CBSE Class 10 Maths Formulas PDF Download

Learning maths formulas in class 10 may seem like a daunting task, but it is actually a crucial step towards building a strong foundation in mathematics. These formulas are not only important for your current class, but they will also be useful in higher-level maths courses and in various industries and careers.

By understanding and memorizing these formulas, you will be able to solve problems more accurately and quickly, which will not only help you perform better in exams but also in real-world applications. Imagine being able to calculate complex measurements or financial transactions with ease, just by recalling a formula you learned in class!

Moreover, as you progress to higher education levels and professional careers, you will encounter more complex problems that build on these basic formulas. So, mastering them in class 10 is an essential step towards your future academic and professional success.

In this EduRev article, you will find all the essential formulas for class 10 Maths, covering all the important units including Algebra, Geometry, Trigonometry, Statistics and Probability, Mensuration, Coordinate Geometry, and Number Systems. 

Important Formulas to Memorise for Class 10 Maths

Below, you will find a list of important formulas for class 10 Maths. While it may be tempting to simply memorize them, it's important to remember that the real value of these formulas lies in their application. By practicing these formulas through problem-solving, you will not only reinforce your understanding of them but also build a solid foundation for future studies.
Therefore, I urge you to not just memorize these formulas but also implement them in solving problems. This will help you to develop a better understanding of how these formulas work and how they can be applied in different scenarios. Additionally, practicing these formulas regularly will help to solidify them in your memory and make them easier to recall when needed.

Class 10 Algebra Formulas

In class 10, algebra typically involves solving linear and quadratic equations, simplifying expressions, and manipulating algebraic equations using various techniques such as factorization, completing the square, and using the quadratic formula.

Pair of Linear Equations in two Variables

The general form of a pair of linear equations in two variables x and y is
a₁x + b₁y + c₁ = 0, and

a₂x + b₂y + c₂ = 0
where a₁, b₁, c₁, a₂, b₂, c₂ are all real numbers and the coefficients of x and y cannot be zero simultaneously.
Conditions for Consistency/Inconsistency

To learn the methods for solving a system of two linear equations in two variables, it is recommended that you refer to the following resource. Important Definitions & Formulas: Pair of Linear Equations in Two Variables

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Quadratic Equations

If ax₂ + bx + c = 0 is a quadratic equation, then the value of x is given by the following formula:

Just plug in the values of a, b and c, and do the calculations. The quantity in the square root is called the discriminant or D.
Nature of Roots

Based on the value of the discriminant, D=(b² − 4ac), the roots of a quadratic equation can be of three types.

For acquiring the methods to solve quadratic equations, it is suggested that you access the following resource. Important Definitions & Formulas: Quadratic Equations

Algebraic Identities

• (a + b)² = a² + 2ab + b²
• (a – b)² = a² – 2ab + b²
• a² – b² = (a+b) (a-b)
• (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
• (a + b)³ = a³ + b³ + 3ab (a + b)
• (a – b)³ = a³ – b³ – 3ab (a – b)
• a³ + b³ = (a + b) (a² – ab + b²)
• a³- b³ = (a - b) (a²+ab+b²)
• a³ + b³ + c³ – 3abc = (a + b + c)(a² + b² + c² – ab – bc – ca)

Arithmetic Progressions

General Form of an AP : a, a + d, a + 2d, a + 3d………………..
Where, ‘a’ is the first term and ‘d’ is the common difference.
Then,
nth term = a + (n-1) d
Sum of the first n terms in Arithmetic Progression;
S_n = n/2 [2a + (n-1)d]

You may access the detailed notes for arithmetic progression: Chapter Notes: Arithmetic Progressions

Class 10 Geometry Formulas

Class 10 Geometry consists of three chapters - Triangles, Circles, and Constructions - which are part of the fourth unit in the mathematics syllabus. In this unit, students learn about the properties of triangles and circles.

