Maths Formulas for Class 10

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Maths Formulas for Class 10

You must have heard about the importance of class 10 from your parents, teachers and seniors. There is no dyeing to the fact that this particular class plays a vital role in the identification of your career pathway along with laying a foundation for the same. Out of all the subjects in class 10, Maths is considered as the toughest one by many students. This blog will serve as a one-stop for all the key Maths Formulas for class 10 to help you solve problems faster. So, just sit back, relax and read through the end!

All Formulas of Maths Class 10

Here is a list of other important formulas for class 10-

  1. (a+b)2 = a2 + b2 + 2ab
  2. (a-b)2 = a2 + b2 – 2ab
  3. (a+b) (a-b) = a2 – b2
  4. (x + a)(x + b) = x2 + (a + b)x + ab
  5. (x + a)(x – b) = x2 + (a – b)x – ab
  6. (a + b)3 = a3 + b3 + 3ab(a + b)
  7. (a – b)3 = a3 – b3 – 3ab(a – b)
  8. (x – a)(x + b) = x2 + (b – a)x – ab
  9. (x – a)(x – b) = x2 – (a + b)x + ab
  10. (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2xz
  11. (x + y – z)2 = x2 + y2 + z2 + 2xy – 2yz – 2xz
  12. (x – y + z)2 = x2 + y2 + z2 – 2xy – 2yz + 2xz
  13. (x – y – z)2 = x2 + y2 + z2 – 2xy + 2yz – 2xz
  14. x3 + y3 + z3 – 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz -xz)
  15. x2 + y2 =½ [(x + y)2 + (x – y)2]
  16. (x + a) (x + b) (x + c) = x3 + (a + b +c)x2 + (ab + bc + ca)x + abc
  17. x3 + y3= (x + y) (x2 – xy + y2)
  18. x3 – y3 = (x – y) (x2 + xy + y2)
  19. x2 + y2 + z2 -xy – yz – zx = ½ [(x-y)2 + (y-z)2 + (z-x)2]

Maths Formulas for Class 10 All Chapters

Now let us quickly go through Maths formulas for class 10 of all the chapters-

Chapter 1: Real Numbers

The first chapter of class 10th mathematics will equip you with a variety of concepts related to Natural numbers, Whole Numbers and Real Numbers, etc. Let us have a look at maths formula for class 10-

Numbers  Details 
Natural Numbers N ={ 1, 2,3,4,5 … } 
Whole Numbers  W={ 0, 1, 2, 3, 4, 5… }
Rational Numbers Those numbers which can be presented in the form of a/b are called Rational Numbers. 
Re Numbers  Real Numbers can be found on a number line 

Try solving these BODMAS Questions!

Class 10 Maths Chapter 1 NCERT PDF

Chapter 2 Polynomials

Through the Polynomials chapter, you will have a firm understanding regarding various degree Polynomials such as Linear, Quadratic, Cubic etc. Here are the important formula for this chapter 

Polynomials General Form Formula

Take This Maths Quiz If You Consider Yourself Genius!

Class 10 Maths Chapter 2 NCERT PDF

Chapter 3: Pair of Linear Equations in Two Variables

It is an integral chapter containing a variety of important Maths formula for class 10 especially from the competitive exams point of view. Tabulated below are some of the formula of this chapter:

  • Linear equation in one variable: ax +b =0 
  • Linear equation in two variables: ax+ by+ c =0 
  • Linear equation in three variables: ax+ by+ cz= 0

Class 10 Maths Chapter 3 NCERT PDF

Chapter 4: Quadratic Equations 

One of the most essential chapters which aim to create a sound foundation for upcoming higher studies in this subject. Refer below for the integral formulas of this chapter- 

Category Formula
Square/ Quadratic Method 

Checkout the CBSE Class 10 Maths Syallbus!

Class 10 Maths Chapter 4 NCERT PDF

Chapter 5: Arithmetic Progression 

Arithmetic Progression is a crucial chapter for class 10th as it constitutes a majority of the questions both in scholastic as well as competitive exams. Here are some important maths formulas for class 10: 

Category Formula
Common difference on an AP: 
nth term of Arithmetic Progression:
Sum of the nth item in Arithmetic Progression: 

Class 10 Maths Chapter 5 NCERT PDF

Chapter 6: Triangles 

The sixth chapter onwards, your journey regarding the geometrical mathematics will begin. Through this unit, you will get to know about the application of various properties of triangles as well as how to use them in mathematical questions. 

Are you planning to give some competitive exam? Here are some tips on Maths for competative exams!

Class 10 Maths Chapter 6 NCERT PDF

Chapter 7: Coordinate Geometry 

Going through the coordinate geometry chapter, you will be through with a variety of concepts which will be an integral part of higher-level mathematics in class 11th and 12th. Main topics and maths formula for class 10th are

Category Formula
Distance Formula
Section Formula
Area of Triangle 

Class 10 Maths Chapter 7 NCERT PDF

Chapter 8: Trigonometry 

A highly interesting chapter covering a wide range of formulas and topics which is also an important element of the class 10th board exams. Having a firm grip over Trigonometry formulas will help you achieve your dream score in exams: 

θ 30° 45° 60° 90° 180°
Sin  0 1/2 1/2 3/2 1 0
Cos  1 3/2 1/2 1/2 0 -1
Tan   0 1/3 1 3 0
Cot  3 1 1/3 0
Sec  1 2/3 2 2 -1
Cosec  2 2 2/3 1
  • Sinθ= 1/ Cosecθ or Sin θ.Cosecθ= 1
  • Cosθ= 1/Secθ or Cos θ.Secθ= 1
  • Tanθ= 1/Cotθ or Tanθ.Cotθ= 1
  • Sin (A+B)= SinA.CosB + CosA.SinB
  • Sin (A-B)= SinA.CosB – CosA.SinB
  • Cos (A+B)= CosA.CosB- SinA.SinB
  • Cos (A-B)= CosA.CosB+SinA.SinB
  • Tan (A+B)= (TanA + TanB)/ (1-TanA TanB)
  • Tan (A-B)= (TanA- TanB)/ (1+TanA TanB)

Here is a complete list of Trignometry formulas!

