Math
List of Maths Formulas for Class 10th CBSE
Table of Contents
Important Maths Formulas for Class 10
People are math phobic and they think that they could not master the math formulas at all. This negative attitude affects their progress and they are nervous during their exams too. To get rid of this situation, students should have a strong hold on the basics of this subject. With a depth understanding of mathematical formulas, this is possible to score maximum marks in the exam and crack most difficult mathematics problems too.
Chapterwise Marks in Exam
Formulas are the basic building blocks that are vital to learning from the future perspective of a child. They are used to clear tough competitive exams too and can be downloaded in PDF format online. Here, in this section, we have given the chapterwise marking scheme for different mathematics chapter.
Chapter  Marking Scheme 
Algebra  26 
Geometry  12 
Trigonometry  10 
Circle Theory  22 
Probability  12 
Mensuration  10 
Coordinate Geometry  8 
Chapter of Maths for Class 10
Maths is a crucial subject and an integral part of the study during your early schools. For the class 10^{th} standard, there is a critical phase when students have to learn typical mathematics formulas. These formulas are the solid foundation of your study in class 10^{th} and they should be practiced wisely.
Here, we have a complete list of chapters of maths for class 10^{th}.
 Chapter 1 Real Numbers
 Chapter 2 Polynomials
 Chapter 3 Linear Equations in Two Variables
 Chapter 4 Quadratic Equations
 Chapter 5 Arithmetic Progressions
 Chapter 6 Triangles
 Chapter 7 Coordinate Geometry
 Chapter 8 Introduction to Trigonometry
 Chapter 9 Some Applications of Trigonometry
 Chapter 10 Circles
 Chapter 11 Constructions
 Chapter 12 Areas Related to Circles
 Chapter 13 Surface Areas and Volume
 Chapter 14 Statistics
 Chapter 15 Probability
Chapterwise Maths Formulas for Class 10
These days online coaching is at the top where you may get almost everything in an easy format. The same is true for mathematical formulas too. Online you may download a complete list of chapterwise maths formulas for class 10^{th} CBSE for Algebra, Trigonometry, Geometry, Probability, and Mensuration etc.
 a^{2} – b^{2} = (a – b)(a + b)
 (a+b)^{2} = a^{2} + 2ab + b^{2}
 a^{2} + b^{2} = (a – b)^{2} + 2ab
 (a – b)^{2} = a^{2} – 2ab + b^{2}
 (a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2ab + 2ac + 2bc
 (a – b – c)^{2} = a^{2} + b^{2} + c^{2} – 2ab – 2ac + 2bc
 (a + b)^{3} = a^{3} + 3a^{2}b + 3ab^{2} + b^{3} ; (a + b)^{3} = a^{3} + b^{3} + 3ab(a + b)
 (a – b)^{3} = a^{3} – 3a^{2}b + 3ab^{2} – b^{3}
 a^{3} – b^{3} = (a – b)(a^{2} + ab + b^{2})
 a^{3} + b^{3} = (a + b)(a^{2} – ab + b^{2})
 (a + b)^{3} = a^{3} + 3a^{2}b + 3ab^{2} + b^{3}
 (a – b)^{3} = a^{3} – 3a^{2}b + 3ab^{2} – b^{3}
 (a + b)^{4} = a^{4} + 4a^{3}b + 6a^{2}b^{2} + 4ab^{3} + b^{4})
 (a – b)^{4} = a^{4} – 4a^{3}b + 6a^{2}b^{2} – 4ab^{3} + b^{4})
 a^{4} – b^{4} = (a – b)(a + b)(a^{2} + b^{2})
 a^{5} – b^{5} = (a – b)(a^{4} + a^{3}b + a^{2}b^{2} + ab^{3} + b^{4})
 If n is a natural number, a^{n} – b^{n} = (a – b)(a^{n1} + a^{n2}b+…+ b^{n2}a + b^{n1})
 If n is even (n = 2k), a^{n} + b^{n} = (a + b)(a^{n1} – a^{n2}b +…+ b^{n2}a – b^{n1})
 If n is odd (n = 2k + 1), a^{n} + b^{n} = (a + b)(a^{n1} – a^{n2}b +… b^{n2}a + b^{n1})
 (a + b + c + …)^{2} = a^{2} + b^{2} + c^{2} + … + 2(ab + ac + bc + ….
 Laws of Exponents
(a^{m})(a^{n}) = a^{m+n }(ab)^{m} = a^{m}b^{m }(a^{m})^{n} = a^{mn}  Fractional Exponents
a^{0} = 1
aman=am−naman=am−n
amam = 1a−m1a−m^{ }a−ma−m = 1am
A.Trigonometry Formulas involving Periodicity Identities:
 \(sin(x+2\pi )=sin\; x\)
 \(cos(x+2\pi )=cos\; x\)
 \(tan(x+\pi )=tan\; x\)
 \(cot(x+\pi )=cot\; x\)
B.Trigonometry Formulas involving Cofunction Identities – degree:
 \(sin(90^{\circ}x)=cos\; x\)
 \(cos(90^{\circ}x)=sin\; x\)
 \(tan(90^{\circ}x)=cot\; x\)
 \(cot(90^{\circ}x)=tan\; x\)
C.Trigonometry Formulas involving Sum/Difference Identities:
 \( \sin (x + y) = \sin(x) \cos(y) + \cos(x) \sin(y)\)
 \(\cos(x + y) = \cos(x) \cos(y) – \sin(x) \sin(y)\)
 \(\tan(x+y)=\frac{\tan\: x+\tan\: y}{1\tan\: x\cdot \tan\: y}\)
 \(\sin(x – y) = \sin(x) \cos(y) – \cos(x) \sin(y)\)
 \(\cos(x – y) = \cos(x) \cos(y) + \sin(x) \sin(y)\)
 \(\tan(xy)=\frac{\tan\: x – \tan\: y}{1+\tan\: x\cdot tan\: y}\)
D.Trigonometry Formulas involving Double Angle Identities:
 \(\sin(2x) = 2\sin(x).\cos(x)\)
 \(\cos(2x) = \cos^{2}(x) – \sin^{2}(x)\)
 \(\cos(2x) = 2 \cos^{2}(x) 1\)
 \(\cos(2x) = 1 – 2 \sin^{2}(x)\)
 \(\tan(2x) = \frac{[2\: \tan(x)]}{[1 \tan^{2}(x)]}\)
E.Trigonometry Formulas involving Half Angle Identities:
 \(\sin\frac{x}{2}=\pm \sqrt{\frac{1\cos\: x}{2}}\)
 \(\cos\frac{x}{2}=\pm \sqrt{\frac{1+\cos\: x}{2}}\)
 \(\tan(\frac{x}{2}) = \sqrt{\frac{1\cos(x)}{1+\cos(x)}}\)
Also, \(\tan(\frac{x}{2}) = \sqrt{\frac{1\cos(x)}{1+\cos(x)}}\\ \\ \\ =\sqrt{\frac{(1\cos(x))(1\cos(x))}{(1+\cos(x))(1\cos(x))}}\\ \\ \\ =\sqrt{\frac{(1\cos(x))^{2}}{1\cos^{2}(x)}}\\ \\ \\ =\sqrt{\frac{(1\cos(x))^{2}}{\sin^{2}(x)}}\\ \\ \\ =\frac{1\cos(x)}{\sin(x)}\)
So, \(\tan(\frac{x}{2}) =\frac{1\cos(x)}{\sin(x)}\)
F.Trigonometry Formulas involving Product identities:
 \(\sin\: x\cdot \cos\:y=\frac{\sin(x+y)+\sin(xy)}{2}\)
 \(\cos\: x\cdot \cos\:y=\frac{\cos(x+y)+\cos(xy)}{2}\)
 \(\sin\: x\cdot \sin\:y=\frac{\cos(x+y)\cos(xy)}{2}\)
G.Trigonometry Formulas involving Sum to Product Identities:
 \(\sin\: x+\sin\: y=2\sin\frac{x+y}{2}\cos\frac{xy}{2}\)
 \(\sin\: x\sin\: y=2\cos\frac{x+y}{2}\sin\frac{xy}{2}\)
 \(\cos\: x+\cos\: y=2\cos\frac{x+y}{2}\cos\frac{xy}{2}\)
 \(\cos\: x\cos\: y=2\sin\frac{x+y}{2}\sin\frac{xy}{2}\)<
6). rigonometry Formulas involving Pythagorean Identities