Triangles 

Types of Triangles
On the basis of Sides:

On the basis of Angles:

Similarity of Triangles

Two triangles are said to be similar, if

• Their corresponding angles are equal
• Their corresponding sides are in the same ratio

Criterias for Similarity of Triangles

Access the following resource on triangles for better understanding: Important Definitions & Formulas: Triangles

Circles

• Circumference of the circle = 2 π r
• Area of the circle = πr²
• Length of an arc of a sector of angle θ = (θ/360) × 2πr
• Area of the sector of angle θ = (θ/360) × πr
• Area of segment of a circle = Area of corresponding sector - area of corresponding triangle
• Where, r is the radius of circle

For more formulas on circles click the link below: Important Formulas: Circles

Class 10 Trigonometry Formulas

Trigonometry in class 10 involves the study of the relationships between the angles and sides of a right-angled triangle. Students learn about trigonometric ratios such as sine, cosine, and tangent, and how to apply them to find the unknown sides or angles of a triangle.
Trigonometry Formulas and Identities
For a right-angled triangle ABC:
Let opposite = a, Adjacent = b, Hypotenuse = c then

Let opposite = a, Adjacent = b, Hypotenuse = c then

Values of trigonometric functions for different values of angles:

 Important Trigonometric Identities
(a) sin²θ + cos²θ = 1
(b) sec²θ = 1 + tan²θ
(c) cosec²θ = 1 + cot²θ

Co-Function Formula

• sin (90 - θ) = cos θ
• cos (90 - θ) = sin θ
• tan (90 - θ) = cot θ
• cosec (90 - θ) = sec θ
• sec (90 - θ) = cosec θ
• cot (90 - θ) = tan θ

You may also read:

• Important Definitions & Formulas: Introduction to Trigonometry
• Important Definitions & Formulas: Some Application of Trigonometry

Download the notes CBSE Class 10 Maths Formulas

Download as PDF

Download as PDF

Class 10 Statistics Formulas

Class 10th Statistics involves the collection, description, analysis, and inference of conclusions from quantitative data.
Mean:

The mean can be calculated by the following formulae :

where A = assumed mean and di = xi - A

Median:
The median of a grouped frequency distribution can be calculated by:

l = lower limit of median class

l = frequency of median class

h = width of median class

c.f. = cumulative frequency of the class preceding the median class.

Mode:

The mode of a continuous frequency distribution may be computed by the following formulae:

where

l = lower limit of the modal class.

f1 = frequency of modal class.

f2 = frequency of class succeeding the modal class.

fo = frequency of class preceding the modal class.

h = size of the class interval.

Mode = 3 Median - 2 Mean
You may also read: Important Definitions & Formulas: Statistics

Class 10 Mensuration Formulas

It is branch of mathematics which is concerned about the measurement of length ,area and Volume of plane and Solid figure

Surface, Areas and Volumes

Cube and Cuboid formulas

Sphere Formulas

Cone Formulas

Cylinder Formulas

You may also read for detailed definition and formulas: Important Formulas: Surface Area & Volumes 

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Class 10 Coordinate Geometry Formulas

Coordinate Geometry is the study of Geometry with coordinate points. This branch of Mathematics is like a bridge between Algebra and Geometry.

• Distance Formula Between 2 Points P and Q in a 2D Plane
  
• Section Formula when the Line Segment joining points A(x₁,y₁) and B(x₂,y₂) separated Internally by a Point P(x,y)
  
• Heron’s formula for area of the Triangle:
  

Where ‘s’ is the semi perimeter of the triangle and a, b and c are the sides of the triangle.
Semi perimeter of the triangle, s = (a + b + c)/2

Some other Important Formulas

Here are the formulas of some other important chapters of Class 10 Maths:

• Important Definitions & Formulas: Real Numbers
• Formulas : Polynomials
• Important Definitions & Formulas: Areas Related to Circles
• Important Definitions & Formulas: Probability

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