Most people have a hard time memorizing mathematical formulas. Yet, some tests require memorizing formulas and students have a hard time with it.
I have developed a technique to learn those formulas quickly and keep them in memory for weeks without thinking about them again. I used it in my last statistics exam to memorize almost 60 formulas and after half a year I am still able to write them down.
The hardest part of this technique is to be able to find the right formula for the given question.
Because it is not about understanding the formula. It is about memorizing each part of it. Quickly.
Here is how you do it in three steps:
- Break the formula up in all parts you need to memorize (variables, numbers, operands)
- Substitute all parts with something you can remember (there is a simple method to it, which I will cover in just a second)
- Glue all parts back together by telling a crazy story
After you determined what parts you need to remember in step 1, you will now learn how you can substitute those abstract parts with something we can remember.
By the way, I have recorded a free video explaining the whole concept on an example (namely the quadratic formula). Look for the link below.
After you have understood how this technique is working you should create your own substitution rules because they usually work better that way. Until then, here are mine:
- Variables: Animals starting with the letter of the variable
- Numbers: If numbers are combined with variables, picture “two apes” for “2a”. If its like “a+2” I picture an ape running towards two things (like bananas).
- Plus: Everything combined with a plus I picture in a row like little ducks running behind their mother one after another.
- Minus: I remember minus like the plus sign, but the minus sign makes whatever comes after it annoyed or angry.
- Multiplication is parallel for me. All parts of the equation want to do something at the same time.
- The division line puts everything underneath below the earth surface.
- Power: I always take whatever the base is and picture babies of it. As a general rule I put everything in the exponent in “baby form”.
- Square root (sqrt): Most of the time I visualize a bus-stop or a giant wooden root covering everything in it.
Now that we have a substitution of all parts of the formula, we can move to step three and tell a story, that helps us memorize all parts in order.
First, we should pick a base. Look around you and take something that you can remember. I, for instance, have a glass of water in front of me, that I am going to use as my base. It is a good idea to take a different base for each formula to avoid confusion.
Here is an example:
We will memorize this formula: (x – y)^3 = x^3 – 3x^2y + 3xy^2 – y^3
Our formula parts are:
- x… X-ray fish (a fish with a highly transparent body)
- y… yak (The yak is a long-haired bovine found throughout the Himalayan region)
Now, I will visualize my glass of water and create a story of all parts while reading the formula from left to right:
There is a giant glass of water in front of my table. In it, a x-ray fish and a yak are fighting to save their children from drowning. Two fish-yak baby hybrids made it already out of the glass, the third one is just getting pushed up by the angry yak. The yak is angry, because he told the kits not to play near the giant water-glass and yet they did and fall into it. All this is getting observed by an x-ray fish mother walking by, carrying her three babies safely on her shoulders. (picture a fish with shoulders and walking on their fins.)
The mother fish is so in a brown study, that she oversees three other animals and crashes with them: an x-ray fish father, with his two kits (twins!) and a yak mother pushing an empty baby buggy. And an invisible animal which she cannot see, but smell: it smells awful! “Can’t you pay attention when you are walking?” the three animals yell at the mother angrily.
The mother-fish walks away and after some time she thinks she has a deja-vu: Again, three animals (those invisible animals really stink – what are they?) are walking towards her. But when she looks closer, she sees that this time there are no kits on the fish-shoulders, but twins on the yak-shoulder, while the baby buggy is still empty. The mother-fish avoids crashing into them and all pass by happily.
The mother fish looks back, wondering why the yak is carrying their kits on the shoulder instead of putting them in the baby buggy, as she crashes into a big body-builder-yak. “Where are you looking at?” the body-builder-yak is yelling. The mother fish ducks and walks faster to get away. What a yak! He had muscles that looked like three kits are sitting on his back!
I recommend to go through the story in your head and look at the formula at the same time to make sure you have memorized everything correctly.
After that, you should be able to write the formula down without looking at it again. If that is not the case I recommend to create your own story.
To create a story that you can remember it is important to not just put story parts together, but let them interact with each other. I, for instance, would not let the mother-fish just walk down the street seeing those two hybrid families. By letting her crash into them, I created a connection I will memorize. Then I used the similarity of 3x^2y and 3xy^2 to my advantage by letting her have a deja-vu.
This technique might look complicated when you read it the first time, but is not when you used it once on your own. Just try it on a simple formula like this one: V = (4 pi r^3) / 3
Math Formula Memorization Techniques - How to Memorize Formulas in Minutes