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Standard Foundation Program/TPP

Mathematical Methods

MATH1232E

Graphing Assignment

Context and Task

Polynomial curves can  be found  in  numerous  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 can be 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 (not including the title page, table of contents, references list and appendices). You must use a software package such as Microsoft Excel, MATLAB 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,  MATLAB  or  Desmos)  throughout  your response.