Class 10 Maths Formulas

Memorizing class 10 maths formulas is highly crucial for students to score better in the board exam as well as entrance exams. These formulas form the core of advanced-level math studies that determine a students’ success. Learning class 10 math formulas also makes it simpler to solve complex problems with ease and accuracy. Math formulas are methods to compute quantities and evaluate values precisely that are also used in practical situations. 

Apart from mathematics, the use of class 10 math formulas can also be seen prominently in several other fields and occupations. For instance, Class 10 math formulas related to trigonometry, statistics, probability, equations, and many more are applied in the fields of accounting, medicine, architecture, finance, engineering, computer science, etc. Nearly every industry employs these formulas in one or the other way. Thus, learning class 10 math formulas is important to make our lives easy.

List of Important Class 10 Math Formulas

A list of some basic class 10 maths formulas related to most important topics covered under various school boards is given below:

• (a + b)³ = a³ + b³ + 3ab(a + b)
• (a – b)³ = a³ - b³ - 3ab(a – b)
• (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2xz
• an = a + (n - 1) d
• Sn= n/2 [2a + (n - 1)d]
• sin² θ + cos² θ = 1 ⇒ sin² θ = 1 - cos² θ ⇒ cos² θ = 1 - sin² θ
• cosec² θ - cot² θ = 1 ⇒ cosec² θ = 1 + cot² θ ⇒ cot² θ = cosec² θ - 1
• sec² θ - tan² θ = 1 ⇒ sec² θ = 1 + tan² θ ⇒ tan² θ = sec² θ - 1
• sin θ cosec θ = 1 ⇒ cos θ sec θ = 1 ⇒ tan θ cot θ = 1
• Vol of Sphere = 4/3 ×π r³
• Surface Area of Sphere = 4πr²

Class 10 Algebra Formulas

Algebra is the study of mathematical statements that represent terms equal to each other. For example, polynomial equations are among the most common algebraic equations that involve equating polynomials. Learning class 10 algebra formulas will help in converting various word problems into their mathematical forms. After knowing these formulas students can easily learn to recognize the equation’s type and apply rules to solve them. These algebraic formulas have varying inputs and outputs with different interpretations. Here are all important Class 10 Algebra Formulas:

• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab + b²
• (a + b) (a - b) = a² - b²
• (x + a)(x + b) = x² + (a + b)x + ab
• (x + a)(x - b) = x² + (a - b)x - ab
• (x - a)(x + b) = x² + (b - a)x - ab
• (x - a)(x - b) = x² - (a + b)x + ab
• (a + b)³ = a³ + b³ + 3ab(a + b)
• (a - b)³ = a³ - b³ - 3ab(a - b)
• (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2xz
• (x + y - z)² = x² + y² + z² + 2xy - 2yz - 2xz
• (x - y + z)² = x² + y² + z² - 2xy - 2yz + 2xz
• (x - y - z)² = x² + y² + z² - 2xy + 2yz - 2xz
• x³ + y³ + z³ - 3xyz = (x + y + z)(x² + y² + z² - xy - yz - xz)

Class 10 Arithmetic Progression Formulas

Many things in our daily life follow a certain pattern. These patterns are generally known as sequences. Two such sequences are arithmetic and geometric sequences. The various numbers occurring in a sequence are called its terms. Terms of sequence are denoted by a¹ a², a³, …………… aⁿ. An arithmetic progression is a sequence of numbers such that the difference between the consecutive terms is equal.

• a_n = a + (n - 1) d, where an is the nth term.
• S_n= n/2 [2a + (n - 1)d]

Class 10 Trigonometry Formulas

Trigonometry is the science of relationships between the sides and angles of a right-angled triangle. Trigonometric ratios are ratios of sides of the right triangle. Here are some important trigonometric formulas related to trigonometric ratios.

• sin(90° - A) = cos A
• cos(90° - A) = sin A
• tan(90° - A) = cot A
• cot(90° - A) = tan A
• sec(90° - A) = cosec A
• cosec(90° - A) = sec A
• sin² θ + cos² θ = 1 ⇒ sin² θ = 1 - cos² θ ⇒ cos² θ = 1 - sin² θ
• cosec² θ - cot² θ = 1 ⇒ cosec² θ = 1 + cot² θ ⇒ cot² θ = cosec² θ - 1
• sec² θ - tan² θ = 1 ⇒ sec² θ = 1 + tan² θ ⇒ tan² θ = sec² θ - 1
• sin θ cosec θ = 1 ⇒ cos θ sec θ = 1 ⇒ tan θ cot θ = 1

Class 10 Circle Formulas

A circle is a collection of all points in a plane that are at a constant distance from a fixed point.

