Mnemonics...

Memorisation's Not Easy, Memory Often Needs Initial Clues

Being able to memorise facts and information is absolutely essential for success.

However, it can often be extremely difficult to remember information, especially when so many maths formulas are just a series of numbers and letters.

Don't panic. There is a system that can help.

Using acronyms, rhymes and songs can help to 'download' complex information. These are known as mnemonics and are systematic procedures for enhancing memory.

I am sure you have already come across these in school, perhaps without even realising it! They can be applied to all subjects to help with the memorisation of important facts. Mnemonics help you to remember an idea or phrase with letter patterns, number patterns or by relatable associations. They include rhymes, poems, acronyms, songs, outlines, images and much more.

There are so many examples of mnemonics; 'i before e, except after c,' is very well known for spelling in English. I know how to spell 'because', because I know that 'Big Elephants Can't Always Use Small Exits.' I no longer need to repeat it out loud, but I always repeat the rhyme in my head, even now as an adult.

For me these are one of the best ways to help remember tricky maths formulas or strategies for an exam. There are often multiple versions for remembering the same fact or idea, and there is no hard and fast rule as to which ones should be used, which ever ones work best for you.

I have collected below some of the most used mnemonics to help you with your mathematical study. Some you might already know, others, I hope will help you!

BIDMAS

Possibly the most widely known mnemonic in maths, but, arguably the most useful. Sometimes called BODMAS. This funny looking word can be used no matter what level of maths you are studying, so it is well worth getting this one down.

Here the letters of the word represent the order for which calculations should be performed in an equation.

B = Brackets

I = Indicies

D = Division

M = Multiplication

A = Addition

S = Subtraction

This is how it works...

Solve:

4 + 2(10 - 7)

We use BIDMAS to tell us that the first thing we need to do is look at the brackets.

So '10 - 7 = 3'

So we now have... 4 + 2( 3 )

Next we need to do the multiplication 2( 3 ) which means 2 x 3 = 6

Leaving us... 4 + 6

Lastly we do the addition 4 + 6 = 10

So, we have the answer 10.

This is a relatively simple example, however it can be an extremely useful system when the equations are long and complex. Especially, since even for this straightforward example, performing the calculations in any other order would give the incorrect answer.

FOIL

Similar to BIDMAS, the letters for FOIL, represent the order to help multiply double brackets out correctly. This is a strategy I return to time and time again to ensure correct multiplication of brackets. The letters are as follows:

F = First

O = Outer

I = Inner

L = Last

This is how it is to be applied...

Multiply out the brackets:

(x + 2)(x + 5)

F - First. So we multiply together the first two terms in the brackets, which are x and x.

Giving us x^2. (This means 'x to the power of two' or 'x squared')

O - Outer. Next we multiply together the outer terms in the brackets, which are x and 5. This equals 5x.

I - Inner. Now we multiply together the inner terms in the brackets, which are 2 and x, equalling 2x.

L - Last. Finally we multiply together the last terms in the brackets, which are 2 and 5. This equals 10.

So we can write out these individual terms together to give:

x^2 + 5x + 2x + 10

Finally, to complete this we collect like terms:

x^2 + 7x + 10

A great mnemonic to guarantee you are multiplying out ALL the terms in the brackets correctly, otherwise it can become confusing and unclear which terms you have expanded. A word of caution, it is important to note + and - signs of the terms inside the brackets and be careful to multiply correctly.

This leads me to my next mnemonic...

Minus Times a Minus is a Plus

A simply little phrase, but again one that repeats in my head even now. Multiplication and division of negative numbers can become a nightmare especially when involved in an algebraic equation.

This mnemonic can be a great one to return to if you find yourself a little confused or flustered in an exam.

Just take a breathe and remember that 'a minus times a minus is a plus'.

Also, 'a minus divided by a minus is a plus'.

This is how it is to be applied...

What is:

(-4) x (-3)

We know that 4 x 3 is 12, and we can see that both the numbers are negative therefore, the answer is positive.

so, (-4) x (-3) = 12

Here is another example, but a little more in depth...

Multiply out the brackets:

(x - 2)(x - 5)

F - First. So we multiply together the first two terms in the brackets, which are x and x.

Giving us x^2. (This means 'x to the power of two' or 'x squared')

O - Outer. Next we multiply together the outer terms in the brackets, which are x and -5. This equals -5x. (Minus times a plus is minus)

I - Inner. Now we multiply together the inner terms in the brackets, which are -2 and x, equalling -2x. (Minus times a plus is minus)

L - Last. Finally we multiply together the last terms in the brackets, which are -2 and -5. This equals 10. (A minus times a minus is a plus!)

So we can write out these individual terms together to give:

x^2 - 5x - 2x + 10

Finally, to complete this we collect like terms:

x^2 - 7x + 10

This is a great example of how to use two mnemonics and rules in conjunction with each other.

SOH CAH TOA

A key mnemonic for those studying GCSE mathematics!

SOH CAH TOA refers to trigonometry and how to calculate the side lengths or angles of a right angled triangle. The mnemonic helps you to remember and decide which trigonometric ratio is the one to use for the question you have been given.

It means:

SOH > Sin(x) = side Opposite the angle / Hypotenuse

CAH > Cos(x) = side Adjacent to the angle / Hypotenuse

TOA > Tan(x) = side Opposite the angle / side Adjacent to the angle

With a right angled triangle that looks like this:

I can remember the word SOHCAHTOA because it sounds like the volcano Krakatoa. However, for those who might struggle with just the word, there are a few mnemonic rhymes to help.

Some of these are...

Some Of Her Children Are Having Trouble Over Algebra

Some Old Horses Can Always Hear Their Owner’s Approach

Silly Old Harry Chased A Horse Through Our Attic

or you can always make your own.

Circle Formulas

I would always get confused with circle formulas. Which one was circumference and which one was area?

This super handy little rhyme is a great one to help if you are like me and get the formulas mixed up.

It goes as follows...

Cherry pie's delicious!

Apple pies are too!

Here both the words and letters relate to the formula.

C=πd

A=πr^2

Let's break it down with the rhyme.

Cherry pie's delicious!

Circumference = π x d

Apple pies are too

Area = π x r ^ 2

This is the perfect example of how mnemonics work not only with letter associations, but with sounds as well.

Get Creative!

These are just a few of the endless systematic procedures to enhance your memory this exam season! Mnemonics, can be used to help you remember more than just maths formulas, for example, mnemonics to help remember History dates, English essay quotes and so much more.

Use them in all subjects areas to really take your revision to the next level.

Dont be afraid to create your own mnemonic if you can't find one that works for you.

There aren't really any rules, as long as you can remember it thats all that matters.

You can even find mnemonic device generators online!

If you need more help with your maths revision book in with me for a revision and exam prep session. We will use tools like mnemonics and more to ensure your are as prepared as you can be for your exam.