AUSTRALIAN ISLAMIC COLLEGE

Transcription

1 AUSTRALIAN ISLAMIC COLLEGE Western Australian Curriculum Mathematics 2018 Year 9 Project Based Learning Investigation Name: Student ID: Teacher: Instructions: Read the project carefully There is a lot of information to read through. Answer every question and ALWAYS show your working out Have fun with it Be creative with your trip and group Due Date: Term 3 Friday 20 th July 2018 Any submissions after this date will receive a penalty of -10% each day until Friday 27 th July, after which you will receive 0% Course Content: Solve problems involving direct proportion. Explore the relationship between graphs and equations corresponding to simple rate problems (ACMNA208) Find the distance between two points located on the Cartesian plane using a range of strategies, including graphing software (ACMNA214) Sketch linear graphs using the coordinates of two points and solve linear equations (ACMNA215) Declaration of Authenticity: I hereby declare that this submission is my own work and to the best of my ability it contains no plagiarised material. Signed: Date

2 The Road Trip The Application If you received this application, it means you may be selected to appear on The Road Trip. The Road Trip is a new TV show where groups of people get $20,000 for a road trip across Australia that will be an unique, life-changing and watchable experience. The journey starts in Melbourne and finishes in Perth. The money you spend will mainly go towards two types of expenses; living (hotel and food) and vehicle (hire and fuel). Plan carefully, as groups who don t spend at least $19,000 of the money will not be considered. The possibilities for your trip are limited only by your ability to budget the money. The TV crew can drive its production vehicles along the path and has an agreement with the petrol stations, hotels and restaurants to provide you with what you need to finish your journey. Due to filming restrictions, your trip can be as short as 14 days or as long as 28 days. We will only support an impressive and detailed road trip, with the most important thing to the show being how you manage the money. This means your road trip needs to cost between $19,000 and $20,000, and as long as the ideas are well thought out, we will consider any proposal. The Sign-Up Sheet Who will attend the trip? You may bring up to 7 other people. On the lines below write the names of your friends, family, and even famous celebrities (We can pull the strings if need be): Note: Enter your name in Position 1.

3 Part 1: 1 The Road Trip Route The Road Trip is a journey from Melbourne to Perth, where you have between 14 and 28 days to make the journey and can stop anywhere along the way. A few things you need to remember when planning your trip; You may only travel up to 1000kms per day and You will need to list where you are planning on staying each night and how long for. You will need to create a map for your trip below; 1. Go to: 2. In the top left corner, click on the Directions button 3. Change the from location to Melbourne, VIC. 4. Change the destination location to your first stop 5. Click Add destination to include your next destination. Ensure your last destination is Perth, WA 6. Look over your route and check if you want to change anything 7. Once you are happy with the route, write down the information below. Origin Destination Kilometres Nights Stay Melbourne How many nights does your journey take? How does this compare to the Google Maps duration? Why do you think there such a difference?

4 Part 2: 2 Living Expenses Your main expenses for this trip, outside of the car, will be accommodation and food, which are calculated separately. We will provide you with three different types of each, remembering you ll need accommodation for everyone going. Accommodation: Luxury Suites Hotel Rooms Campsites Rating Cost $500 per day $300 per day $30 per day Occupancy Up to 2 people Up to 4 people Up to 2 people Food: Prestige Standard Cheap Rating Cost $120/day per person $70/day per person $30/day per person Description High quality cuisine in fine dining restaurants Healthy meals in family-style diners What type of Accommodation and Food did you choose and why? Fast food meals Given the number of people going on the trip, what is the total amount you will spend on Accommodation and Food each day? Using the amount you spend on Accommodation and Food, make an equation (in =+ form) that will give you the expenses for any given amount of days?

5 Part 3: Vehicle Expenses We will allow you the free use of the following vehicles for your trip because of our agreements with the car dealers. Make sure you have enough room for ALL your passengers. Pay attention to the litres per 100 kilometres as you will need to pay for petrol as well. Make/ Model Toyota Corolla Toyota Camry Toyota Kluger Porsche Boxter Capacity 5 Seats 5 Seats 7 Seats 2 Seats Hire Cost $70 per day $90 per day $120 per day $320 per day Fuel Consumption 7lts / 100kms 9lts / 100kms 15lts / 100kms 18lts / 100kms What type of vehicle did you choose and why? Once you choose a vehicle, using the fuel consumption figures, how many litres it will take you to finish your trip? We will have petrol available throughout the trip at our corporate rate of $1.40/ litre. How much will your total cost on petrol be? Using the amount you spend on vehicle hire and petrol, make an equation (in =+ form) that will give you the expenses for any given amount of days?

6 Part 4: Calculating Costs Use your equations (enter in the table below) from Part 2 and 3 to calculate the cost of a 2, 3 or 4- week trip. Calculate the total cost of the 2-week trip, showing you working out below and write your results in the table below. Complete the remaining cells in the table below. Days = Living Expenses: = Vehicle Expenses: Total Cost ($) If you can t find a suitable trip in the table above, then you should be able to use the tables below to determine what the longest possible trip could be (this doesn t have to be with in the 14 to 28 days requirement). REMEMBER THE TRIP MUST BE BETWEEN $19,000 AND $20,000. Try different lengths of trips in the spaces below. Days = Living Expenses: = Vehicle Expenses: Total Cost ($)

7 Did you have to make any changes to your equations by adjusting the living or vehicle expenses? If so, explain your changes below. Part 5: The Bonus You are given an additional $2,000 to spend in the last 3 days (not before) of your trip. Using your formulas from above, how would you adjust your Living and Vehicle expenses in the last 3 days to complete the trip with a cost between $21,000 to $23,000? Show all your working out below. (Hint: You will need to work out how much the trip has cost up to 3 days before you finish and work out how much money you have remaining to spend)

8 Working Out Paper

9 Part 6: : Linear Relationships Graph the Living Expense Equation and Vehicle Expenses Equation below. Include labels on the x and y axis, a title, a key, and very neat graph.

10 Graph the Distance from Melbourne and the Total Expenses Equation below You will need to setup a y-axis on the left for distance and a y-axis on the right for cost. Include labels on the x and y axis, a title, a key, and very neat graph.

11 Graph the Adjusted Living Expenses Equation and Adjusted Vehicle Expenses Equation with the included bonus below. Include labels on the x and y axis, a title, a key, and very neat graph.