# Math Formulas

Math formulas are expressions that have been created after several decades of research that help to solve questions quickly. It is easy to perform simple arithmetic calculations such as addition, subtraction, and so on. However, when it comes to algebraic expressions, geometry, and other topics you need mathematical formulas to simplify the process of reaching the answer and saving time in the process. At Cuemath you will not only find formulas for each and every topic but will also get an idea of how that equation was developed. Thus, you will not have to memorize formulas, as you understand the concept behind them.

Use these formulas to solve problems creatively and you will automatically see an improvement in your mathematical skills. Given below is the list of formulas alphabetically arranged for your convenience. Hence, you can easily find formulas that need to be revised or require to be referenced.

The links to the list of math formulas available on different topics have been arranged alphabetically for your convenience. So pick a topic and start learning!

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## List of All Math Formulas

Depending on what grade you belong to and what topic is being attempted, you can find all possible math formulas. All variations of the math formulas available with their proofs and derivations are given below. So what are you waiting for? Get started on your learning journey today!

## Importance of Math Formulas for Students

Math formulas were created by some of the most intelligent people for a reason. They help kids to solve questions with speed and accuracy. It also helps to make the process of reaching a solution to a sum much easier as opposed to attempting it from scratch. The benefits of math formulas are given below:

- A child has to follow the curriculum set by the school which is time-sensitive. At periodic intervals, kids are tested on their knowledge through different examinations such as units, half-yearlies, and finals. Thus, to ensure that students have prepared the subject matter in time with a buffer for revision they require math formulas.
- While revising, a child probably isn’t going to solve several questions using a pen and paper. Thus, in order to have a quick glance at sums and how to solve them children need to know formulas as they are the keys to getting correct answers.
- During examinations, kids do not have the luxury to derive an entire formula to solve a question implying that they cannot start from step 1. They must know and remember formulas in order to complete their question paper within the given amount of time thus, helping them in scheduling and organizing their time.
- For students who are attempting competitive exams, they need to not only know formulas but also the various tips and tricks associated with them. As these exams are usually in the form of MCQs thus, kids must have a very good grasp of math formulas.

## Important Math Formulas

Before we see the list of the most important math formulas, it is very important to keep in mind that every topic in mathematics is interlinked. If you are not comfortable with a few formulas, irrespective of whether they appear in exams more frequently, you must work on your skills and build a robust understanding of them. Thus, knowledge of all formulas is a must; however, the given list gives you an idea of what kind of math formulas are usually used to solve examination questions.

**1. **Algebra

- Arithmetic mean or average = sum of all values/ number of values
- Quadratic Formula: x = [-b ± (√b
^{2}- 4ac)]/2a

- Distance Formula: d=√[(x₁ - x₂)
^{2}+ (y₁ - y₂^{2}] - Slope-Intercept: y = mx + b
- Midpoint Formula: [(x₁ + x₂)/2, (y₁ + y₂)/2]

**3. **Plane Geometry

- Pythagorean Theorem: a
^{2}+ b^{2}= c^{2} - Area of Triangle = (1/2) × base × height
- Area of Rectangle = length × width

4. Trigonometry

- Sine = perpendicular/hypotenuse
- Cosine = base /hypotenuse

## Tips To Memorize Math Formulas

There are hundreds of math formulas that kids have to learn during their entire school life career. Thus, it is important for students to have a few tips that can help them in remembering the math formulas accurately. **A few tricks are given below:**

**Understanding:**It is essential that a child comprehends the concept behind a math formula. If he knows the derivation and has a clear concept formation of the purpose behind the math formula then chances are that a child won’t even have to memorize it. He will automatically know how and when to apply the correct math formula.**Practice:**Till you do not solve a question that requires the use of a particular formula it will be very difficult for you to gauge the use of it. By solving numerous questions, you start remembering a formula through muscle memory. Hence, you won’t have to make an active effort in learning formulas as you already know the application of it.**Make revision sheets:**Once you are introduced to a topic and start attempting questions on the same, make a sheet of all the math formulas that you are using. Keep updating it as you continue your learning cycle. When the time comes for you to have a quick look at these formulas or if you want to memorize them, this sheet can be consulted. Additionally, you can also take the help of Cuemath with the math formulas listed above**Mnemonics and memory techniques:**There are many mnemonic devices available that can assist you in learning math formulas. For example, if you want to learn the basic trigonometric formulas, the mnemonic available is “**S**ome**P**eople**H**ave,**C**urly**B**rown**H**air,**T**hrough**P**roper**B**rushing.” Thus, the highlighted letters help you to memorize the formulas, sine = perpendicular/hypotenuse, and so on. If you use these memory techniques or come up with your own innovative mnemonics, it will become very easy for you to learn math formulas.

