CBSE Class 10 Maths Formulas and Important Equations

• NCERT Solutions for Class 10 Math

• Math Revision Notes for Class 10

• CBSE Previous Year Question Papers for Class 10 with Solutions

Math Important Formulas and Equations of Class 10

Linear Equations Formulas Class 10

Pair of Linear Equations in Two Variables Formula Class 10

Where,

$a_1, b_1, c_1, a_2, b_2,$ and $c_2$ are all real numbers and

$a_{12} + b_{12} \neq 0$ and $a_{22} + b_{22} \neq 0$

Additionally, it's worth noting that we can represent linear equations in two variables graphically.

Quadratic Equations Formula Class 10

Algebraic Formulas Class 10

$(a+b)^2=a^2+b^2+2 a b \\ (a-b)^2=a^2+b^2-2 a b \\ (a+b)(a-b)=a^2-b^2 \\ (x+a)(x+b)=x^2+(a+b) x+a b \\ (x+a)(x-b)=x^2+(a-b) x-a b \\ (x-a)(x+b)=x^2+(b-a) x-a b \\ (x-a)(x-b)=x^2-(a+b) x+a b \\ (a+b)^3=a^3+b^3+3 a b(a+b) \\ (a-b)^3=a^3-b^3-3 a b(a-b) \\ (x+y+z)^2=x^2+y^2+z^2+2 x y+2 y z+2 x z \\ (x+y-z)^2=x^2+y^2+z^2+2 x y-2 y z-2 x z \\ (x-y+z)^2=x^2+y^2+z^2-2 x y-2 y z+2 x z \\ (x-y-z)^2=x^2+y^2+z^2-2 x y+2 y z-2 x z \\ x^3+y^3+z^3-3 x y z=(x+y+z)\left(x^2+y^2+z^2-x y-y z-x z\right) \\ x^2+y^2=1 / 2\left[(x+y)^2+(x-y)^2\right] \\ (x+a)(x+b)(x+c)=x^3+(a+b+c) x^2+(a b+b c+c a) x+a b c \\ x^3+y^3=(x+y)\left(x^2-x y+y^2\right) \\ x^3-y^3=(x-y)\left(x^2+x y+y^2\right) \\ x^2+y^2+z^2-x y-y z-z x=1 / 2\left[(x-y)^2+(y-z)^2+(z-x)^2\right]$

Basic Formulas for Powers of Class 10

$p^m \times p^n = p^{m+n}\\ \dfrac{p^m}{p^n} = p^{m-n}\\ (p^m)^n = p^{mn}\\ p^{-m} = \dfrac{1}{p^m}\\ p^1 = p\\ P^0 = 1$

Arithmetic Progression Formula Class 10

Trigonometry Formula Class 10

In 10th class trigonometry formulas focus on three main functions: Sine, Cosine, and Tangent, which apply to right-angled triangles. These functions are useful for calculating angles and sides in such triangles. Additionally, we can derive formulas for secant, cosecant, and cotangent using the sine, cosine, and tangent formulas.

Consider a right-angled triangle ABC, where angle θ is at point B.

1. $\sin \theta = \dfrac{\text{Side opposite to angle}}{\text{Hypotenuse}} = \dfrac{\text { Perpendicular }}{\text { Hypotenuse }} = P/H$

2. $\cos \theta = \dfrac{\text { Adjacent side to angle } \theta}{\text { Hypotenuse }} = \dfrac{\text { Base }}{\text { Hypotenuse }} = B/H$

3. $\tan \theta = \dfrac{\text {Side opposite to angle }\theta}{\text {Adjacent side to angle }\theta} = P/B$

4. $\sec \theta = \dfrac{1}{\cos \theta}$

5. $\cot \theta = \dfrac{1}{\tan \theta}$

6. $\text{cosec} \theta = \dfrac{1}{\sin \theta}$

7. $\tan \theta = \dfrac{{Sin} \theta}{{Cos} \theta}$

Trigonometry Table

Circles Formula Class 10

• Circumference = 2 π r

• Area = π r2

• Area of the sector of angle θ = (θ/360) × π r2

• Length of an arc of a sector of angle θ = (θ/360) × 2 π r

Surface Area and Volumes Formulas Class 10

When it comes to cubes, all the sides are the same length, and we call that length 'a'. Now, if you want to find the surface area or volume of a cube, you just need to use 'a' for all the sides. Easy, right? No need to repeat the same lengths for length, breadth, and height in that case. Keep it simple!

Statistics Class 10 Formulas

The statistics Class 10 Formulas focuses on figuring out the mean, median, and mode of grouped data.

