Maths Formulas for Class 10 – All Chapters

Many Class 10 students lose marks in Maths due to weak formula recall. Maths formulas for Class 10 are key equations from each chapter that help you solve exam questions quickly and correctly.

Students who revise important formulas regularly improve speed and accuracy in the exam. Strong formula knowledge also helps in quick revision before tests and reduces mistakes in problem-solving.

This page provides CBSE Class 10 Maths formulas for all chapters based on the latest NCERT syllabus. You will get a chapter-wise Maths formulas PDF download, practice questions, and simple tips to help you remember each formula and apply it with confidence in the board exam.

Class 10 Maths Formula Chart (PDF Download)

Don’t want to miss out on important formulas during your class 10 Maths board exam prep? Well, all you need are the Maths formulas for class 10 combined in one convenient place. No need to waste time writing everything down manually, you can get quick and easy access to every important formula by simply clicking the link for the Maths formulas for Class 10 PDF free download here.

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Basic Maths Formulas for Class 10

Before we get into the chapter-wise Maths formulas for class 10, let’s start with the basics. These are formulas that every class 10 student should have at their fingertips, as they are simple and frequently used in the majority of sums.  

Chapter-Wise Maths Formulas for Class 10

Chapter-wise formula learning in Maths is important, so you don’t miss out on any formulas suggested by your board of education. It also helps with revision and works as a handy checklist for important formulas. That’s why we’ve categorised Maths formulas for class 10 state board on the basis of all 15 chapters below:

1. Real Numbers

This chapter is the simplest and includes very few formulas. Most of the questions are based on logic and number properties. Thus, stated below are the Maths formulas for class 10 for Real Numbers: 

• Euclid’s Division Lemma:

For any two integers a and b (where a>b),

a = bq+r, where 0 ≤r <b

(Used to find the HCF of two large numbers using repeated division)

• HCF (Highest Common Factor): Break both numbers into prime factors and multiply the common ones. 

• LCM (least common multiple) = Product of two numbers/HCF

2. Polynomials

This chapter is also easy and formula-based, mainly focusing on identities and the degree of polynomials. Moreover, out of all formulas of Maths class 10, these are the most commonly used algebra formulas class 10. They can be stated as follows:

• Identities:

(a+b)² = a² + 2ab +b²

(a−b)² = a² − 2ab +b²

a²−b² = (a−b)(a+b)

(x+a)(x+b) = x²+(a+b)x +ab

• Degree:

Degree of a term = sum of exponents of all variables in that term.

Degree of a polynomial = highest degree among all its terms.

• Factor Theorem:

If p(a)=0, then x−a is a factor of p(x)

3. Pair of Linear Equations in Two Variables

Moderate in difficulty yet scoring, this chapter is about solving equations using 3 methods. Complete all sums from this chapter and just practice 2-3 sums before each exam and you will be good to go. For easy revision, stated below is the formula used and the methods:

• Standard Form: ax + by = c

• Methods of solving:

1. Substitution: Solve one equation for a variable and substitute it into the other equation to find the second variable.

2. Elimination: Multiply equations (if needed) to make the coefficients of one variable equal, then either add or subtract to eliminate that variable and solve.

3. Graphical method: Plot both equations as lines on a graph; the point where they intersect gives the solution (x,y)(x,y).

4. Quadratic Equations

This is a formula-based and scoring chapter. Once you learn how to identify and apply the correct formula, it becomes easy. If you prepare this chapter once and revise before each exam, you can get a full score. Thus, stated below are the important algebra formulas class 10: 

• General form: ax² +bx +c = 0 

• Discriminant: D = b²−4ac

• Roots: 
• (Sridharacharya formula)

5. Arithmetic Progressions

A very easy and scoring chapter with only two main Maths formulas for class 10. It carries only 5-7 marks in the board exam. You can only refer to formulas before your exam to be able to solve the sums from this chapter. We’ve added them below to help you:

• nth Term: a_n = a+(n−1)d
• Sum of the first n terms:

6. Triangles

Triangles cover sums related to similarity, congruency, and the famous Pythagoras Theorem. These sums are of a moderate difficulty level and require practice throughout the year. Listed below are their key formulas:

• Pythagoras Theorem: 

a² + b² = c² (in a right-angled triangle)

• Similarity Rules:

AAA (Angle-Angle-Angle)

SSS (Side-Side-Side)

SAS (Side-Angle-Side)

• Basic Proportionality Theorem (Thales): If a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.

7. Coordinate Geometry

Coordinate Geometry is a moderately difficult chapter. With a good grasp of formulas and consistent practice in visualising points and lines, you can solve most problems with ease. Thus, added below are the 3 most important formulas of this chapter:

• Distance formula: 

• Midpoint formula:

• Section formula: 

8. Introduction to Trigonometry

Trigonometry is usually considered one of the trickiest chapters. However, if you practice all sorts of problems, you will be able to understand where to use which formula. Moreover, the introduction to trigonometric formulas for class 10 will create a solid foundation for higher studies if you choose to pursue Maths. So, keep in mind the following formulas:

• Trigonometric ratios:

sin θ = 1/cosec θ

cos θ = 1/sec θ

tan θ = 1/cot θ

cosec θ = 1/sin θ    

sec θ = 1/cos θ

cot θ = 1/tan θ

• Trigonometric ratios for a right-angled triangle (based on Pythagoras theorem):

sin θ = perpendicular/hypotenuse

cos θ = base/hypotenuse

tan θ = perpendicular/base

sec θ = hypotenuse/base

cosec θ = hypotenuse/perpendicular

cot θ = base/perpendicular

• Trigonometric identities: 

Sin⁡²θ+cos^⁡2θ = 1

1+tan^⁡2θ = sec⁡²θ

1+cot⁡²θ = cosec⁡²θ

• Standard trigonometric table:

9. Applications of Trigonometry

This chapter applies trigonometric ratios to real-life problems like calculating heights and distances. The overall concept is considered to be of medium difficulty. However, if you struggle with understanding the question and visualising the diagram in terms of a right-angled triangle, it can become challenging to apply the formulas correctly. In such cases, consistent practice throughout the year is required to score full marks in this chapter. Thus, stated below are trigonometry formulas of class 10 in terms of application:

• Height (h) = d.tanθ
• Distance (d) = h/tanθ
• To find height using slant or hypotenuse (L): h = L.sinθ
• To find distance using slant or hypotenuse (L): d = L.cosθ

10. Circles

This chapter deals with properties of tangents and angles in circles. There are no specific formulas to apply. The following concepts are used in this chapter:

• Tangent Properties: A tangent to a circle is perpendicular to the radius at the point of contact. From an external point, two tangents to a circle are equal in length.

• Angle Subtended by Arc: The angle subtended by an arc at the centre is twice that at any point on the remaining part of the circle.

11. Constructions

This chapter focuses on geometric constructions using a compass. No formulas are needed; only regular practice is required. The following are constructed in this chapter:

• Division of a line segment

• Construction of tangents to a circle

• Construction of similar triangles

12. Areas Related to Circles

This chapter teaches how to calculate areas involving sectors and segments, commonly found in real-life objects like pies or wheels. It gets tricky if you do not know how to apply Maths formulas for class 10 in circle problem sums. Thus, stated below are formulas for the chapter:

• Area of a circle: πr²
• Circumference of a circle: 2πr
• Area of a segment: Area of a sector – area of a triangle 
• Area of a sector: (θ/360) × πr²

13. Surface Areas and Volumes

This chapter covers formulas for surface areas and volumes of 3D shapes such as cubes, cuboids, cylinders, cones, and spheres, which have been stated below:

• Cube:

Total surface area: 6a²

Lateral surface area: 4a²

Volume: a³

• Cuboid:

Total surface area: 2(lb + bh + hl)

Lateral surface area: 2h(l + b)

Volume: l×b×h

• Cylinder:

Total surface Area: 2πr(h + r)

