# How to learn math formulas

By Murray Bourne, 25 Jan 2009

In a recent IntMath Poll, readers indicated that the hardest thing about math was learning the formulas.

Here are 10 things you can do to improve your memory for math formulas.

## 1. Read ahead

Read over tomorrow’s math lesson today. Get a general idea about the new formulas in advance, before your teacher covers them in class.

As you read ahead, you will recognize some of it, and other parts will be brand new. That’s OK - when your teacher is explaining them you already have a "hook" to hang this new knowledge on and it will make more sense — and it will be easier to memorize the formulas later.

This technique also gives you an overview of the diagrams, graphs and vocabulary in the new section. Look up any new words in a dictionary so you reduce this stumbling block in class.

This step may only take 15 minutes or so before each class, but will make a huge difference to your understanding of the math you are studying.

I always used to read ahead when I was a student and I would be calm in class while all my friends were stressed out and confused about the new topic.

## 2. Meaning

All of us find it very difficult to learn meaningless lists of words, letters or numbers. Our brain cannot see the connections between the words and so they are quickly forgotten.

Don’t just try to learn formulas by themselves — it’s just like learning that meaningless list.

When you need to learn formulas, also learn the **conditions** for each formula (it might be something like "if x > 0").

Also draw a relevant diagram or graph each time you write the formula (it might be a parabola, or perhaps a circle). You will begin to associate the picture with the formula and then later when you need to recall that formula, the associated image will help you to remember it (and its meaning, and its conditions).

During exams, many of my students would try to answer a question with the wrong formula! I could see that they successfully learned the formula, but they had no idea how to apply it. Diagrams, graphs and pictures always help.

Most of us find it difficult to learn things in a vacuum, so make sure you learn the formulas in their right context.

When you create your summary list of formulas, include conditions and relevant pictures, graphs and diagrams.

## 3. Practice

You know, math teachers don’t give you homework because they are nasty creatures. They do it because they know repetition is a very important aspect of learning. If you practice a new skill, the connections between neurons in your brain are strengthened. But if you don’t practice, then the weak bonds are broken.

If you try to learn formulas without doing the practice first, then you are just making it more difficult for yourself.

## 4. Keep a list of symbols

Most math formulas involve some Greek letters, or perhaps some strange symbols like ^ or perhaps a letter with a bar over the top.

When we learn a foreign language, it’s good to keep a list of the new vocabulary as we come across it. As it gets more complicated, we can go back to the list to remind us of the words we learned recently but are hazy about. Learning mathematics symbols should be like this, too.

Keep a list of symbols and paste them up somewhere in your room, so that you can update it easily and can refer to it when needed. Write out the symbol in words, for example: ∑ is "sum"; ∫ is the "integration" symbol and Φ is "capital phi", the Greek letter.

Just like when learning whole formulas, include a small diagram or graph to remind you of where each symbol came from.

Another way of keeping your list is via flash cards. Make use of dead time on the bus and learn a few formulas each day.

## 5. Absorb the formulas via different channels

I've already talked about writing and visual aids for learning formulas. Also process and learn each one by hearing it and speaking it.

An example here is the formula for the derivative of a fraction involving x terms on the top and bottom (known as the "Quotient Rule"). Then in words, the derivative is:

dy/dx = bottom **times** derivative of top **minus** top **times** derivative of bottom **all over** bottom squared.

The formula is actually as follows, if we let u = numerator and v = denominator of the fraction, then:

## 6. Use memory techniques

Most people are capable of learning lists of unrelated numbers or words, as long as they use the right techniques. Such techniques can be applied to the learning of formulas as well.

One of these techniques is to create a story around the thing you need to learn. The crazier the story, the better it is because it is easier to remember. If the story is set in some striking physical location, it also helps to remember it later.

## 7. Know why

In many examinations, they give you a math formula sheet so why do you still need to learn formulas? As mentioned earlier, if students don’t know what they are doing, they will choose a formula randomly, plug in the values and hope for the best. This usually has bad outcomes and zero marks.

I encourage you to learn the formulas, even if they are given to you in the exam. The process of learning the conditions for how to use the formula and the associated graphs or diagrams, means that you are more likely to use the correct formula and use it correctly when answering the question. This is also good for future learning, because you have a much better grasp of the basics.

## 8. Sleep on it

Don’t under-estimate the importance of sleep when it comes to remembering things. Deep sleep is a phase during the night where we process what we thought about during the day and this is when more permanent memories are laid down. During REM (rapid eye movement) sleep, we rehearse the new skills and consolidate them.

Avoid cramming your math formulas the night before an exam until late. Have a plan for what you are going to learn and spread it out so that it is not overwhelming.

## 9. Healthy body, efficient brain

The healthier you are, the less you need to worry about sickness distracting from your learning. Spend time exercising and getting the oxygen flowing in your brain. This is essential for learning.

