Getting started (approximately 150 words for each question)
1. Analyse the problem to show your understanding of it.
2. Interpret and give meaning to any numerical data given.
3. Select and briefly describe a method of solution.
Calculations (the length will depend on the type of calculations and figures used)
1. Perform the necessary calculations.
2. Communicate the solution in a logically sequenced way
Conclusion (approximately 250 words for each question)
1. Evaluate and analyse your results and method.
2. Comment on any assumptions or limitations that affected your results.
3. Justify the practicality of the method of solution
4. Discuss alternative methods that could have been used
5. Discuss the relevance to the real world
Question 1 Landscaping
As part of an urban redevelopment, a new community library is constructed. The new building features irregularly shaped exterior features and will involve significant landscaping. The plan of the new building and gardens is illustrated on the next page and includes trees, a pond (blue) and pathways (yellow).
All garden beds will be mulched except for defined areas around the base of each plant species, the pond and the paths. Mulch will be spread so that it is 15cm deep.
The team also has a choice between two different types of mulch. Owing to budget constraints, local authorities have decided that they can only afford to rejuvenate and replace the mulch a certain number of times within a five year budget cycle.
Using the information given (and the diagram on the next page) calculate the total volume of mulch to be purchased and determine which type of mulch would be most cost-effective over a maintenance period of ten years.
Steps to help answer this question
1. Calculate the surface area of the building, pathways and garden beds separately
2. Use the above surface area to determine the surface area of the spaces to be mulched.
3. Determine the volume of mulch required and use this to determine the proposed costs.
4. Consider the replacement frequency of each type of mulch over the decade.
1. The following areas do not need mulch:
A. Plant species A is a large tree, with an overhanging canopy 2.26m across
B. Plant species B is circular and has a diameter of 1.12 metres
C. Plant species C is circular and has a diameter of 0.68 metres
D. The circular pond (blue) has a diameter 1.51 metres
E. Two pathways
2. Mulch is either
A. Type 1: Degrades completely after 18 months. Cost $95.00 per cubic metre.
B. Type 2: Degrades completely after 14 months. Cost $78.00 per cubic metres.
3. A funding cap for mulch replacement is set at $21 000 per decade.
Question 2 Sports Training
Sport scientists at the Australian Institute of Sport (AIS) have been testing elite football players and want to know if there is a relationship between the weight lifted in a back squat exercise and height of a vertical jump or the time for a 10 m sprint. They want to do this to understand if they need to modify their training program to meet the specific needs of the elite footballers.
Explore the relationships between maximum back squat and the vertical jump and maximum back squat and the 10m sprint exercises. Include in your exploration a discussion of the correlation between the two exercises.
Steps to help answer the question
1. Graph the data in Table 2.1 for each relationship in separate graphs
2. Describe each relationship using an equation for a straight line. (Excel may be used but equations must be confirmed using hand calculations)
3. Use a statistical measure to determine the strength of each relationship.
4. Explain the differences between the relationships and any meaning you can draw from your data
Table 2.1: Relationship between weight lifted in a back squat and height (cm) of a vertical jump and time (seconds) for a 10 m sprint for 20 athletes.
Question 3 Temperature changes
The Bureau of Meteorology (BOM) routinely records temperatures in locations across Australia. They publish these data to help Australians understand temperature changes. Data of the daily maximum temperatures were collected by the BOM for the Coffs Harbour region in the month of January in 1970, 1990 and 2010 (see below).
Investigate and compare the maximum temperatures for January in 1970, 1990 and 2010 and use these data to help understand whether temperature will increase or stay the same by 2020 in this region.
Steps to help answer the question
1. Calculate and display graphically a five number summary for each data set. Show the working to calculate the five number summary for one data set only.
2. Graphically display the 3 five number summaries in box and whisker plots.
3. Use Excel to calculate the mean and associated measure of spread for each data set.
4. Use these measures to compare the three data sets and discuss whether there are any implications for the temperature in 2020.
Table 3.1: Daily maximum temperatures (degrees C) for January collected from the Coffs Harbour region in 1970, 1990 and 2010.
Data extracted from the BOM (http://www.bom.gov.au/climate/change/acorn-sat/#tabs=Data- and- networks
Note no further data are required to answer this question.