Maths Formulas for Class 10 PDF Free Download

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Maths Formulas for Class 10 PDF is available for download, check the download button at the end of this post. Many students struggle with the subject of mathematics, particularly when it comes to class 10 maths formulas. This is often due to a lack of understanding and connection with the subject. Without a strong foundation, it can be difficult to build upon and excel in this subject.

Consider the example of building a house. A strong and solid foundation is necessary to ensure that the house can withstand any storm. Similarly, in mathematics, having a solid grasp of the basic concepts and formulas is essential for success.

While scoring well in math may seem difficult, it is achievable. The key is to have a thorough understanding of the formulas and techniques required to solve problems. Unlike other subjects, math requires the correct steps to be taken in order to arrive at the right answer.

By reading through our comprehensive articles and resources, you will gain a better understanding of class 10 math formulas and develop the skills needed to excel in this subject.

General Class 10 Maths Formulas

  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]

Class 10 Maths Formulas for All Chapters

Check all the chapter-wise formulas of class 10 maths. Students do not have to check any other article after reading this because you will get all the formulas in table and pdf form in one place. Check all formulas below:

Class 10 Maths Chapter 1 Real Numbers Formulas

Chapter 1 real numbers mostly consist of very few formulas. Check all the formulas in the table given below.

Natural NumbersN ={ 1, 2,3,4,5 … }
Whole NumbersW={ 0, 1, 2, 3, 4, 5… }
Rational NumbersThose numbers which can be presented in the form of a/b are called Rational Numbers.
Re NumbersReal Numbers can be found on a number line

Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Formulas

All the formulas of Chapter 3 pair of linear equations in two variables are given below.

  1. Linear equation in one variable: ax +b =0 
  2. Linear equation in two variables: ax+ by+ c =0 
  3. Linear equation in three variables: ax+ by+ cz= 0

Class 10 Maths Chapter 5 Arithmetic Progression Formulas 

Terms of sequence are denoted by a1 a2, a3, …………… an. An arithmetic progression is a sequence of numbers such that the difference between the consecutive terms is equal.

  1. an = a + (n – 1) d, where an is the nth term.
  2. Sn= n/2 [2a + (n – 1)d]

Class 10 Maths Chapter 8 Trigonometry Formulas

Class 10 chapter 8 trigonometry basically covers three parts sine, cosine, and tangent and the opposite of these are sec, cosec, and cot. Below are all the formulas used in the trigonometry chapter.

Sin θ = Side opposite to angle θ/ Hypotenuse = Perpendicular/Hypotenuse = P/H

Cos θ = Adjacent side to angle θ/ Hypotenuse = Base/ Hypotenuse = B/H

Tan θ = Side opposite to angle θ/ Adjacent side to angle θ = P/B

Cosec θ = 1/ sin θ

Sec θ = 1/ cos θ

Cot = 1/ tan θ

Tan θ = sin θ/ cos θ

Trigonometry Table for Class 10 Chapter 8 Trigonometry

  • Sinθ= 1/ Cosec θ or Sinθ.Cosθ= 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)

Additional Maths Formulas for Class 10 Trigonometry

In addition to the formulas covered in the chapter, there are several other formulas that are essential for solving problems related to class 10 Trigonometry Chapter 8. These formulas will be commonly used in various questions throughout the chapter. A list of these formulas is provided below for easy reference.

  1. sin θ = Side opposite to angle θ/ Hypotenuse = Perpendicular/Hypotenuse= P/H
  2. cos θ = Adjacent side to angle θ/ Hypotenuse= Adjacent Side/ Hypotenuse= B/H
  3. tan θ = Side opposite to angle θ/ Adjacent side to angle θ
  4. sec θ = 1/ cosθ
  5. cot θ = 1/ tanθ
  6. cosec θ = 1/ sinθ
  7. tan θ = Sinθ/ Cosθ
  8. sin (90° – θ) = cos θ
  9. cos (90° – θ) = sin θ
  10. tan (90° – θ) = cot θ
  11. cot (90° – θ) = tan θ
  12. sec (90° – θ) = cosecθ
  13. cosec (90° – θ) = secθ
  14. sin2θ + cos2 θ = 1
  15. sec2 θ = 1 + tan2θ for 0° ≤ θ < 90°
  16. Cosec2 θ = 1 + cot2 θ for 0° ≤ θ ≤ 90°

Class 10 Maths Chapter 10 Area of Circle Formulas

All the formulas of chapter 10 area of the circle have these two formulas which are given below.

