Sample work Mathematics Standard 1 Year 12: buying a car and planning a Year 12 formal

Nature of the task

This task has two parts. The first part requires students to research different methods for purchasing a new car and evaluate each method. In the second part, students research the cost of holding a Year 12 Formal and determine how much to charge each person who attends the event. They use simultaneous equations to model the costs and expenses involved.

Context

Students have engaged in learning for the subtopics, Investment and Types of Relationships. They have participated in activities to develop knowledge of the concepts of spending, saving and borrowing money. They have analysed different financial situations and calculated the best options for given circumstances and to solve financial problems. They have participated in activities to develop knowledge of the concepts of simultaneous equations, graphing and interpretation of relationships, and skills to solve a variety of problems.

Outcomes assessed

MS1-12-1 uses algebraic and graphical techniques to critically evaluate arguments in a range of familiar and unfamiliar contexts

MS1-12-5 makes informed decisions about financial situations likely to be encountered post-school

MS1-12-6 represents the relationships between changing quantities in algebraic and graphical forms

MS1-12-9 chooses and uses appropriate technology effectively and recognises appropriate times for such use

MS1-12-10 uses mathematical argument and reasoning to evaluate conclusions, communicating a position clearly to others

Assessment criteria

Students will be assessed on their ability to:

• solve problems based on a scenario
• select and use appropriate mathematical processes, technologies and language to investigate problems, organise and interpret graphs and relationships
• use reasoning to evaluate solutions and justify conclusions.

Questions

Part A

You want to save money to purchase a new car. Consider three different options for saving money and evaluate each method based on its merits.

Task 1 – Find a Car

Research a brand new car that you would be interested in buying. State the make, model and cost.

Task 2 – Regular Contributions to Savings

Research interest rates for savings accounts from a bank of your choice and use a savings calculator to determine the monthly contributions you would need to make to save enough money to buy your car in 4 years’ time. Record your results.

Task 3 – Lump Sum

Use a present value calculator and the same interest rate used in Task 2 to determine how much money you would need as a lump sum to invest to achieve the same amount of savings in 4 years’ time with interest compounded monthly. Record your results.

Task 4 - Loan

Research interest rates on car loans from a bank of your choice. Use a loan calculator to determine how much you would need to pay off in total if you took out a loan to purchase the car over 4 years. Record your results.

Task 5 - Which way to go?

Based on your results, comment on the different ways of purchasing the car and evaluate each method. Include information about the availability of money, the total amount to be paid, the time until you can purchase the car and the circumstances under which you would choose each option.

Part B

You are a part of the Year 12 Formal Planning Committee and your job is to research the cost of holding the Formal and determine how much to charge each student who attends.

Task 1 – Fixed Costs

You will need to determine the cost of booking and setting up the Formal location.

Find some costs for the following in the local area:

1. Hire of Venue
2. Decorations
3. Band/DJ
4. Audio Visual Equipment
5. Any other expenses (printing invites etc)
6. Total Fixed Costs

Task 2 – Covering the Costs

Question 1: Write a linear equation for the Cost $C of running the event for n people using your fixed costs from Task 1 if the venue charges $45 per person for catering.

Question 2: Write a linear equation for the Income $I you will receive if n people attend if you were to charge $50 per person for tickets.

Question 3: Graph both functions using technology. Adjust the scales so that a break-even point can be clearly seen.

Question 4: How many people do you expect to attend the Year 12 Formal? By referencing your graph, will you be charging enough to cover the costs of the formal for the number of people you expect to attend?

Question 5: Given the number of people you expect to attend, calculate the actual cost per person you will need to charge and modify your equation for the Income accordingly.

Question 6: Create a new graph showing the Cost and Income for the event and clearly label the Break Even Point.