Class 9 Maths Formulas

Mathematics is often feared by students as it comes with the complexity of learning the formulas. A glimpse of formulas can raise the anxiety of students, and this is the reason many of them are reluctant to study the subject. To help students calm down and have an easy approach to learning the class 9 math formulas, this article provides a summary of all the important formulas and some helpful tips to remember them.

List of Important Class 9 Math Formulas 

Here is a summarized list of the important Class 9 Math formulas.

• (a + b) (a - b) = a² - b²
• (a + b)² = a² + 2ab + b²
• (a - b)³ = a³ - b³ - 3ab(a - b)

• Heron’s Formula to find the area of a triangle = √s(s - a)(s - b)(s - c), where ‘s’ is the semi perimeter of the triangle and is calculated with the formula, s = (a + b + c)/2

• Curved Surface Area of a Cone = 1 /2 × l × 2πr = πrl, where ‘r’ is its base radius and ‘l’ its slant height. ‘l’ = Square root of (r² + h²)

• Volume of a Cuboid = Base Area × Height = Length × Breadth × Height
• Volume of a Cone = (1 / 3 )πr²h
• Volume of a Sphere = (4/3) π r³
• Volume of a Hemisphere = (2/3) πr³
• Mean = Sum of the observations / Total number of observations

Number System Class 9 Math Formulas

Number system class 9 math formulas cover important facts about rational and irrational numbers which help to strengthen the math foundation. Suppose, a number ‘a’ is rational, and ‘b’ is irrational, then ‘a + b’, and ‘a - b’ are irrational numbers, ‘ab’ and ‘a/b’ are irrational numbers, and ‘b’ is not equal to zero.

For ‘a’ and ‘b’ positive real numbers the following entities will be true:

• √ab = √a √b
• √(a/b) =  √a / √b
• (√a + √b) (√a - √b) = a - b 
• (√a + √b)² = a + 2√ab + b
• (a + √b) (a - √b) = a² - b
• (a + b) (a - b) = a² - b²

Algebra Formulas for Class 9 Maths

The fundamental properties and theorems of polynomials form the building blocks for higher algebra polynomials. The process of factorization of polynomials helps in finding the roots of an equation, and it is an important concept that can improve the understanding of algebra in students.

• (a + b)² = a² + 2ab + b²
• (a - b)³ = a³ - b³ - 3ab(a - b)

Area and Volume Class 9 Math Formulas

We come across shapes of all sorts in our daily life, and hence, the need to find their measurements arise, further leading to calculations of area and volume. 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 9 maths formulas regarding the same can be found as below:

• Surface Area of a Cuboid = 2(lb + bh + hl), where ‘l’, ‘b’ and ‘h’ are the length, breadth, and height respectively.

• Curved Surface Area of a Cone = 1 /2 × l × 2πr = πrl, where ‘r’ is its base radius and ‘l’ its slant height

           Then, ‘l’ = Square root of (r² + h²)

• Surface Area of a Sphere = 4 π r²
• Volume of a Cuboid = Base Area × Height = Length × Breadth × Height
• Volume of a Cube = a³ where ‘a’ is the edge of the cube.

• Volume of a Cylinder = πr²h , where, ‘r’ and ‘h’ are radius and height respectively.

• Volume of a Cone = (1 / 3)πr²h
• Volume of a Sphere = (4/3) πr³
• Volume of a Hemisphere = (2/3) πr³

Statistics and Probability Formulas for Class 9 Maths

Statistics plays a crucial role in practically every aspect of life. The concept of probability is all about the prediction of events, and the formulas regarding the same have their usage almost everywhere including the prediction of weather and several fields of science. To draw the essential conclusions from data, one must first learn how to analyze data, and the following formulas help doing the same. 

• Class-mark = (Upper limit + Lower limit)/ 2
• Mean = Sum of the observations / Total number of observations
• Mode = The observation occurring the most frequent times
• Experimental Probability Formula: The trial counts in which the event (E) has occurred / The sum of trials

Applications of Class 9 Maths Formulas

Class 9 Maths formulas are applied in various fields. Let us see how these formulas play a role in our everyday life. 

• Mathematics is ingrained in our daily lives, starting from the measurements in the kitchen to any transaction done in the shop, numbers play an important role in almost all walks of life. A proper understanding of numbers can help students in their money management too. Hence, an understanding of the number system is one of the important skills to learn for not only higher math topics but also for life in general.

• Shapes are everywhere around us. Hence, the study of geometry formulas helps us identify and solve real life problems occurring while analytically analyzing them. Whether it is to decide how much paint will be required to paint a hall, or how many bricks are required to construct a wall, class 9 maths formulas help with this real life problem solving.

• Data is everywhere and it can give amazing insights when analyzed properly. The statistics and probability formulas class 9 help in making sense of data and derive logical conclusions with it.

Tips to Memorize Class 9 Maths Formulas 

• To get a good grasp on the class 9 maths formulas it is essential to use them through a variety of problems. The more the students will practice, the easier it will become to memorize these formulas on their fingertips.
• The students can get their hands on the formula images from online resources. They can set these as screensaver or wallpaper on their digital devices. In this way whenever they will use their device, they will be prompted to have a look at the formulas throughout the day resulting in a quick revision.
• The students can study with their friends which will not only help them in clearing out their doubts with each other but can make learning easy through the sharing of ideas.

Class 9 Maths Formulas Examples

Example 1: Simplify the following expression: (3 + √7)(3 - √7)

Solution: Using the formula, (a + b)(a - b) = a² - b²

We can solve it as (3 + √7)(3 - √7) = 9 - 7 = 2

Example 2 : A school building is to be supported using cylindrical pillars. If the height of the pillars = 10 m and radius of the pillar = 20 cm, how much concrete is needed to make 7 cylindrical pillars?

Solution: To know how much concrete is needed we need to find the volume of a cylinder and then multiply it with the number of cylinders needed.

We know that the volume of cylinder = πr²h

so, substituting the value of radius = 0.2 m and height = 10 m we get, 

= 22/7 × 0.2 × 0.2 × 10

= 8.8 / 7 = 1.257 m³

Since 7 pillars are needed, the net concrete needed is, 

8.8/7× 7 = 8.8 m³

Students can download the printable Maths Formulas Class 9 sheet from below: