Examiners in the HSC Advanced Mathematics (2 unit) course have commented that many students become confused when the constant 𝜋 is used in calculations. What is it about 𝜋 that causes problems? Students from an early age learn that 𝜋 is the ratio of the circumference of a circle to its diameter and so this reinforces the geometrical interpretation of 𝜋. However, 𝜋 can be involved in problems that have no connection with circles and this is when confusion in examination answers can arise. Some students convert an answer involving 𝜋 into revolutions or degrees just because of the connection of 𝜋 to the geometry of a circle. Pi is a number, an irrational number, and should be treated like any other number in calculations. In the 2015 Mathematics examination question 15 c involved calculating the time when the volume of water in a pool first started to decrease given the rate of change of the volume. The answer was 2𝜋 seconds and many candidates lost marks by converting this into degrees.
Physics and Mathematics
What are the concepts in Physics and Mathematics that students find difficult? In this blog I will post tutorial points that I hope will stimulate thinking and so broaden the knowledge and understanding of students allowing them to write thorough examination responses. Tutorial sheets, structured from a student's point of view, will be posted on the HSC, IB and university level topics of Relativity, Electromagnetism, Mechanics, Quantum Physics and Calculus. The overall purpose of these pages is to encourage and promote learning in Physics and Mathematics and so open new horizons in learning.