91946 – Worked Solutions - 2025

1.3 (AS 91946) – 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 2 (a)

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Question 2 (b)

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Question 2 (c)

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Question 2 (d)

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QUESTION TWO

Question 2

The graph below shows the relationship between the price ($NZ) of a pair of sports shoes and the size of the sports shoes based on 117 randomly selected pairs.

Question 2 (a)

(a)

Describe and interpret TWO different features of the relationship shown in Resource 2A.

Question 2 (a)

(a)

Describe and interpret TWO different features of the relationship shown in Resource 2A.

Question 2 (a)

(a)

Describe and interpret TWO different features of the relationship shown in Resource 2A.

• We can see that there is a positive linear relationship: generally as the size of the shoe increases, so does the price of the shoe.
• The relationship appears to be of moderate / weak strength, as there is a bit of scatter either side of the trend line.
• There appears to be two groups of prices. One group goes from size 1 to size 6, and the other group is from size 7 to size 10. This could be due to the two groups of adults’ and children’s shoes.
• There is an unusual result of shoe size 6 that cost $150, which is much more expensive than the other shoes of this size.

Question 2 (a)

(a)

Describe and interpret TWO different features of the relationship shown in Resource 2A.

• We can see that there is a positive linear relationship: generally as the size of the shoe increases, so does the price of the shoe.
• The relationship appears to be of moderate strength, with a bit of scatter either side of the trend line.
• There appears to be two groups of prices. One group goes from size 1 to size 6, and the other group is from size 7 to size 10. This could be due to the two groups of adults’ and children’s shoes.
• There is an unusual result of shoe size 6 that cost $150, which is much more expensive than the other shoes of this size.

Question 2 (a)

(a)

Describe and interpret TWO different features of the relationship shown in Resource 2A.

• We can see that there is a positive linear relationship: generally as the size of the shoe increases, so does the price of the shoe.
• The relationship appears to be of moderate strength, with a bit of scatter either side of the trend line.
• There appears to be two groups of prices. One group goes from size 1 to size 6, and the other group is from size 7 to size 10. This could be due to the two groups of adults’ and children’s shoes.
• There is an unusual result of shoe size 6 that cost $150, which is much more expensive than the other shoes of this size.

Question 2 (a)

(a)

Describe and interpret TWO different features of the relationship shown in Resource 2A.

• We can see that there is a positive linear relationship: generally as the size of the shoe increases, so does the price of the shoe.
• The relationship appears to be of moderate strength, with a bit of scatter either side of the trend line.
• There appears to be two groups of prices. One group goes from size 1 to size 6, and the other group is from size 7 to size 10. This could be due to the two groups of adults’ and children’s shoes.
• There is an unusual result of shoe size 6 that cost $150, which is much more expensive than the other shoes of this size.

Question 2 (a)

(a)

Describe and interpret TWO different features of the relationship shown in Resource 2A.

• We can see that there is a positive linear relationship: generally as the size of the shoe increases, so does the price of the shoe.
• The relationship appears to be of moderate strength, with a bit of scatter either side of the trend line.
• There appears to be two groups of prices. One group goes from size 1 to size 6, and the other group is from size 7 to size 10. This could be due to the two groups of adults’ and children’s shoes.
• There is an unusual result of shoe size 6 that cost $150, which is much more expensive than the other shoes of this size.

Looking for two features, described in context

Question 2 (b)

(b)

Adina needs to buy a new pair of size 6 sports shoes.

Using the graph in Resource 2A, what price should Adina expect to pay?

• How confident can you be in using this graph to predict shoe price?

• Support your answer with statistical reasoning.

Question 2 (b)

(b)

Adina needs to buy a new pair of size 6 sports shoes.

Using the graph in Resource 2A, what price should Adina expect to pay?

• How confident can you be in using this graph to predict shoe price?

• Support your answer with statistical reasoning.

Question 2 (b)

(b)

Adina needs to buy a new pair of size 6 sports shoes.

Using the graph in Resource 2A, what price should Adina expect to pay?