1. Mean: In this, the grouped data can be found by 3 methods

1. Direct Method: $\bar{x}=\frac{\sum_{i=1}^n f_i x_i}{\sum_{i=1}^n f_i}$

2. Assumed mean method: $\bar{x}=a+\frac{\sum_{i=1}^n f_i d_i}{\sum_{i=1}^n f_i}$

3. Step deviation method: $\bar{x}=a+\frac{\sum_{i=1}^n f_i u_i}{\sum_{i=1}^n f_i} \times h$

2. Mode: $\text { Mode }=l+\dfrac{f_1-f_0}{2 f_1-f_0-f_2} \times h$

3. Median: $\text { Median }=l+\dfrac{\frac{n}{2}-cf}{f} \times h$

Section Formula Class 10

\[x = \frac{{x_1 \cdot m + x_2 \cdot n}}{{m + n}}\]

\[y = \frac{{y_1 \cdot m + y_2 \cdot n}}{{m + n}}\]

Here, $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of the endpoints of the line segment.

m and n are the ratios in which the line segment is divided.

Keep in mind, the sum of m and n should be equal to 1. Section Formula Class 10 helps find the coordinates of a point P that divides a line segment AB in the given ratio m:n.

Formula for Class 10 Mathematics

Consolidation of CBSE Class 10 Maths formulas is not an easy task for the students but also very essential. It is necessary for Class 10 board exams and Math is one of the compulsory subjects in Class 10 which can help the students to get good percentages. This exam is of 100 marks and covers all the basic topics of Mathematics and we at Vedantu have covered all class ten math formula NCERT PDF for your preparation. This exam gives students 3 hours of duration to attempt and you will only be able to attempt the entire paper if you are aware of the concepts and their formulas because this is a time-consuming paper because of its problem solving and calculative nature. So you need to master these 10th Class Mathematics formulas for which you can use PDFs created by Vedantu.

Why Should You go for all Formulas of Math Class 10 NCERT PDF?

Formulas are the basic requirement for a subject like Mathematics, and concise notes of class tenth math formula will be beneficial for the students in many ways such as:

• Class 10 Math formulas PDF will help the students to cover important formulas of all the chapters easily.

• Students can get all the formulas of each chapter in one place which they can download with the internet.

• These formulae notes are prepared by the Math experts according to the latest syllabus of the CBSE and as per the demand of each chapter. 

• The experts have included all the necessary formulas in the CBSE 10th class  Math formulas list pdf so that students can revise all the important things in one place before any test or exam.

• We know that it takes a lot of time to prepare precise notes of any topic or subject and it also should be made in a way that becomes easy to revise at the end and which are inclusive of everything necessary. Vedantu solved this problem for the students by providing 10th Class Mathematics Formulas PDF of each chapter.

• Students can use these 10th Class Maths formulas list and align them along with their preparation and start solving problems according to them.

• Chapters like Trigonometry and surface area volume have a lot of formulas without which problems can not be solved. Thus, these PDFs will help you to cover important class ten math formulas.

Chapters Covered in the PDF

CBSE Class 10 Maths formula PDF covers all the chapters of Class 10 CBSE individually and you can download formulas PDF of each chapter individually on the Vedantu platform. The chapters it covers include real numbers, polynomial equations, and quadratic equations pair of linear equations in two variables, arithmetic progressions, triangles, coordinate geometry, Introduction to trigonometry, applications of trigonometry, circles, surface area and volume, statistics, probability. All NCERT Class 10 Maths formula PDF download of these chapters are linked here and you can search them separately as well and then can download the PDFs and start your preparation.

Tips for Preparating Class 10 Maths formula

Here are some general tips for preparing 10th class Mathematics formulas:

• Firstly, make sure you have a strong understanding of the fundamental concepts before diving into formulas. Knowing the basics will help you apply the formulas correctly.

• Compile a formula sheet that includes all the essential formulas in one place. This will make it easier for you to revise and refer to them whenever needed.

• Practice is key in mastering mathematical formulas. Work on a variety of problems that involve different formulas to reinforce your understanding and application skills.

• Create flashcards with the formula on one side and its application or significance on the other. This will help you memorize and understand the context in which each formula is used.

• Solve sample papers and previous years' question papers to get a sense of the types of questions that may appear in exams. This will also improve your time management skills.

• Mathematics is not just about memorizing formulas; it's about problem-solving. Practice solving problems using the formulas to enhance your problem-solving skills.

• Teaching someone else is an effective way to reinforce your own understanding. Explain the formulas and concepts to a friend or family member to ensure you truly grasp them.

• If you encounter difficulties or have doubts about any formula, don't hesitate to ask your teacher or peers for clarification. Understanding the formulas thoroughly is crucial.

• Join or create study groups where you can discuss and solve mathematical problems together. Explaining concepts to peers can deepen your understanding and help you learn from others.

• Consistency is key in mathematics. Set aside regular study time for math and stick to it. Consistent practice will improve your confidence and proficiency with the formulas.

General Tips for Class 10 Math Preparation

Conclusion

CBSE Class 10 Maths Formulas play a pivotal role in understanding and solving mathematical problems. Mastering these formulas, including those for trigonometry, surface area and volume, section formula, and statistics, is crucial for success in the 10th-grade mathematics curriculum. Vedantu provides a valuable resource for students, offering a comprehensive 10th Class maths formulas list. These formulas serve as the foundation for tackling various mathematical concepts, fostering a deeper understanding of the subject. Regular practice and application of these formulas not only enhance problem-solving skills but also empower students to approach mathematical challenges with confidence and proficiency.