You must have heard about the importance of class 10 from your parents, teachers and seniors. There is no denying 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 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:
 Maths Formulas for Class 10 Algebraic Equations
 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
Maths Formulas for Class 10 Algebraic Equations
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 the 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 of various degree Polynomials such as Linear, Quadratic, Cubic etc. Here are the important formulas for this chapter
Polynomials  General Form  Formula 
Linear  ax+b=0  a≠0 and a&b are real numbers 
Quadratic  ax+by+c = 0  a≠0 & b≠0 and a,b & c are real numbers 
Cubic  ax+by+cz+d=0  a≠0, b≠0, c≠0 and a,b,c,d are real numbers 
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 formulas for class 10, especially from the competitive exams point of view. Tabulated below are some of the formulas 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 aims to create a sound foundation for upcoming higher studies in this subject. Refer below for the integral formulas of this chapter
Category  Formula 
Factorization  ax^{2}+bx+c=0 where a ≠ 0and 
Square/ Quadratic Method  x = (b ± √(b² – 4ac)) / 2a 
Check out the CBSE Class 10 Maths Syllabus!
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 
The common difference between an AP:  d = a₂ – a₁ 
nth term of Arithmetic Progression:  n^{th} term = a + (n1) d 
Sum of the nth item in Arithmetic Progression:  Sn = n/2 [2a + (n – 1)d] 
Class 10 Maths Chapter 5 NCERT PDF
Chapter 6: Triangles
From the sixth chapter onwards, your journey regarding 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.
1. Angle Sum Property of a Triangle:
 The sum of the angles in a triangle is always 180 degrees.
 Formula: A + B + C = 180°
2. Exterior Angle Property of a Triangle:
 An exterior angle of a triangle is equal to the sum of the two opposite interior angles.
 Formula: Exterior angle = ∠A + ∠B (where A and B are the opposite interior angles)
3. Pythagoras Theorem (for rightangled triangles):
 In a rightangled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
 Formula: c² = a² + b² (where c is the hypotenuse, and a and b are the other two sides)
4. Area of a Triangle:
 Formula 1: Area = 1/2 * base * height
 Formula 2 (Heron’s formula for any triangle): Area = √(s * (s – a) * (s – b) * (s – c)), where s is the semiperimeter (s = (a + b + c)/2)
Are you planning to take some competitive exams? Here are some tips on Maths for competitive 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 classes 11th and 12th. The main topics and maths formula for class 10th are
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  πr² 
Circumference of Circle  2πr 
Length of the Arch  (θ/360) * 2πr 
Area of the sector  (θ/360) * πr² 
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  π(R² – r²) 
Perimeter of Semicircle  πr + 2r 
Perimeter of Sector  (θ/360) * 2πr + 2r/θ * r + 2r 
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 the 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 
Cuboid  (TSA) = 2(lb + bh + hl) (LSA) = 2h(l + b) Volume = lbh 
Cube  TSA = 6a² LSA = 4a² Volume = a³ 
Cylinder  Curved Surface Area (CSA) = 2πrh Total Surface Area (TSA) = 2πr(h + r) Volume = πr²h 
Cone  Curved Surface Area (CSA) = πrl Total Surface Area (TSA) = πr(l + r) Volume = 1/3 πr²h 
Sphere  Surface Area = 4πr² Volume = 4/3 πr³ 
Hemisphere  Total Surface Area (TSA) = 3πr² Curved Surface Area (CSA) = 2πr² Volume = 2/3 πr³ 
Class 10 Maths Chapter 13 NCERT PDF
Chapter 14: Statistics
Important maths formulas for class 10th of this chapter are
Terms  Formulas 
Mean  Individual Series: Mean = Σx/n Discrete Series: Mean = Σfx/Σf Continuous Series: Mean = A + Σfd/Σf 
Median  Discrete Series: Median = l + [(n/2 – cf)/f] × h Continuous Series: Median = l + [(n/2 – cf)/f] × h 
Mode  Discrete Series: Mode = Value with the highest frequency Continuous Series: Mode = l + [(f1 – f0)/(2f1 – f0 – f2)] × h 
Check out 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 of 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. Stay tuned with the Leverage Edu webpage.

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𝓣𝓱𝓪𝓷𝓴 𝔂𝓸𝓾
Thank you
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My thoughts is iam winning for 10 results is 500 plus marks