  1. The tangent to a circle equation x2 + y2 = a2 for a line y = mx + c is given by the equation y = mx ± a √[1+ m2].
  2. The tangent to a circle equation x2 + y2 = a2 at (a1,b1) is xa1 + yb1 = a2

Class 10 Maths Chapter 13 Surface Area and Volume Formulas

The common formulas of Chapter 13 surface area and volume are given in the table below.

Volume of Sphere4/3 ×π r3
Lateral Surface Area of Sphere (LSA)4π r2
Total Surface Area of Sphere (TSA)4πr2
Right Circular Cylinder
Lateral Surface Area of the Right Circular Cylinder (LSA)πr2h
Lateral Surface Area of the Prism (LSA)2×(πrh)
Total Surface Area of Right Circular Cylinder (TSA)2πr×(r + h)
Volume of Hemisphere⅔ x (πr3)
Lateral Surface Area of Hemisphere (LSA)2πr2
Total Surface Area of Hemisphere (TSA)3πr2
Volume of PrismB × h
Lateral Surface Area of Prism (LSA)p × h

Class 10 Maths Chapter 14 Statistics Formulas

Chapter 14 Statistics mostly deals with finding mean, mode, and median. Check all the statistics formulas in the table below.

Mean of Grouped Data
Mean Direct Method
where ∑fi xi is the sum of observations from value i = 1 to n
And ∑fi is the number of observations from value i = 1 to n
Assumed Mean Method
where a is assumed mean and di is deviation of a from each of the xi.
Also, di = xi – a
Stop Deviation Method

and h is class size
Mode of Grouped Data
l=lower limit of modal class.
h= size of the class interval
f1= frequency of modal class.
f0= frequency of the class preceding the modal class.
f2= frequency of the class succeeding the modal class.
Median of Grouped Data
l=lower limit of median class.
n= number of observations.
cf= cumulative frequency of class preceding the median class.
f= frequency of median class
h= class size

Class 10 Maths Chapter 15 Probability Formulas

The essential formula for the Probability chapter is: 

P(E)= Number of outcome favorable/ Number of all possible outcomes of the experiment

Maths Formulas for Class 10 PDF: File Details

File NameMaths Formulas for Class 10 PDF Free Download
File TypePDF
File Size159 KB
PDF QualityVery Good
No. of Pages10
CategoryMath PDF

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Tips to Memorise Class 10 Maths Formulas

To effectively understand and recall all of the formulas required for class 10 mathematics, it is important to follow some helpful tips. These tips can make it easier to remember formulas in the long run and can improve your overall comprehension of the subject.

Tip 1: Create Mnemonics

Mnemonics are useful memory aids that use a combination of words, letters, numbers, and images to help you recall formulas quickly. By creating your own mnemonics, you can develop a personalized system for remembering mathematical formulas. Explore the various methods below to discover how you can create effective mnemonics for your own use.

Here are the four ways to remember mnemonics better:

[1] Acronyms

One effective way to remember formulas is to create an acronym by taking the first letter of each word in the formula. This can help to easily recall the formula when needed. For instance, the value of Pi (π) to 7 decimal places can be remembered using the acronym “May I have a large container of coffee?”, with each word representing a digit – 3.1415926.

[2] Rhymes

Rhymes to find the Area of a circle

“To find the area of a round space,
Pi times radius squared is the case.”

Another one for the Pythagorean Theorem

“To find the side that is unknown,
Square the two that are clearly shown.
Add them up, and then you’ll see,
The square root is the missing degree.”

By using the mnemonics it becomes easier to recall formulas, which directly helps us to solve problems and make our calculations more efficient.

Tip 2: Break It Down

Breaking down a formula into its individual components can be a helpful way to understand how they all relate to one another. This approach makes it easier to comprehend and remember the formula. By identifying the variables and practicing their use, you can become more proficient in applying the formula and arriving at the correct result.

Tip 3: Repetition

Repetition is a highly effective method for learning mathematical formulas more quickly. Repeating a formula multiple times helps to reinforce it in your memory and makes it easier to recall. There are several ways to incorporate repetition into your studying, such as taking quizzes, using flashcards, daily practice, repeating formulas in various formats, and regular repetition. Through consistent repetition, a formula becomes more familiar and ingrained in your memory, making it easier to recall in the long run.


All the formulas for class 10 math have been listed above, so students don’t need to search for them elsewhere. By practicing these formulas, you can improve your preparation and become more proficient in solving mathematical problems with speed and accuracy. Furthermore, a solid understanding of these formulas can help you tackle more advanced math questions with confidence. Strengthening your preparation through regular practice is crucial for achieving success in mathematics.

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