Maths Formulas for Class 10 [Download Chapterwise PDF]

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 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!

Maths Formulas for Class 10 Algebraic Equations

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 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	ax2+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:	nth term = a + (n-1) 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 right-angled triangles):

• In a right-angled 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 semi-perimeter (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 higher-level mathematics in classes 11th and 12th. The main topics and maths formula for class 10th are

Category	Formula
Distance Formula	d = √[(x2 – x1)2 + (y2 – y1)2]
Area of 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 semi-perimeter (s = (a + b + c)/2)

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 (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	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

Chapter 12: Areas Related to Circle

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 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 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

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.