## Real Life Applications of Math Formulas

While learning a topic it is helpful for students to know the real-life applications of the associated math formulas as it makes the subject more relatable. **Some of the areas where mathematical formulas are used are listed below:**

**Algebra:**

Algebraic formulas are widely used in the field of computer science for performing various analytical functions. They are also used in cryptography for the protection of financial information. Additionally, you use algebra on a daily basis, knowingly and unknowingly, to plan your schedule and do your tasks.

**Calculus:**

Integration and differentiation formulas in calculus are widely used in engineering. It is also used for rocket trajectory analysis, materials science, shock wave physics code development, modeling airflow over aerodynamic bodies, heat transfer, seismic wave propagation for earthquake analysis, signal processing, and so on.

**Geometry:**

Geometry formulas are widely used in construction and architecture to build different types of structures. They are also used in terrain modeling, design of mechanical parts, cryptology, and airflow patterns.

**Probability and Statistics:**

The probability and statistics formulas, as well as techniques learned in school, can be applied to real-life examples. They are used in fields such as Monte Carlo simulation, signal processing, reliability analysis, risk analysis, stock market prediction models, computer network designs, pricing insurance, estimation of ocean currents in geostatistics, etc.

## FAQs on Maths Formulas

### What is Math Formula?

A Math formula can be seen as an expression that is used as a key to solving problems quickly and effectively. They also include identities which are statements that hold true for all values of a particular variable. Thus, math formulas are very important for children to learn and understand.

### Do you Need to Memorize all the Math Formulas?

It is crucial for kids to understand the concept behind a math formula. Once a child has in-depth knowledge then he can move on to learning and memorizing formulas as he will have to quickly recall them during exams. However, if he knows how the math formula was derived and the meaning behind it, a child will automatically remember a formula.

### What are the Most Important Math Formulas?

Important math formulas refer to those formulas that appear frequently in most school or competitive exams. However, you should give equal importance to all formulas in order to receive a holistic mathematical development. The list of important math formulas is given below.

- Average = sum of all values/total number of values
- Area of Triangle = (1/2)*(base)*(height)
- Perimeter of Square = 4 * side
- Determinant of a quadratic equation = b
^{2}- 4ac

### What are the Basic Math Formulas?

The basic math formulas can be used to solve simple questions or are required to build up more complicated formulas. Here is the list of some basic math formulas.

- Algebraic Identities: (a + b)
^{2}= a^{2}+ b^{2}+ 2ab, (a - b)^{2}= a^{2}+ b^{2}- 2ab, a^{2}- b^{2}= (a + b) (a - b) - Pythagoras Theorem: perpendicular
^{2}+ base^{2}= hypotenuse^{2} - Distance Formula: d=√(x₁ - x₂)
^{2}+ (y₁ - y₂)^{2} - Slope of a Line: m = y2 - y1 / x2 - x1

### Why are Math Formulas so Important?

Math formulas give children an easy and quick way to solve difficult problems. All kids need to do is figure out the correct formula to solve the questions and they can proceed seamlessly. Especially, when we consider the scenario of an examination that is timed, it becomes necessary to use these math formulas so that the paper can be finished well within the given limit.

### Is It Necessary to Know How Does a Math Formula Work?

It is very crucial for students to know how math formulas work. Kids need to start with developing an understanding of the concept behind a formula and building a clear foundation of the derivation. If children have this knowledge then they won’t have to memorize the formulas. Even if they forget what math formula to apply for a particular question during a test paper they will know the method and not get stuck.

### How do you Teach Math Formulas?

The first step in teaching math formulas is to explain to students the meaning behind the formula. The next step is to introduce children to the derivation of the formula. Finally, you need to show kids how to apply the math formula to questions, both simple and complex.

### How Can We Apply Math Formulas in Everyday Life?

When we talk about a topic such as fractions or decimals, we apply the formulas to activities such as cross-checking whether the receipt we get from a purchase is correct or not, when we have to divide an object such as a pizza amongst people, and so on. Thus, knowingly or unknowingly, we make use of math formulas to go about our daily lives effectively.