To apply mathematics to the real world, mathematicians will convert real-life situations and problems into mathematical terms, and then attempt to solve the resulting equations. The real-life situations are usually (at first anyway) simplified by making certain assumptions. We call this process Mathematical Modelling, and it’s a key part of the A Level maths curriculum.
Modelling helps us understand the world and design the technology of the future. With modelling, we can travel far into the universe, look into the depths of the atom, or understand the future of our climate.
Modelling is so important for A Level maths students to learn because it helps you form connections between maths and other STEM subjects like physics and engineering.
Common mathematical modelling terms
The following table shows some common terms in physics and mechanics and the assumptions they bring with them when used in models.
|
Model |
Assumption |
|
Air Resistance |
Usually ignored. |
|
Bead – a particle with a hole in it for threading on a wire or string |
Moves freely along a wire or string. Tension is the same on either side of the bead. |
|
Beam – like a pole |
Ignore its thickness. Its mass is concentrated along a line. It does not bend. |
|
Gravity |
It’s uniform, acts vertically downwards and is about 9.8 m s-2 unless stated otherwise. |
|
Inextensible |
It does not stretch. |
|
Lamina – like a sheet of paper |
It has an area but ignore its thickness. |
|
Light object |
Ignore its mass. |
|
Particle – like a single point |
Assume it has no mass or dimensions. |
|
Peg – a support from which something can hang |
Ignore its dimensions. |
|
Rod – see Beam |
See Beam. |
|
Rough |
Take friction into account. |
|
Smooth |
Ignore any friction. |
|
Uniform |
Its mass is either evenly spread throughout the body or is concentrated at a single point. |
|
Wire – like a thin metal beam/rod |
See Beam. |
SI Units
To understand how models are put into practice, we also have to understand SI units. SI stands for the French words Système International d’unités – The International System of Units.
It consists of just three base units from which other units are derived.
The base units are Mass, Length and Time.
Quantity Unit Symbol
Mass kilogram kg
Length metre m
Time second s
Speed, for example, is measured in the base units metres per seconds : m s-1.
Force is measured in the base units kilograms, metres and seconds : kg m s-2 (or Newtons).
Understanding these concepts will set students up for top results in their A Level maths exams. As a TuitionWorks tutor, I work with students to help them master these core concepts, and more, through a course of personalised, one-to-one lessons.
If you think you could benefit from advanced A-Level maths tutoring from a qualified teacher, get in touch for a free consultation.
Rajiv B
Maths tutor at TuitionWorks
I have been teaching and tutoring for over 35 years now, with an excellent rate of success and glowing references from literally scores of past pupils.
About me: At the age of 10, I was awarded a 7-year scholarship to Loughborough Grammar School and went on to study Mathematics at Keele University and then at Oxford University.