• How confident can you be in using this graph to predict shoe price?

• Support your answer with statistical reasoning.

The price of size 6 sports shoes looks to have a range of about $28 through to $70, with the majority of these shoes sitting around the trend line of about $65. I would expect Adina to pay around $65 for a pair of size 6 sports shoes.

Question 2 (b)

(b)

Adina needs to buy a new pair of size 6 sports shoes.

Using the graph in Resource 2A, what price should Adina expect to pay?

• How confident can you be in using this graph to predict shoe price?

• Support your answer with statistical reasoning.

The price of size 6 sports shoes looks to have a range of about $28 through to $70, with the majority of these shoes sitting around the trend line of about $65. I would expect Adina to pay around $65 for a pair of size 6 sports shoes.

I would be hesitant with predictions of the cost of size 6 (or size 11) shoes, because quite a few data points lie below the line of best fit, so estimates might be too large. Also, we have the one outlier at $150 (for size 6). So, generally, I am not that confident as there is a lot of variation of prices for each shoe size. Plus, the relationship is not that strong.

Question 2 (c)

RESOURCE 2B

The table on the next slide shows the costs and special offers offered by three different online companies selling sports shoes for football (soccer). All prices are in New Zealand dollars (NZD).

Shipping cost is the additional cost that the company charges to send the shoes to a customer’s home address.

GST is 15% extra to the cost of the item being purchased.

For all three companies, the special offers below apply only to shoe sizes 1–7.

For larger shoe sizes, prices are likely to be higher.

Question 2 (c)

RESOURCE 2B

Question 2 (c)

(c)

Resource 2B summarises three different sports shoe companies’ prices and their special offers.

Ricky wants to buy new size 7 football (soccer) sports shoes, and will choose from these companies.

Ricky wonders whether he should buy one or two pairs of sports shoes.

Which company should Ricky choose?

Make your recommendations, with reasons and considerations, using the information provided in Resource 2B, as well as including your own personal world views.

Question 2 (c)

(c)

Resource 2B summarises three different sports shoe companies’ prices and their special offers.

Ricky wants to buy new size 7 football (soccer) sports shoes, and will choose from these companies.

Ricky wonders whether he should buy one or two pairs of sports shoes.

Which company should Ricky choose?

Make your recommendations, with reasons and considerations, using the information provided in Resource 2B, as well as including your own personal world views.

Question 2 (c)

Question 2 (c)

Question 2 (c)

Question 2 (c)

Question 2 (c)

Question 2 (c)

Question 2 (c)

Question 2 (c)

Question 2 (c)

Divide all the “2 shoe” options by 2 to determine the price of a single shoe

Question 2 (c)

Question 2 (c)

We can see that if Ricky was to buy one pair of shoes, his cheapest choice would to be buy through Footy Fields with a price of $80.34.

However, we can see that if Ricky was to buy two pairs of shoes, then his cheapest choice would to be buy through Kick Off with a price of $120.75, if picking up from the factory. This is equivalent to being $60.38 per shoe.

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Examples of “personal world views” could include:

• It is not always best to buy the cheapest shoe – could be a poor quality
• Why buy two pairs of football boots?
• How far away from the Kick Off factory does he live?
• Is the quality of the shoes comparable as you can’t check on the internet?

Question 2 (d)

(d) Ricky is currently wearing size 7 sports shoes, but he is growing quickly. His mother thinks that he will need larger size sports shoes next season.

Using both Resource 2A and Resource 2B, recommend the best option for Ricky when buying his sports shoes for next season.

Question 2 (d)

(d) Ricky is currently wearing size 7 sports shoes, but he is growing quickly. His mother thinks that he will need larger size sports shoes next season.

Using both Resource 2A and Resource 2B, recommend the best option for Ricky when buying his sports shoes for next season.

Question 2 (d)

(d) Ricky is currently wearing size 7 sports shoes, but he is growing quickly. His mother thinks that he will need larger size sports shoes next season.