The fixed point is called the center of the circle and the constant distance from the center is called the radius. A line segment joining any two points on a circle is called a chord. A chord passing through the center of the circle is called the diameter. It is the longest chord. When a line meets the circle at one point the line is known as a tangent. The tangent to a circle is perpendicular to the radius through the point of contact. 

• The tangent to a circle equation x₂ + y₂ = a₂ for a line y = mx + c is given by the equation y = mx ± a √[1+ m₂].
• The tangent to a circle equation x₂ + y₂ = a₂ at (a₁,b₁) is xa₁ + yb₁ = a₂

Class 10 Surface Area and Volume Formulas

Three-dimensional shapes are an important part of our daily life, and hence, it is vital to learn class 10 area and volume formulas to determine the various dimensions of these shapes. These calculations are required in daily life whether one needs to figure out how much liquid is needed to fill a container or one needs to calculate the surface area of any object. The class 10 math formulas regarding the same can be found as below:

Sphere:

• Volume of Sphere = 4/3 ×π r³
• Lateral Surface Area of Sphere (LSA) = 4π r²
• Total Surface Area of Sphere (TSA) = 4πr²

Right Circular Cylinder

• Volume of Right Circular Cylinder = πr²h
• Lateral Surface Area of Right Circular Cylinder (LSA) = 2×(πrh)
• Total Surface Area of Right Circular Cylinder (TSA) = 2πr×(r + h)

Hemisphere

• Volume of Hemisphere = ⅔ x (πr³)
• Lateral Surface Area of Hemisphere (LSA) = 2πr²
• Total Surface Area of Hemisphere (TSA) = 3πr²

Prism

• Volume of Prism = B × h
• Lateral Surface Area of Prism (LSA) = p × h

Applications of Class 10 Maths Formulas 

Class 10 Maths formulas are the cornerstone of numeracy skills. They hold a great significance in our lives. Class 10 math formulas are applied in various calculations to determine several values. Below are some of the common applications of class 10 maths formulas.

• Class 10 quadratic equation formulas are used in situations where we can represent the location or value of any object through quadratic equations. For example, for calculating the profit or loss earned through sales we can use these equations.
• Class 10 trigonometry formulas are used to determine height and distance in various fields like the navigation system, architecture, aviation, etc. For instance, these formulas are applied to build parallel and perpendicular walls, inclined roofs, fix tiles, etc. 
• Class 10 statistics and probability formulas are used in the calculation of insurance risks, analysis of statistical data taken by a census, and so on.

Tips to Memorize Class 10 Maths formulas

Students can follow some useful memorization for class 10 math formulas that will help them in their exam preparation.

• One of the best ways to memorize class 10 math formulas is to revise them multiple times. Penning down formulas while applying them to solve questions will help students to learn them better. Therefore, students should write down complex formulas many times or solve as many problems by applying them to remember them faster.
• Connect appropriate visuals with each math formula to remember it quickly. It will help to recall it later. When concepts are connected to visual memory, it becomes relatively simpler to memorize them. 
• It is necessary to comprehend formulas and concepts to memorize them better. When students will understand the logic or rules of a certain formula, it will be easier for them to remember it as it will make more sense then.
• Apply all the formulas as much as possible, understanding the application of the formula helps to retain the information better. Try solving and practicing problems using the formulas.

Class 10 Maths Formulas Examples

Example 1: Check whether the equation is a quadratic equation or not: x + 1/x = 2

Solution: x + 1/x = 2

 x + x^-1 = 2

x + x^-1 - 2 = 0

Since x + x^-1 - 2 = 0 is not a quadratic polynomial, therefore, x + 1/x = 2 is not a quadratic equation. 

Example 2: Find the zeros of the quadratic polynomial 6x² - 3 - 7x

Solution :

Here, p (x) = 6x² - 3 - 7x = 6x² - 7x - 3

= 6x² - 9x + 2x - 3 = 3x (2x - 3) + 1 (2x - 3) 

= (2x - 3) (3x + 1)

= 6(x - 3/2)[x − (−1/3)]

∴ Zeros of p (x) are 3/2 and −1/3

You can download the printable Maths Formulas Class 10 sheet from the link given below: