Maths Formulas for Class 10 PDF Free Download 2024-25

Class 10 is a pivotal year in a student’s academic life, setting the foundation for future career choices and higher studies. Among the various subjects, Maths often stands out as one of the most challenging. Mastering Maths formulas for Class 10 is crucial not only for scoring high in exams but also for developing essential problem-solving and analytical thinking skills.

This blog offers a comprehensive list of Maths formulas for Class 10, neatly organized by topics. It also includes practical tips, detailed examples, real-world applications, and downloadable Maths formulas for Class 10 PDFs for each chapter from the NCERT textbook. All these resources are designed to make your learning process more efficient and help you approach problems with confidence.

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

To enhance your learning experience, you can download the Class 10 Maths Chapter 1 NCERT PDF by clicking the PDF button below. This will allow you to deepen your understanding of the chapter concepts and significantly improve your problem-solving skills.

Try solving these BODMAS Questions!

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

To enhance your learning experience, you can download the Class 10 Maths Chapter 2 NCERT PDF by clicking the PDF button below. This will allow you to deepen your understanding of the chapter concepts and significantly improve your problem-solving skills.

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

To enhance your learning experience, you can download the Class 10 Maths Chapter 3 NCERT PDF by clicking the PDF button below. This will allow you to deepen your understanding of the chapter concepts and significantly improve your problem-solving skills.

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

To enhance your learning experience, you can download the Class 10 Maths Chapter 4 NCERT PDF by clicking the PDF button below. This will allow you to deepen your understanding of the chapter concepts and significantly improve your problem-solving skills.

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:	nthterm = a + (n-1) d
Sum of the nth item in Arithmetic Progression:	Sn = n/2 [2a + (n – 1)d]

To enhance your learning experience, you can download the Class 10 Maths Chapter 5 NCERT PDF by clicking the PDF button below. This will allow you to deepen your understanding of the chapter concepts and significantly improve your problem-solving skills.

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 aright-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)

To enhance your learning experience, you can download the Class 10 Maths Chapter 6 NCERT PDF by clicking the PDF button below. This will allow you to deepen your understanding of the chapter concepts and significantly improve your problem-solving skills.

Are you planning to take some competitive exams? Here are some tips on Maths for competitive exams!

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)

To enhance your learning experience, you can download the Class 10 Maths Chapter 7 NCERT PDF by clicking the PDF button below. This will allow you to deepen your understanding of the chapter concepts and significantly improve your problem-solving skills.

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:

Trigonometry Ratio\Angle	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)

To enhance your learning experience, you can download the Class 10 Maths Chapter 8 NCERT PDF by clicking the PDF button below. This will allow you to deepen your understanding of the chapter concepts and significantly improve your problem-solving skills.

Here is a complete list of Trigonometric formulas!

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

To enhance your learning experience, you can download the Class 10 Maths Chapter 10 NCERT PDF by clicking the PDF button below. This will allow you to deepen your understanding of the chapter concepts and significantly improve your problem-solving skills.

Chapter 11: Constructions

Constructions in Class 10 focuses on drawing accurate geometric figures using basic tools like a ruler, compass, and protractor. It enhances spatial reasoning and is essential for solving geometric problems.

Key Constructions and Formulas:

1. Bisecting an Angle:
   • Steps: Draw arcs from both arms of the angle and use the intersection points to draw the bisector, dividing the angle into two equal parts.
2. Perpendicular Bisector of a Line Segment:
   • Steps: Draw arcs above and below the line from both ends, and connect the intersections to create a perpendicular bisector that divides the segment into two equal parts.
3. Constructing a Triangle (Given Sides):
   • Steps: Draw the first side, then use arcs with the other two side lengths to find the third vertex and complete the triangle.
4. Constructing a Triangle (Given Two Sides and the Included Angle):
   • Steps: Draw the first side, measure the angle at one endpoint, then mark the lengths of the other sides to form the triangle.
5. Constructing a Tangent to a Circle:
   • Steps: From a point outside the circle, draw a line perpendicular to the radius at the point of tangency to form the tangent.

Real-Life Applications:

• Engineering & Architecture: For precise design and construction.
• Art & Design: For creating geometric patterns and logos.
• Navigation: In map-making and determining directions.

To enhance your learning experience, you can download the Class 10 Maths Chapter 11 NCERT PDF by clicking the PDF button below. This will allow you to deepen your understanding of the chapter concepts and significantly improve your problem-solving skills.

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

To enhance your learning experience, you can download the Class 10 Maths Chapter 12 NCERT PDF by clicking the PDF button below. This will allow you to deepen your understanding of the chapter concepts and significantly improve your problem-solving skills.

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

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

To enhance your learning experience, you can download the Class 10 Maths Chapter 13 NCERT PDF by clicking the PDF button below. This will allow you to deepen your understanding of the chapter concepts and significantly improve your problem-solving skills.

Chapter 14: Statistics

Important maths formulas for class 10th of this chapter are

Terms	Formulas
Mean	Individual Series: Mean = Σx/n Discrete Series: Mean = Σfixi/Σfi Continuous Series: Mean = A + Σfidi/Σfi
Median	Discrete Series: Median (if N is odd) = N/2 Median (if N is even) = [(N/2)th observation + {(N/2)+1}th observation]/ 2 Continuous Series: Median = l + [(n/2 – cf)/f] × h
Mode	Discrete Series: Mode = Value with the highest frequency Continuous Series: Mode = L + [(fm – f1) x h] / [(fm – f1) + (fm – f2)].

To enhance your learning experience, you can download the Class 10 Maths Chapter 14 NCERT PDF by clicking the PDF button below. This will allow you to deepen your understanding of the chapter concepts and significantly improve your problem-solving skills.

Check out the list of Mensuration formulas!

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

To enhance your learning experience, you can download the Class 10 Maths Chapter 15 NCERT PDF by clicking the PDF button below. This will allow you to deepen your understanding of the chapter concepts and significantly improve your problem-solving skills.

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 + cos²θ = 1
• sec²θ = 1 + tan²θ for 0° ≤ θ < 90°
• Cosec²θ = 1 + cot²θ for 0° ≤ θ ≤ 90°

Take This Maths Quiz If You Consider Yourself Genius!

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 on Maths Formulas for Class 10

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.