Class 10 Maths Chapter 8 NCERT PDF

Chapter 10: Area of Circle 

By going through this mathematics chapter regarding Circles, you will get to learn about various fundamentals which are involved in higher-level programs such as Engineering, Architecture, etc. 

Terms  Formula
Area of Circle
Circumference of Circle
Length of the Arch 
Area of the sector

Class 10 Maths Chapter 10 NCERT PDF

Circles comprise of a multitude of figures inside it, hence via this chapter you will learn about other geometrical aspects of those figures. 

Terms  Formula
Area of the Ring
Perimeter of Semicircle 
Perimeter of Sector

Here are some Ratio and Proportion questions for you to practise!

Class 10 Maths Chapter 12 NCERT PDF

Chapter 13: Surface Area and Volume

Out of all, this chapter has been an integral part of maths syllabus since class 6th or 7th. Hence, in class 10th this chapter involves a variety of formulas to have a sound understanding of the concept. 

Terms  Formulas 
Surface Area of a Cuboid 
Total Surface Area of a Cylinder 
Total Surface Area of a Cone
Surface Area of a Sphere
Total Surface Area of a Frustum of a Cone

Class 10 Maths Chapter 13 NCERT PDF

Source: Mathematics Class X

Chapter 14: Statistics

Important maths formulas for class 10th of this chapter are 

Terms  Formulas 

Checkout the list of Mensuration formulas!

Class 10 Maths Chapter 14 NCERT PDF

Chapter 15: Probability

The essential formula for the Probability chapter is: 
P(E)= Number of outcome favourable/ Number of all possible outcomes of the experiment

Class 10 Maths Chapter 15 NCERT PDF

Maths Formulas for Class 10 PDF

Here is a PDF of the above-mentioned formulas-

Additional Maths Formulas for Class 10 Trigonometry

  • sin θ = Side opposite to angle θ/ Hypotenuse = Perpendicular/Hypotenuse= P/H
  • cos θ = Adjacent side to angle θ/ Hypotenuse= Adjacentside/ Hypotenuse= B/H
  • tan θ = Side opposite to angle θ/ Adjacent side to angle θ
  • sec θ = 1/ cosθ
  • cot θ = 1/ tanθ
  • cosec θ = 1/ sinθ
  • tan θ = Sinθ/ Cosθ
  • sin (90° – θ) = cos θ
  • cos (90° – θ) = sin θ
  • tan (90° – θ) = cot θ
  • cot (90° – θ) = tan θ
  • sec (90° – θ) = cosecθ
  • cosec (90° – θ) = secθ
  • sin2θ + cos2 θ = 1
  • sec2 θ = 1 + tan2θ for 0° ≤ θ < 90°
  • Cosec2 θ = 1 + cot2 θ for 0° ≤ θ ≤ 90°

Practice Questions

Now that you are aware 10th class maths formulas list, Here are some practice questions to test yourself from NCERT:

The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form, p/ q what can you say about the prime factors of q? 

  1. 43.123456789
  2. 0.120120012000120000. . . 
  3. 43.123456789

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following :

  1. p(x) = x 3 – 3x 2 + 5x – 3, g(x) = x 2 – 2 
  2. p(x) = x 4 – 3x 2 + 4x + 5, g(x) = x 2 + 1 – x 
  3. p(x) = x 4 – 5x + 6, g(x) = 2 – x 2 

The ages of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Dharam differ by 30 years. Find the ages of Ani and Biju.

A box contains 12 balls out of which x are black. If one ball is drawn at random from the box, what is the probability that it will be a black ball? If 6 more black balls are put in the box, the probability of drawing a black ball is now double what it was before. Find x

Let ABC be a right triangle in which AB = 6 cm, BC = 8 cm and ∠ B = 90°. BD is the perpendicular from B on AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle


Q1: What is the formula of mode class 10?

The mode is a type of data value that is understood as the value appearing the most number times in a particular sample. It is defined as a topic that appears the most number of times in a given data. The formula to calculate mode is: L + (fm – f1) x h / (fm – f1) + (fm – f2).

Q2: How do you solve an equation?

An equation is a combination of numbers, variables and operations arranged in a particular order. An equation can be of different types ranging on the degree and number of terms. Thus, the process of solving an equation varies from question to question!

Q3: What is the formula of trigonometry?

Trigonometry has 6 different functions that are tangent, sine, cosine, co-tangent, secant and co-secant. Based on these 6 functions there is a wide range of trigonometry formulas used in Maths class 10.  

Q4: How many theorems are there in maths class 10?

Trigonometry has 6 different functions that are tangent, sine, cosine, co-tangent, secant and co-secant. Based on these 6 functions there is a wide range of trigonometry formulas used in Maths class 10.  c

This was all on Maths formulas for class 10th. As soon as you complete the milestone- class 10th board exams, the decision of stream selection has to be made. You must seek expert guidance for this step. Get in touch with our Leverage Edu experts and they will guide you about trending careers and courses of every Commerce, Science and Arts. Call us immediately at 1800 57 2000 for a free 30-minute counselling session.

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