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 onestop 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!
This Blog Includes:
 All Formulas of Maths Class 10
 Maths Formulas for Class 10 All Chapters
 Chapter 1: Real Numbers
 Chapter 2 Polynomials
 Chapter 3: Pair of Linear Equations in Two Variables
 Chapter 4: Quadratic Equations
 Chapter 5: Arithmetic Progression
 Chapter 6: Triangles
 Chapter 7: Coordinate Geometry
 Chapter 8: Trigonometry
 Chapter 10: Area of Circle
 Chapter 12: Areas Related to Circle
 Chapter 13: Surface Area and Volume
 Chapter 14: Statistics
 Chapter 15: Probability
 Maths Formulas for Class 10 PDF
 Additional Maths Formulas for Class 10 Trigonometry
 Practice Questions
 FAQs
All Formulas of Maths Class 10
Here is a list of other important formulas for class 10
 (a+b)2 = a2 + b2 + 2ab
 (ab)2 = a2 + b2 – 2ab
 (a+b) (ab) = a2 – b2
 (x + a)(x + b) = x2 + (a + b)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 – a)(x + b) = x2 + (b – a)x – ab
 (x – a)(x – b) = x2 – (a + b)x + ab
 (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)
 x2 + y2 =½ [(x + y)2 + (x – y)2]
 (x + a) (x + b) (x + c) = x3 + (a + b +c)x2 + (ab + bc + ca)x + abc
 x3 + y3= (x + y) (x2 – xy + y2)
 x3 – y3 = (x – y) (x2 + xy + y2)
 x2 + y2 + z2 xy – yz – zx = ½ [(xy)2 + (yz)2 + (zx)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 
Linear  
Quadratic  
Cubic 
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 
Factorization  
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 higherlevel 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  0°  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 (AB)= SinA.CosB – CosA.SinB
 Cos (A+B)= CosA.CosB SinA.SinB
 Cos (AB)= CosA.CosB+SinA.SinB
 Tan (A+B)= (TanA + TanB)/ (1TanA TanB)
 Tan (AB)= (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 higherlevel 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
Chapter 14: Statistics
Important maths formulas for class 10th of this chapter are
Terms  Formulas 
Mean  
Mode  
Median 
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 abovementioned 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?
 43.123456789
 0.120120012000120000. . .
 43.123456789
Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following :
 p(x) = x 3 – 3x 2 + 5x – 3, g(x) = x 2 – 2
 p(x) = x 4 – 3x 2 + 4x + 5, g(x) = x 2 + 1 – x
 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
FAQs
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).
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!
Trigonometry has 6 different functions that are tangent, sine, cosine, cotangent, secant and cosecant. Based on these 6 functions there is a wide range of trigonometry formulas used in Maths class 10.
Trigonometry has 6 different functions that are tangent, sine, cosine, cotangent, secant and cosecant. 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 30minute counselling session.

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8 comments
Superb
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𝓣𝓱𝓪𝓷𝓴 𝔂𝓸𝓾
Thank you
That’s really useful and great..
My thoughts is iam winning for 10 results is 500 plus marks