Sin^{2}x + Cos^{2}x = 1
1 + tan^{2}x = sec^{2}x
1 + cot^{2}x = cosec^{2}x
7). Trigonometry Formulas involving Pythagorean Identities in Radical Form
sinx = ∓√1–cos2x
tanx = ∓√sec2x1
cosx = ∓√1–sin2x
8). Trigonometry Formulas involving OddEven Identities
Also called negative angle identities
Sin(x)=sin x
cos(x)=cos x
tan(x)=tan x
cot(x)=cot x
sec(x)=sec x
cosec(x)=cosec x
Ratio or Quotient Identities are given as:
Sinθ = Cosθ X Tanθ
Cosθ = Sinθ X Cotθ
Tanθ = ^{Sinθ }⁄_{Cosθ}
Cotθ = ^{Cosθ}⁄_{Sinθ}
\(\sin \theta = \frac{Opposite}{Hypotenuse}\)
\(\sec \theta = \frac{Hypotenuse}{Adjacent}\)
\(\cos\theta = \frac{Adjacent}{Hypotenuse}\)
\(\tan \theta =\frac{Opposite}{Adjacent}\)
\(csc \theta = \frac{Hypotenuse}{Opposite}\)
\(cot \theta = \frac{Adjacent}{Opposite}\)
The Reciprocal Identities are given as:
\(cosec\theta =\frac{1}{\sin\theta }\)
\(sec\theta =\frac{1}{\cos\theta }\)
\(cot\theta =\frac{1}{\tan\theta }\)
\(sin\theta =\frac{1}{csc\theta }\)
\(cos\theta =\frac{1}{\sec\theta }\)
\(tan\theta =\frac{1}{cot\theta }\)
Getting good mathematics teachers who focus on studies completely are difficult to find. So, the best find idea is to make a list of formulas yourself or download them online start practicing right away. During practice, you will face problems too but never lose the hope because every time there is some problem, there is one solution too.
Try to improve your weaknesses with the right practice and efforts. Design an effective study plan and give more time to the topics that seem difficult than others. You should utilize a set of problems for practice and try to solve them in a given timeframe only. The topics given in the syllabus of class 9^{th} and 10^{th} are the foundation of mathematics especially for the students who want to get into engineering and research studies.
If you are not sure of basic problems then how can you solve typical problems in the future. Math concepts are used everywhere around us. Construction, shapes, motion, and manufacturing, machines are the result of mathematical applications in the realtime. So, a deep understanding is vital for effective learning in the future as well. Also, this is easy for you to get into higher studies and passing competitive exams in first attempt only.

Math2 years ago
Surface Area of a Triangular Prism Formula & Volume of a Triangular

Math2 months ago
Average Rate Of Change Formula Made Simple

Math2 months ago
Math Formulas Made Simple: A StepbyStep Guide

Math2 years ago
Percentage Formulas  How to Calculate Percentages of a Number?

Math1 year ago
Triangular Pyramid Formula  Volume & Surface Area of a Triangular Pyramid

Math2 years ago
What is Integration? List of Integration by Parts Formulas

Math2 months ago
Algebra Formulas and Expression with Example

Math2 years ago
List of Pyramid Formula – Surface Area, Volume of Pyramid