Assessment 1
Context
What does mathematics have to do with the costs associated with purchasing a car? In the years following high school, you may need to purchase a car and there are many factors that need to be considered. The age of the car is regarded as a significant factor when researching potential purchases. However, it could be argued that the overall distance the car has travelled (odometer reading) is of greater importance. The relationship between the purchase price of the car and the distance the car has travelled is useful to know when considering a car purchase.
Task
You are in the market for a second-hand car. Using carsales.com.au as your source, you are to investigate the purchase prices of a particular model of car (e.g. Mazda 2, 2010). Your teacher will provide you with a unique make, model and year of a car available to research on carsales.com.au. Investigate whether there is a relationship between the advertised price of the car and the odometer reading. Develop a mathematical model to represent the relationship of the advertised price and the odometer reading.
You are to produce a report based on the results of your mathematical research and investigation. Within this report you will use your mathematical model to make an informed decision regarding the relationship between the odometer reading and the price of the car. You will then make a prediction of the price of a demonstration model of that particular car, given an odometer reading of 200 kilometres. You must then evaluate the suitability of your model for this purpose.
Authentication strategies
- You must acknowledge all sources.
- Your teacher will ensure class cross-marking occurs.
- Your teacher will observe you completing work in class.
- You will be provided 3 hours class time for task completion.
- You will use plagiarism-detection software, Turnitin, to submit your response.
- You will provide documentation of your progress at the indicated checkpoint.
- You will each produce a unique response by using individualised data, and producing a unique report.
- You will provide screenshots of each car selected from carsales.com.au in your appendix.
Assessment Summary
Assessment Context:
This task focuses on applying mathematics to real-world financial decisions, specifically the cost of purchasing a second-hand car. Students are asked to investigate how the odometer reading (distance travelled) impacts the advertised price of a car. This requires understanding relationships between variables and developing a mathematical model to support informed purchasing decisions.
Key Pointers to be Covered:
- Data Collection: Gather advertised prices and odometer readings for a specific make, model, and year from carsales.com.au.
- Data Analysis: Determine if there is a relationship between the car’s price and its odometer reading.
- Mathematical Modelling: Develop a model representing the relationship between price and odometer reading.
- Prediction: Use the model to predict the price of a demonstration car with a specific odometer reading (e.g., 200 km).
- Evaluation: Assess the suitability and accuracy of the mathematical model.
- Documentation: Include screenshots, acknowledgments of sources, and evidence of progress at checkpoints.
- Submission Compliance: Follow authentication strategies including plagiarism detection and in-class observation.
Learning Objectives Covered:
- Apply mathematics to real-world financial decisions.
- Analyze data and identify relationships between variables.
- Develop and evaluate mathematical models.
- Communicate findings clearly in a structured report.
- Demonstrate ethical academic practices and proper documentation.
Approach Guided by the Academic Mentor
Step 1: Understanding the Task
The mentor first helped the student interpret the assessment requirements, ensuring clarity on the aim: exploring the relationship between odometer readings and car prices. They discussed the importance of selecting reliable and individualised data from carsales.com.au.
Step 2: Data Collection Guidance
The mentor guided the student to:
- Select the specific make, model, and year assigned.
- Record a sample of advertised prices and odometer readings.
- Take screenshots for the appendix as evidence of data collection.
- Maintain an organised dataset for analysis.
Step 3: Analysis and Model Development
The mentor walked the student through:
- Plotting the collected data to visually examine trends.
- Identifying the type of relationship (linear, exponential, or otherwise).
- Developing a mathematical model (e.g., linear regression) to represent the relationship between odometer reading and price.
- Using the model to make predictions for given odometer readings, like 200 km.
Step 4: Evaluation of the Model
The mentor guided the student to:
- Test the model’s accuracy using sample data points.
- Reflect on assumptions and limitations (e.g., variation due to car condition or market factors).
- Include a critical evaluation in the report about the suitability of the model for making pricing predictions.
Step 5: Report Structuring
The mentor advised on structuring the report to ensure clarity and logical flow:
- Introduction and context.
- Data collection methods and presentation (including screenshots).
- Analysis and model development.
- Prediction using the model.
- Evaluation and conclusion.
Step 6: Compliance and Documentation
The mentor ensured that the student followed authentication strategies:
- Citing all sources appropriately.
- Submitting work via Turnitin.
- Providing progress documentation at checkpoints.
Outcome Achieved
- The student successfully gathered individualised data for the assigned car model.
- A clear mathematical model showing the relationship between price and odometer reading was developed.
- Predictions for specific odometer readings were made and evaluated.
- The final report was well-structured, properly documented, and aligned with authentication and academic integrity standards.
Learning Objectives Met:
- Mathematical modelling of real-life scenarios.
- Data analysis and interpretation skills.
- Ability to make evidence-based predictions.
- Critical evaluation of model suitability.
- Effective communication of mathematical findings in a professional report format.
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