**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.

**Chapter-wise 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 chapter-wise marking scheme for different mathematics chapter.

Chapter | Marking Scheme |

Algebra | 26 |

Geometry | 12 |

Trigonometry | 10 |

Circle Theory | 22 |

Probability | 12 |

Mensuration | 10 |

Co-ordinate 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

**Chapter-wise 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 chapter-wise 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^{n-1}+ a^{n-2}b+…+ b^{n-2}a + b^{n-1})**If n is even**(n = 2k), a^{n}+ b^{n}= (a + b)(a^{n-1}– a^{n-2}b +…+ b^{n-2}a – b^{n-1})**If n is odd**(n = 2k + 1), a^{n}+ b^{n}= (a + b)(a^{n-1}– a^{n-2}b +…- b^{n-2}a + b^{n-1})- (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

- \(sin(x+2\pi )=sin\; x\)
- \(cos(x+2\pi )=cos\; x\)
- \(tan(x+\pi )=tan\; x\)
- \(cot(x+\pi )=cot\; x\)

- \(sin(90^{\circ}-x)=cos\; x\)
- \(cos(90^{\circ}-x)=sin\; x\)
- \(tan(90^{\circ}-x)=cot\; x\)
- \(cot(90^{\circ}-x)=tan\; x\)

- \( \sin (x + y) = \sin(x) \cos(y) + \cos(x) \sin(y)\)
- \(\cos(x + y) = \cos(x) \cos(y) – \sin(x) \sin(y)\)
- \(\tan(x+y)=\frac{\tan\: x+\tan\: y}{1-\tan\: x\cdot \tan\: y}\)
- \(\sin(x – y) = \sin(x) \cos(y) – \cos(x) \sin(y)\)
- \(\cos(x – y) = \cos(x) \cos(y) + \sin(x) \sin(y)\)
- \(\tan(x-y)=\frac{\tan\: x – \tan\: y}{1+\tan\: x\cdot tan\: y}\)

- \(\sin(2x) = 2\sin(x).\cos(x)\)
- \(\cos(2x) = \cos^{2}(x) – \sin^{2}(x)\)
- \(\cos(2x) = 2 \cos^{2}(x) -1\)
- \(\cos(2x) = 1 – 2 \sin^{2}(x)\)
- \(\tan(2x) = \frac{[2\: \tan(x)]}{[1 -\tan^{2}(x)]}\)

- \(\sin\frac{x}{2}=\pm \sqrt{\frac{1-\cos\: x}{2}}\)
- \(\cos\frac{x}{2}=\pm \sqrt{\frac{1+\cos\: x}{2}}\)
- \(\tan(\frac{x}{2}) = \sqrt{\frac{1-\cos(x)}{1+\cos(x)}}\)

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, \(\tan(\frac{x}{2}) =\frac{1-\cos(x)}{\sin(x)}\)

- \(\sin\: x\cdot \cos\:y=\frac{\sin(x+y)+\sin(x-y)}{2}\)
- \(\cos\: x\cdot \cos\:y=\frac{\cos(x+y)+\cos(x-y)}{2}\)
- \(\sin\: x\cdot \sin\:y=\frac{\cos(x+y)-\cos(x-y)}{2}\)

- \(\sin\: x+\sin\: y=2\sin\frac{x+y}{2}\cos\frac{x-y}{2}\)
- \(\sin\: x-\sin\: y=2\cos\frac{x+y}{2}\sin\frac{x-y}{2}\)
- \(\cos\: x+\cos\: y=2\cos\frac{x+y}{2}\cos\frac{x-y}{2}\)
- \(\cos\: x-\cos\: y=-2\sin\frac{x+y}{2}\sin\frac{x-y}{2}\)<

Sin^{2}x + Cos^{2}x = 1

1 + tan^{2}x = sec^{2}x

1 + cot^{2}x = cosec^{2}x

sinx = ∓√*1*–*cos*2x

tanx = ∓√*sec*2x-*1*

cosx = ∓√*1*–*sin*2x

*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

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 real-time. 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.