CLASS-10 MATHS FORMULAS

       MATHS FORMULAS OF CLASS 10 

Class 10 Math Formulas:-

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

 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

 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)

 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.

an = a + (n - 1) d, where an is the nth term.

Sn= n/2 [2a + (n - 1)d]

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

 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

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