PSMT Math Methods

Summary:

This note concerns a task on PSMT Math Methods, completed in 2020 for the Mathematical Methods Unit 1, intended for Year 11 students. The objective of the task was to develop proficiency in creating parabolic models using a bridge image. The assignment was assessed using the marking criteria established by the Queensland Curriculum and Assessment Authority (QCAA) and received a score of 20/20.

Excerpt:

PSMT Math Methods

Introduction
All architectural structures are formed from a combination of basic and complex shapes, regardless of their purpose. For instance, domes, arches, and beams are all simplistic components of large constructs. Certain
qualities of these design features can all be expressed mathematically in terms of mathematical equations.
Structures that have curvature or arches, such as bridges, can be described in polynomial terms, where the apex of the arch can be considered as the vertex. This report is going to investigate how various mathematical functions can be generated to model the shape of the Walterdale Bridge in Edmonton, Canada, primarily fixating on polynomial and piece-wise defined functions as well as the sum of two even degree polynomials, of which the form of ?(?) = ??? ? + ??−1? ?−1 + ??−2? ?−2 + ⋯ . . +?1? 1 + ?0 was considered.

To accomplish the purpose of this report, both technological and algebraic procedures were required to develop several models. This included the determination of quadratic and quartic rules and functions, simultaneous equation solving, and technology such as a graphics calculator with its software counterpart. A model’s feasibility was verified by considering the coefficient of determination (R2) using excel and through re-modeling functions in a graphical manner on a graphics calculator to highlight possible errors in the calculation process.

Body – Assumptions
Before the calculation process and the generation of models was conducted, several assumptions were made to ensure the problem was solved appropriately to valid solutions. The height and length values concerning the bridge were obtained from a reliable source, Acciona Construction (https://www.accionaconstruccion.com/pressroom/in-depth/2019/julio/walterdale-bridge-major-engineering-feat-enhances-city/), therefore it was assumed these values were true and exact for calculation purposes.