Equations

Equations can be the most daunting element of maths and science. Everything is going along nicely in a lesson, then a big load of numbers and symbols appear on the page, and the mists of confusion descend. In the next few sections, we will give you the tools you need to help clear those mists. We will start by explaining what the elements of equations mean.

First and foremost, the meaning of the word equation is important. It means that what’s written on one side of an equals sign always equals what’s written on the other. Or at least it does if you have got it right! The bits of an equation on either side of the equals sign are simply called sides.

The items in the equations that represent numbers or values are known as terms or variables. For example, increment y or r2 are terms in an equation.

In maths, science, and technology, Greek symbols are often used in equations. These symbols have different meanings depending on where they are used. The link below provides some more information:

https://www.electronics-notes.com/articles/basic_concepts/letters-symbols/greek-alphabet-characters-list.php

With the horizontal lines used in equations, what is written above the line is divided by what is written below the line, just like in the fractions we saw earlier. As in a fraction, the term(s) on the top is called the numerator, and the term(s) below the line is the denominator. For example:

fraction numerator increment y b to the power of r over denominator increment x space cross times space 10 to the power of negative 12 end exponent end fraction space equals space 15 alpha space minus space 22

The numerator increment y b to the power of r is divided by denominator  increment x space cross times space 10 to the power of negative 12 end exponent.

Brackets in equations mean that everything in the bracket is subject to the action shown on the outside. For example, in (2a + c2)b the 2a + c2 is raised to the power of b.

Equations don’t tend to feature the multiplication sign × they just show the two numbers or terms next to each other without a gap. In CIBD lessons, we don’t use the multiplication sign × so when you see 2b this means 2 × b. If you see an × it may be in an order of magnitude like b × 103.

Equations are mathematical expressions of actions that are done to numbers. As a very simple example, if you get paid $200 per hour for your standard eight-hour shift and then $300 per hour for every hour after, you can use this formula to calculate how much you earn when working an 11.5-hour day (and you are very lucky).

a space equals space t o t a l space w o r k i n g space h o u r s x space equals space p a y y space equals space s tan d a r d space p a y space r a t e mu equals o v e r t i m e space p a y space r a t e delta equals s tan d a r d space s h i f t space h o u r s

x space equals space left parenthesis y space cross times space delta right parenthesis space plus space mu space left parenthesis a space minus space delta right parenthesis

x space equals space left parenthesis $ 200 space cross times space 8 space h o u r s right parenthesis space plus space $ 300 space left parenthesis 11.5 space h o u r s space minus space 8 space h o u r s right parenthesis

P a y space equals space $ 1 comma 600 space plus space $ 1 comma 050 space equals space $ 2 comma 650

When dealing with equations, keep in mind what everything means. If you understand what is being asked and what information is provided, you are much more likely to notice when a mistake is made. It is also important to include units in calculations as these will help you check your answer.

Equations in CIBD exams

In the CIBD online exam system it is not possible to set equations out in the same way as in the lessons. Instead you need to show them in the linear format. In the linear format the equation below:

r space equals space square root of fraction numerator open parentheses 2 a space plus space 7 b close parentheses space d over denominator c end fraction end root

Would be shown like this:

r = √((2a + 7b)d)/c

And this one for Stoke's law:

v space equals space 2 over 9 fraction numerator open parentheses p subscript p space minus space p subscript f close parentheses over denominator mu end fraction space g R squared

Would be shown as:

v = 2/9 x [(ρp - ρf)/μ] x g x R^2

You can still write out the equation on paper in the same format as in the lessons, you just need to input them in the system in the linear format. There is more guidance on maths notation on the start page of your Diploma learning materials.

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