 to 2020 is summarised below.

​

​

​

​

​

​

​

1. dd
2. Explain why the probabilities calculated from this data might not correctly represent the probability of a student playing ultimate frisbee, compared to other sports, in those years.

​

Possible responses:

• The given probabilities only compare participation in ultimate frisbee and archery. They ignore students who participated in other sports, or those who did not play any sport.
• If overall student sports participation increased, the proportion of students playing ultimate frisbee may not have changed significantly, even if raw numbers increased. If the number of students in other sports also grew, ultimate frisbees’ true proportion among all sports could be lower than the calculated values.
• The data might not represent all schools or regions, leading to bias. Changes in data collection methods over time, such as more accurate counting or the inclusion of more schools, could affect comparisons.
• The probabilities are useful for comparing ultimate frisbee relative to archery, but not for evaluating ultimate frisbees popularity overall. A more accurate measure would require total school sports participation data.

Question 3 (a) ii

(a) The School Sports Census data for ultimate frisbee and archery from 2005 to 2020 is summarised below.

​

​

​

​

​

​

​

1. dd
2. Explain why the probabilities calculated from this data might not correctly represent the probability of a student playing ultimate frisbee, compared to other sports, in those years.

​

Possible responses:

• The given probabilities only compare participation in ultimate frisbee and archery. They ignore students who participated in other sports, or those who did not play any sport.
• If overall student sports participation increased, the proportion of students playing ultimate frisbee may not have changed significantly, even if raw numbers increased. If the number of students in other sports also grew, ultimate frisbees’ true proportion among all sports could be lower than the calculated values.
• The data might not represent all schools or regions, leading to bias. Changes in data collection methods over time, such as more accurate counting or the inclusion of more schools, could affect comparisons.
• The probabilities are useful for comparing ultimate frisbee relative to archery, but not for evaluating ultimate frisbees popularity overall. A more accurate measure would require total school sports participation data.

Question 3 (a) ii

(a) The School Sports Census data for ultimate frisbee and archery from 2005 to 2020 is summarised below.

​

​

​

​

​

​

​

1. dd
2. Explain why the probabilities calculated from this data might not correctly represent the probability of a student playing ultimate frisbee, compared to other sports, in those years.

​

Possible responses:

• The given probabilities only compare participation in ultimate frisbee and archery. They ignore students who participated in other sports, or those who did not play any sport.
• If overall student sports participation increased, the proportion of students playing ultimate frisbee may not have changed significantly, even if raw numbers increased. If the number of students in other sports also grew, ultimate frisbees’ true proportion among all sports could be lower than the calculated values.
• The data might not represent all schools or regions, leading to bias. Changes in data collection methods over time, such as more accurate counting or the inclusion of more schools, could affect comparisons.
• The probabilities are useful for comparing ultimate frisbee relative to archery, but not for evaluating ultimate frisbees popularity overall. A more accurate measure would require total school sports participation data.

Question 3 (a) ii

(a) The School Sports Census data for ultimate frisbee and archery from 2005 to 2020 is summarised below.

​

​

​

​

​

​

​

1. dd
2. Explain why the probabilities calculated from this data might not correctly represent the probability of a student playing ultimate frisbee, compared to other sports, in those years.

​

Possible responses:

• The given probabilities only compare participation in ultimate frisbee and archery. They ignore students who participated in other sports, or those who did not play any sport.
• If overall student sports participation increased, the proportion of students playing ultimate frisbee may not have changed significantly, even if raw numbers increased. If the number of students in other sports also grew, ultimate frisbees’ true proportion among all sports could be lower than the calculated values.
• The data might not represent all schools or regions, leading to bias. Changes in data collection methods over time, such as more accurate counting or the inclusion of more schools, could affect comparisons.
• The probabilities are useful for comparing ultimate frisbee relative to archery, but not for evaluating ultimate frisbees popularity overall. A more accurate measure would require total school sports participation data.

Question 3 (a) ii

(a) The School Sports Census data for ultimate frisbee and archery from 2005 to 2020 is summarised below.

​

​

​

​

​

​

​

1. dd
2. Explain why the probabilities calculated from this data might not correctly represent the probability of a student playing ultimate frisbee, compared to other sports, in those years.

​

Possible responses:

• The given probabilities only compare participation in ultimate frisbee and archery. They ignore students who participated in other sports, or those who did not play any sport.
• If overall student sports participation increased, the proportion of students playing ultimate frisbee may not have changed significantly, even if raw numbers increased. If the number of students in other sports also grew, ultimate frisbees’ true proportion among all sports could be lower than the calculated values.
• The data might not represent all schools or regions, leading to bias. Changes in data collection methods over time, such as more accurate counting or the inclusion of more schools, could affect comparisons.
• The probabilities are useful for comparing ultimate frisbee relative to archery, but not for evaluating ultimate frisbees popularity overall. A more accurate measure would require total school sports participation data.

Identifies one reason not representative AND discusses TWO reasons for increase in context.

Question 3 (b) i

Question 3 (b) i

Question 3 (b) i

Question 3 (b) i

Question 3 (b) i

Question 3 (b) ii

Question 3 (b) ii

Question 3 (b) ii

Question 3 (b) ii

Question 3 (b) ii

Question 3 (c)

(c) A school sports coach uses observers to classify players from tryouts as ‘selected’ for the squad, or ‘not selected’. Students who perform at the required standard should be selected, and those who perform below the required standard should not be selected. The coach has a goal of 90% accuracy of selecting the correct players based on their ability.

75 students attended the tryouts. An observer correctly selected 42 out of 50 players who performed at the required standard, but also selected 12 players from the 25 students who performed below the required standard. The results of the tryouts are summarised in the table below.

Question 3 (c)

(c) A school sports coach uses observers to classify players from tryouts as ‘selected’ for the squad, or ‘not selected’. Students who perform at the required standard should be selected, and those who perform below the required standard should not be selected. The coach has a goal of 90% accuracy of selecting the correct players based on their ability.

75 students attended the tryouts. An observer correctly selected 42 out of 50 players who performed at the required standard, but also selected 12 players from the 25 students who performed below the required standard. The results of the tryouts are summarised in the table below.

Question 3 (c) i

(i) Calculate the proportion of students who received the correct result of ‘selected’ or ‘not selected’, based on their performance.

Question 3 (c) i

(i) Calculate the proportion of students who received the correct result of ‘selected’ or ‘not selected’, based on their performance.

Question 3 (c) i

(i) Calculate the proportion of students who received the correct result of ‘selected’ or ‘not selected’, based on their performance.

Question 3 (c) i

(i) Calculate the proportion of students who received the correct result of ‘selected’ or ‘not selected’, based on their performance.

Question 3 (c) i

(i) Calculate the proportion of students who received the correct result of ‘selected’ or ‘not selected’, based on their performance.

Question 3 (c) ii

(ii) Comment on the effectiveness of the observer in selecting the correct players for the netball squad.

Support your answer with at least one calculation.

Question 3 (c) ii

(ii) Comment on the effectiveness of the observer in selecting the correct players for the netball squad.

Support your answer with at least one calculation.

Question 3 (c) ii

(ii) Comment on the effectiveness of the observer in selecting the correct players for the netball squad.

Support your answer with at least one calculation.

Question 3 (c) ii

(ii) Comment on the effectiveness of the observer in selecting the correct players for the netball squad.

Support your answer with at least one calculation.

Question 3 (c) ii

(ii) Comment on the effectiveness of the observer in selecting the correct players for the netball squad.

Support your answer with at least one calculation.