Curved surface area:  2πrh

Volume: πr²h

• Cone:

Total surface area: πr(l + r)

Curved surface area: πrl

Volume: 1/3 πr²h

• Sphere:

Surface Area = 4πr²

Volume = 4/3 πr³

14. Statistics

Statistics is a straightforward formula-based chpater. You can get full marks if you practice all types of sums mentioned in your textbook. Thus, stated below are statistics class 10 formulas:

• Mean: 

• Median:

Where l = lower boundary, n = total frequency, cf = cumulative frequency before median class, f = frequency of median class, and h = class width

• Mode:

15. Probability

One of the easiest chapters of your syllabus. It includes the basic concept of probability, helping students calculate the likelihood of events. The basic probability formula has been added below: 

• Probability of an event, P(E) = favourable outcome/total number of outcomes

Class 10 Maths Formulas Practice Questions & Answers

Chapterwise formula learning in Maths is important, so you don’t miss out on any formulas suggested by your board of education. It also helps with revision and works as a handy checklist for important formulas. That’s why we’ve categorised Maths formulas for class 10 state board on the basis of chapters below:

1. A card is drawn from a well-shuffled deck. Find the probability of drawing a king.

Total cards = 52

Kings = 4

Formula used, P(E) = favourable outcome/total number of outcomes 

 P(E) = 4/52 

Answer: 1/13 

2. Find sin⁡30°+cos⁡60°

sin⁡30°= 1/2, cos⁡ 60° = ½

⇒1/2 + ½ =1

Answer: 1

3.  A ladder 15 m long is leaning against a wall. If the base of the ladder is 9 m from the wall, how high up the wall does the ladder reach?

Using Pythagoras Theorem

(Hypotenuse)²=(Base)²+(Height)²

In this case:

Hypotenuse = 15 m (ladder)

Base = 9 m (distance from wall)

Height = unknown (how high the ladder reaches)

We rearrange the Pythagoras Theorem to solve for the height:

Height²=Hypotenuse²−Base²

h²=15²−9² 

h²= 225−81=144

⇒h=144 = 12 m

h2=152−92=225−81=144

⇒h=√144=12 m

Answer: 12 m 

4. Find the volume of a cylinder with radius 7 cm and height 10 cm.

Formula used:

V = πr²h 

22/7 × 7² × 10 

22 × 49 × 10 = 10780 cm³

Answer: 10780 cm³

5. If tan⁡θ=5/12, find sin⁡θ

Let the triangle sides be:

Opp = 5, Adj = 12

Hyp = √5²+12² = 13

Answer: sin⁡θ = 5/13

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Tips to Memorise Class 10 Maths Formulas

Trying to memorise all formulas of Maths class 10 in one go isn’t a good idea. Doing so can lead to confusion between similar formulas and might cause you to forget them during exams. Instead, a smarter approach is to understand and revise formulas regularly while solving problems. That’s why stated below are some easy tips to help you remember Maths formulas for class 10:

• As mentioned earlier, refer to a chapter-wise breakdown of formulas. While solving exercises from a chapter, write down all the formulas you come across. Tick off the ones that are used often, these are usually the most important. By the end of the chapter, you’ll have a list of what’s usually asked.

• Instead of trying to memorise Maths formulas for class 10 all chapters blindly, use them while solving questions. When you solve similar types of problems repeatedly using the same formula, it sticks in your memory automatically. This not only helps in remembering the formula but also builds your understanding of its practical usage.

• After completing a chapter, revise it once a month. Solve 5-10 questions as revision to keep the formulas fresh in your mind. This regular practice helps you identify which formulas you remember well and which ones need to be brushed up on.

• Print out a list of all chapter-wise Maths formulas for class 10 and paste it on your study desk or wall. Seeing them daily helps you keep them in your memory. 

• Chapters like Trigonometry require you to remember specific formulas as well as values. So, memorise the standard table of trigonometric ratios for angles like 0°, 30°, 45°, 60°, and 90°. During your exam, quickly write it down in the rough column to avoid confusion and apply it wherever required. 

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