## 10. Remove distractions

This one is a problem for those of us that love being on the Internet, or listening to music, or talking to our friends. There are just so many things that distract us from learning what we need to learn.

Turn off all those distractions for a set time each day. You won’t die without them. Concentrate on the formulas you need to learn and use all the above techniques.

When you are done, reward yourself with some media time — but only after you have really accomplished something.

## You may also find useful...

How to Understand math Formulas

Ten Ways to Survive the Math Blues

See the 55 Comments below.

26 Jan 2009 at 9:32 am [Comment permalink]

Great list, thanks Zac. This is something all math students should practice.

26 Jan 2009 at 1:53 pm [Comment permalink]

thanks........

27 Jan 2009 at 9:37 am [Comment permalink]

Thank you so much...this list has some brilliant tips and it's really helpful. I've printed them out and stuck them in my file to remind me because I think they will really help me with my maths. Thanks again! š

27 Jan 2009 at 5:35 pm [Comment permalink]

Brilliant idears am so much greatful for them.Thanks to Almighty and you.

27 Jan 2009 at 6:39 pm [Comment permalink]

Thanks it's a great one for all.keep it up.

28 Jan 2009 at 1:18 am [Comment permalink]

Thanks alot, I am going to immediately print it and hang it in my room.

28 Jan 2009 at 2:13 pm [Comment permalink]

Thanks for your advice, hope it will help me alot. I would like to request for some tips in passing statistics and probability.

3 Feb 2009 at 2:43 pm [Comment permalink]

Hi

thanks for the tips.Really helpful.I am easily distracted these days so this is kinda like a wake up call for me.Really need to concentrate so thanks for the advice.Have been doing some of the things you said but not all.Anyway thanks again.

8 Feb 2009 at 1:46 am [Comment permalink]

thanks for your tutor....hope my benefit....but i wonder that is smart in math born with human or its a matter of aquistion..?

13 Feb 2009 at 2:25 am [Comment permalink]

thanks for innovative suggestions.

20 Feb 2009 at 4:24 pm [Comment permalink]

Dear Sir,

I thank you for the valuable information. Actuallyy I would not have come across such a nice tips about maths until I got an e-mail from you. Now I can provide new inputs about maths to some of my student so that they will find it as an interesting one.

Thanks once again. Please keep in touch with me.

4 Mar 2009 at 10:35 pm [Comment permalink]

Wonderful info, I use it in teaching my high school classes and college classes.

31 May 2009 at 3:37 pm [Comment permalink]

thanks

2 Jun 2009 at 5:55 am [Comment permalink]

thank you for the tips and how to learns...

I still dont get trig and the sine and cosine graphs, i guess i may never learn it

nice site

2 Jun 2009 at 8:57 am [Comment permalink]

Hi Eileen. Don't give up on trigonometry! Feel free to use the "Comments? Questions?" facility in Interactive Mathematics to ask your questions.

25 Jun 2009 at 8:16 pm [Comment permalink]

thanks for ur suggestions sir.......

3 Jul 2009 at 1:26 am [Comment permalink]

Please explain the following:

2.38E-06

Thanks.

3 Jul 2009 at 9:13 am [Comment permalink]

Hi Wyatt. You'll see this as a result in MS Excel when the answer is very small (as in this case) or very large.

2.38E-06 means 2.38×10

^{-6}, which is actually0.000 002 38

For more information, see: Scientific Notation

5 Jul 2009 at 5:07 pm [Comment permalink]

thanks a lots carry on

15 Apr 2010 at 6:25 am [Comment permalink]

[...] Murray of squareCircleZ offers some valuable advice for students in How to understand math formulas. This is a great follow-up to his article How to learn math formulas. [...]

19 Apr 2010 at 3:50 pm [Comment permalink]

tips or no tips; maths is always boring!!

......just joking!

what one needs is a little interest in the subject and a good teacher, who of course,always gives good tips!!

23 May 2010 at 10:20 pm [Comment permalink]

thank you for letting me know that and ad

like to learn more

28 Jun 2010 at 5:58 pm [Comment permalink]

Thanks for providing the information.

It is very useful to me.

I have printed this page and on my study table

22 Oct 2010 at 7:16 pm [Comment permalink]

really helpful..I like to learn about language..after read this site, I can't see any reason why I couldn't understand math..thank you so much...^_^

16 Jan 2011 at 6:05 am [Comment permalink]

One way is by applying the formula to solve problems. This gives meaning, indicates the usefulness of the formula and makes it familiar. Thus facilitating retention. Formulas can also be listed in a logical order. For instance, I find it easy presenting the trigonometric identities in the sequence: Basic trigonometric ratios, Pythagorean Square identities, Compound angle identities, Double angle identities, Triple angle identities, the factor formula, and the half angle identities which is based on their relationship to each other.

