MATHEMATICAL METHODS ASSESSMENT 3: GRAPHING PROJECT
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Program
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Standard Foundation Program and Tertiary Preparation Program
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Cohort
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October 2024
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Course
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Mathematical Methods
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Course Code
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MATH1102E
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Assessment Name
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Assessment 3: Graphing Project
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Weighting
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20%
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Context and Task
Polynomial curves are found in many locations in the world. Bridge arches, water fountains, rollercoasters, roads, telecommunications dishes and natural landscapes can all feature polynomials in their outline/structure. Additionally, projectiles and any object/material acted on by gravity when in free motion exhibit a trajectory that is modelled accurately by a parabolic curve.
Photo credit: https://www.dreamstime.com/stock-photo-water-dry-fountain-park-close-up-image98389957#_
Your task is to locate one curve either in nature or in a human-made structure that can be represented effectively by a polynomial. Alongside this, you are to generate one curve in real-life using an object such as a football, tennis ball, a free hanging chain or a water hose. You are to photograph and digitise these two curves using appropriate technology. Software such as ImageJ (https://imagej.nih.gov/ij/) can be useful in the digitisation process.
After this you will develop two separate polynomial functions that precisely model the shape of these two curves. In addition, you are to write a report that explains how you developed and refined your models. This report must be less than 8 pages in length (using single spacing not including the title page, table of contents, references list and appendices). You must use a software package such as Microsoft Excel or Desmos (free to use at www.desmos.com) to develop, modify and display your curve data. You must also verify the validity of your curve models by using analytical techniques (pen and paper methods).
When presenting the development of your mathematical models in the report you must consider, refine and evaluate at least three polynomial functions for your two curves. For assistance on how to structure and write your report please read the following high-level exemplar provided by the Queensland Curriculum and Assessment Authority (QCAA):
https://www.qcaa.qld.edu.au/downloads/senior-qce/mathematics/snr_maths_methods_19_unit1_asr_high_psmt.pdf
To successfully complete this assignment, you must do the following:
• Present your findings as a report based on the approach to problem-solving and mathematical modelling outlined in the exemplar/s provided by your teacher. Your teacher will discuss this with you in more detail during class time.
• Respond with a wide range of understanding and skills, such as using appropriate mathematical language, calculations, and tables of data, graphs and diagrams.
• Provide an authentic response that highlights this real-life application of mathematics. Do NOT use data collected by someone else.
• Respond using a written report format that can be read and interpreted independently of the assignment task sheet.
• Follow the requirements of the Marking Criteria Sheet (Rubric) (see the following page).
• Use both analytic (pen and paper) procedures and technology (Microsoft Excel or Desmos) throughout your response.
The report you produce to present your results must include these components:
• Introduction: Provide a detailed outline of the task, all your assumptions and observations, and clearly define all the mathematical and computational techniques used in the report.
• Results: Include and discuss tabular and graphical representations of the data collected.
• Discussion: Further discuss your results by evaluating the accuracy of your model/s, detail the strengths and limitations of the modelling process that you used, and comment on the reasonableness of your model/s.
• Conclusion: Include a brief summary of your findings, and the strengths and limitations of your best model.
• References List: Use the APA referencing scheme.