The Easiest Ways to Memorize Math Formulas

If you’re preparing for the SAT, you know a simple thing: conquering the test requires mastering a set of math formulas. But who says memorization has to be a mind-numbing chore? There are many tried-and-true techniques to memorize math formulas easily. 

Today, we explore some unconventional yet effective strategies gleaned from students and tutors to help you truly understand and keep those formulas in mind. Read on! 

“Understand Rather Than Memorize” Approach

Here comes one of the biggest insights – many students, as well as tutors, say that you have to understand math and physics formulas before you start memorizing them. It is not shocking at all, but it may be surprising if you were preparing for a memorization marathon. Start with understanding concepts instead of jumping right to learning new formulas. 

Source: Reddit

Whenever possible, find the logic behind the formula. If you can derive it yourself, you’ll be less likely to forget it under pressure. Even if you have a hard time remembering formulas, you will be surprised to learn that when the brain understands something, it will remember it for longer. 

Source: Reddit

Many students also say they tried to find patterns between the formulas. This is what helped them understand those formulas instead of just memorizing them. 

Source: Reddit

The bottom line of this approach is quite simple. The more you practice using calculus formulas for real-world problems, the more intuitive they’ll become. You won’t need to memorize them all as you’ll develop a feel for which formula applies in which situation. Don’t approach memorizing formulas like a chore. It’s a combination of understanding how they work and applying them where they fit. 

Top Mnemonic Devices and Memory Tricks

When it comes to learning mathematics and formulas, you can use memory techniques. Yet, not every single one will fit you. Here are some examples you can try out:  

Skip Acronyms

…and focus on the visuals!

Memorizing long codes or rhymes (acronyms) might seem helpful at first, but if you forget the code, you’re stuck. Instead, try to understand the formula visually. For example, let’s take the binomial theorem formula as an example. 

The binomial theorem formula (x + y)^n is used to expand expressions that involve adding or subtracting two terms raised to a power.

For example, let’s say you have the expression (x + y)^3. This means we’re multiplying (x + y) by itself three times – i.e., (x + y)(x + y)(x + y).

When we multiply these terms together, we’ll get a sum of terms. Each term in the expanded expression represents all the different ways we can choose x’s and y’s from each set of parentheses.

Visualizing this as sections of a square can help us understand how the terms are put together. Imagine a square divided into sections, like a brownie. Each section represents a different combination of x’s and y’s:

• One section for x^3 (since we choose x from each set of parentheses)
• One section for y^3 (since we choose y from each set of parentheses)
• Three sections for x^2y (since we choose x from two sets of parentheses and y from one set)
• Three sections for xy^2 (since we choose x from one set of parentheses and y from two sets)

By understanding this visual representation, you can better grasp how the terms are derived and how they come together in the expanded expression.

This works for other formulas, too! Look for patterns or pictures that explain how the formula works. Also, many formulas build on each other. Once you understand the basic ones, the rest become easier to figure out. It’s like knowing 6 x 6 = 36: you don’t need to add 6 six times; you just know the answer.

Use Pascal’s Triangle Approach 

One of the techniques is memorizing Pascal’s Triangle. What is it? Basically, Pascal’s Triangle is a numeric combination arranged in a triangle. Each number is a sum of the two numbers located above it.  

For example, find 15 in the image below. If you check the numbers right above it, those will be 5 and 10 because 5+10=15.

Source: Wikimedia Commons

Now, let’s see how Pascal’s Triangle helps you remember math formulas:

• Focus on the pattern. Focus on understanding the pattern within the triangle. This pattern allows you to generate the coefficients you need for any binomial expansion. Let’s say you have a binomial expression like (a + b)^n. Now, you can see that each row of Pascal’s Triangle resembles the coefficients for a particular power of (a + b).
• Visual aid. The triangle acts as a visual reference. By seeing the numbers laid out, you’ll easily remember the relationships between them, which is not the case when memorizing random numbers.

Think of it like this: instead of memorizing every single phone number in your contact list, you learn the dialing format (country code, area code, etc.). Pascal’s Triangle helps you understand the “dialing format” for binomial expansions, as well as math problems related to combinatorics and probability. This way, you’ll remember the shape that will hold the rest together. 

Download SAT Math Formula Sheets

Source: Acely

What is essentially a Math section of the SAT? It checks how well you can solve math problems in different areas. Math formula sheets can help you develop a better understanding and boost your visual memory. Here’s why using our SAT math formula sheet can help you:

• Get quick access to important math formulas as you practice.
• Gain confidence during studying, making prep time less stressful.
• Remember formulas easier if you practice using them regularly. Thus, you are more likely to score better on the SAT Math section.

Make Flashcards: The Classic for a Reason

Don’t underestimate the power of the humble flashcard. These tried-and-true tools are fantastic for quick review sessions. To make them even more effective, write the formula on one side. And when it comes to the other side, don’t just give the answer, instead, consider including:

• The definition of each variable in the formula.
• A solved example problem that demonstrates how to apply the formula.
• A brief explanation of the concept behind the formula.

This multi-faceted approach reinforces understanding alongside memorization.

Write Mathematical Formulas Down Again and Again 

To remember things better, try writing them down many times. Just grab some paper whenever you have free time and write the formulas out. Doing this regularly, even for just a few minutes each time, can really help you remember them well. But again, make sure you understand the logic behind each formula. 

Practice Makes It Perfect

Memorization without application is like having a library full of unread books. The true key to mastering formulas is using them! Find practice tests online, and work with them repeatedly. You can also use free practicing solutions in the College Board’s Bluebook App.

Dust off your textbook and boost the learning process. Textbooks often have practice problems at the end of each chapter. Thus, you’ll grasp essential concepts and see how they work. 

There is one more great way to practice memorizing math formulas – working in a study group. Explain formulas to each other and solve problems collaboratively. The more you apply formulas to solve problems, the more ingrained they become in your long-term memory.

Sleep on It!

Have you ever crammed for a test only to forget everything the next day? Many of us have been there, and there’s a scientific reason for that. When you sleep, your brain consolidates memories, transferring them from short-term to long-term storage. 

So, after a productive math session, hit the hay. Think about the formula you wish to memorize before going to bed, and your brain will have a higher probability of retaining it. 

Gamify the Process and Install Apps

Math doesn’t have to be a dry and boring subject. There are tons of math games and apps that make memorization feel less like a chore and more like a fun challenge.

Find Culture References

The distance formula (d = ?((x? – x?)² + (y? – y?)²)) tells you the distance between two points. Here’s the pop culture twist: imagine those points are houses on the streets, like 742 Evergreen Terrace (The Simpsons) and 123 Sesame Street. 

Our formula helps us find the distance between Homer and Big Bird! This may seem a little out there, but consider finding your own references to remember all the formulas. 

Stay Focused

This is not a mnemonic device but a way to boost your ability to remember formulas. Many people today find it hard to remove all distractions: full concentration seems to be impossible to achieve. Still, avoid surfing the internet, listening to music, or messaging while studying. You also need enough sleep to be able to use your cognitive abilities fully. Stay healthy, and don’t forget to rest. 

Conclusion 

Remember, the most effective memorization technique is the one that works for you. Experiment with these strategies and find those that make math formulas mastery a fun and rewarding experience. If you find it hard to develop a working approach by yourself, consider working with a tutor. Don’t forget to check with the students who already passed the SAT. Do practice tests, use visual clues, and you will ace the math. Good luck!