16 Jan 2011 at 11:54 am [Comment permalink]

Good suggestions, Jaff.

28 Mar 2011 at 8:04 pm [Comment permalink]

i agree with evey thing that you say apart from listening to music i find if your in a class room full of kids that dont really want to learn about the subject and there is a few that do putting your head phones in and blocking your self from thoses who dont want to learn is one of the best things that you can do it foucus you to whats in front of you not whats going on around you ... but other than that i agree with every thing

28 Mar 2011 at 8:19 pm [Comment permalink]

Good point, Samuel. But the type of music is important - some can be very distracting, while other types are great for helping you concentrate, and it varies between people.

1 May 2011 at 6:01 pm [Comment permalink]

Thanks a lot well i will keep these in my mind and try to take these formullas

7 May 2011 at 1:23 am [Comment permalink]

Thanks for these words of wisdom.

It is very useful to every students as well as teachers too.

I have already sent these useful hints to my university and High school children.

I wish to all read again and again.

I specially recommend parents that last tip which I am facing too ( 10. Remove distractions )

11 May 2011 at 12:44 am [Comment permalink]

These tips are very useful. I will share them with my students who will be starting their G.C.E. examinations on the 30th of May.

I have also noticed that it is very essential for teachers to alert the students of the formulas they are expected to remember.

9 Jun 2011 at 2:51 am [Comment permalink]

thanks for the information , with this l know solving math will not be a problem for me anymore

23 Jun 2011 at 1:54 pm [Comment permalink]

Thanks Murray,for your tips. They have been very useful.

20 Jul 2011 at 8:56 pm [Comment permalink]

these tips being so useful for me,,,,

23 Jul 2011 at 12:18 am [Comment permalink]

very good ideas

17 Aug 2011 at 11:38 pm [Comment permalink]

m really vry happy by this....useful to me nd evryone wants to grow his knowlegge.......thnx a lot

12 Sep 2011 at 11:56 pm [Comment permalink]

I hav been loaded wit great words 2 d understanding of mathematics thanks alot.am going 2 print mlne now.

30 Nov 2011 at 1:00 am [Comment permalink]

plz .send me how do How to learn math formulas article .

30 Nov 2011 at 4:49 pm [Comment permalink]

@milad: ?? The article is on this page!

20 Jan 2012 at 4:41 pm [Comment permalink]

Thanks 4 dis tip well it my first time of reading such a wonder ways of learning fomular. I wil like 2 knw more abut diffrenciation. Once agian tank u

20 Jan 2012 at 4:48 pm [Comment permalink]

Thanks Paul and I'm glad you found it useful. The Differentiation chapter starts here:

Introduction to Differentiation

There are 2 more chapters on differentiation after that.

3 Feb 2012 at 2:33 pm [Comment permalink]

Thanks. it is very essential for teachers to alert the students of the formulas they are expected to remember.

I am a teacher

24 Mar 2012 at 11:43 pm [Comment permalink]

What a Renaissance Man! You've obviously brushed up on your cognitive psychology - these tips are spot on!

Thanks for your work on this fabulous site!

25 Mar 2012 at 6:57 am [Comment permalink]

@alkaline322: Thanks for your lovely comment - made my day!

8 Jun 2012 at 2:31 pm [Comment permalink]

huge kind of information u give to me.

thanx for that

i alwayas thought that i m not a good mathematician.

but now i realise that

thanx

24 Jun 2012 at 6:37 am [Comment permalink]

Thnx soooo much and you r the best.

17 Oct 2012 at 9:00 pm [Comment permalink]

Thank you for this tips... I hope I become a successful in math world....

23 Jan 2013 at 5:03 pm [Comment permalink]

this is the best way of learning maths formula

16 Feb 2013 at 5:25 am [Comment permalink]

This is really helpful to students,and huge information. thanks a lot

15 Mar 2013 at 5:56 pm [Comment permalink]

Thanks a lot for these tips you ve pasted.God bless more strength to Ur elbow.

29 Mar 2013 at 4:42 pm [Comment permalink]

its really important to all those students, who want to learn maths with fluently. they have to read the formulas and copy them & paste it in thire room. because without of formulas we can not camand on maths.

16 Apr 2013 at 11:13 pm [Comment permalink]

Thanks so much for the skills and advise.I want to be more serious now and I'm sure with your advise I will be able to bombard maths. May God be with you.

26 Mar 2015 at 12:35 am [Comment permalink]

I Really Love These Tips

24 Mar 2016 at 2:53 am [Comment permalink]

Nice tips for memorizing

29 Jun 2016 at 5:58 am [Comment permalink]

I agree that you should have a healthy body in order to study. I think that it is important to be able to be at your best to learn. That way you are not distracted by being tired.