Using both Resource 2A and Resource 2B, recommend the best option for Ricky when buying his sports shoes for next season.

Resource 2A shows that the cost of shoes generally tends to increase as the size of shoes increases.

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This means that Ricky’s next pair of shoes is likely to cost more than what he has paid previously.

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Resource 2B states that the special offers only apply to show sizes 1–7 for all 3 companies.

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Could show cost of shoes for each company without any of the offers.

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Kick Off is still likely to be the best deals as their shipping costs are cheaper or have no cost.

Question 2 (d)

(d) Ricky is currently wearing size 7 sports shoes, but he is growing quickly. His mother thinks that he will need larger size sports shoes next season.

Using both Resource 2A and Resource 2B, recommend the best option for Ricky when buying his sports shoes for next season.

Resource 2A shows that the cost of shoes generally tends to increase as the size of shoes increases.

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This means that Ricky’s next pair of shoes is likely to cost more than what he has paid previously.

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Resource 2B states that the special offers only apply to show sizes 1–7 for all 3 companies.

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Could show cost of shoes for each company without any of the offers.

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Kick Off is still likely to be the best deals as their shipping costs are cheaper or have no cost.

Question 2 (d)

(d) Ricky is currently wearing size 7 sports shoes, but he is growing quickly. His mother thinks that he will need larger size sports shoes next season.

Using both Resource 2A and Resource 2B, recommend the best option for Ricky when buying his sports shoes for next season.

Resource 2A shows that the cost of shoes generally tends to increase as the size of shoes increases.

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This means that Ricky’s next pair of shoes is likely to cost more than what he has paid previously.

​

Resource 2B states that the special offers only apply to show sizes 1–7 for all 3 companies.

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Could show cost of shoes for each company without any of the offers.

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Kick Off is still likely to be the best deals as their shipping costs are cheaper or have no cost.

Question 2 (d)

(d) Ricky is currently wearing size 7 sports shoes, but he is growing quickly. His mother thinks that he will need larger size sports shoes next season.

Using both Resource 2A and Resource 2B, recommend the best option for Ricky when buying his sports shoes for next season.

Resource 2A shows that the cost of shoes generally tends to increase as the size of shoes increases.

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This means that Ricky’s next pair of shoes is likely to cost more than what he has paid previously.

​

Resource 2B states that the special offers only apply to show sizes 1–7 for all 3 companies.

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Could show cost of shoes for each company without any of the offers.

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Kick Off is still likely to be the best deals as their shipping costs are cheaper or have no cost.

Question 2 (d)

(d) Ricky is currently wearing size 7 sports shoes, but he is growing quickly. His mother thinks that he will need larger size sports shoes next season.

Using both Resource 2A and Resource 2B, recommend the best option for Ricky when buying his sports shoes for next season.

Resource 2A shows that the cost of shoes generally tends to increase as the size of shoes increases.

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This means that Ricky’s next pair of shoes is likely to cost more than what he has paid previously.

​

Resource 2B states that the special offers only apply to show sizes 1–7 for all 3 companies.

​

Could show cost of shoes for each company without any of the offers.

​

Kick Off is still likely to be the best deals as their shipping costs are cheaper or have no cost.

Question 2 (d)

(d) Ricky is currently wearing size 7 sports shoes, but he is growing quickly. His mother thinks that he will need larger size sports shoes next season.

Using both Resource 2A and Resource 2B, recommend the best option for Ricky when buying his sports shoes for next season.

Resource 2A shows that the cost of shoes generally tends to increase as the size of shoes increases.

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This means that Ricky’s next pair of shoes is likely to cost more than what he has paid previously.

​

Resource 2B states that the special offers only apply to show sizes 1–7 for all 3 companies.

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Could show cost of shoes for each company without any of the offers.

​

Kick Off is still likely to be the best deals as their shipping costs are cheaper or have no cost.

Comments on increasing trend as sizes go up so therefore the next pair of shoes will cost Ricky more

AND

Reasons to justify the decision that Ricky probably should use the Kick Off deal which would save him money.