**Maths Formulas For Class 10**: Class 10 is one of the most important classes in a student’s life. Class 10 board exam result is a deciding factor in selecting the stream for further studies – PCM, PCB, Commerce, or Arts. Maths is one of the most important subjects as it is a basic requirement for a lot of career choices. Most of the students who are math phobic must know that high school Mathematics is important. Because the concepts covered during this period are asked in various competitive exams, like CAT, MAT, and even government job exams. In this article, we will provide you with the complete list of Maths formulae for Class 10 to help you with board exam preparation.

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## Maths Formulas For Class 10 (Chapterwise)

Before getting into the list of the formulas, let’s check out the major chapters of Class 10 Maths for which formulas are needed:

- 1) Arithmetic Progression Formulas
- 2) Pair of Linear Equation in Two Variables Formulas
- 3) Trigonometry Formulas
- 4) Algebra and Quadratic Equation Formulas
- 5) Circle Formulas
- 6) Surface Area and Volume Formulas
- 7) Statistics Formulas

### Class 10 Maths Formulas For Arithmetic Progression (AP)

If a1, a2, a3, a4….. be the terms of an AP and d be the common difference between each term, then the sequence can be written as: a, a + d, a + 2d, a + 3d, a + 4d…… a + nd. where a is the first term and (a + nd) is the (n – 1) th term. So, the formula to calculate the nth term of AP is given as:

**n ^{th} term = a + (n-1) d**

The sum for the nth term of AP where **a** is the 1st term, **d** is the common difference, and **l** is the last term is given as:

**S _{n} = n/2 [2a + (n-1) d]** or

**S**

_{n}= n/2 [a + l]### Class 10 Maths Formulas For Linear Equations

Linear equations in one, two, and three variables have the following forms:

Linear Equation in one Variable | ax + b=0 | Where a ≠ 0 and a & b are real numbers |

Linear Equation in Two Variables | ax + by + c = 0 | Where a ≠ 0 & b ≠ 0 and a, b & c are real numbers |

Linear Equation in Three Variables | ax + by + cz + d = 0 | Where a ≠ 0, b ≠ 0, c ≠ 0 and a, b, c, d are real numbers |

The pair of linear equations in two variables are given as:

a_{1}x+b_{1}+c_{1}=0 and a_{2}x+b_{2}+c_{2}=0

Where a_{1}, b_{1}, c_{1}, & a_{2}, b_{2}, c_{2} are real numbers & a_{1}^{2}+b_{1}^{2} ≠ 0 & a_{2}^{2 }+ b_{2}^{2} ≠ 0

**Quick Note:** Linear equations can also be represented in graphical form.

### Trigonometry Formulas For Class 10 Maths

The Trigonometric Formulas for Class 10 covers the basic trigonometric functions for a right-angled triangle i.e. Sine (sin), Cosine (cos), and Tangent (tan) which can be used to derive Cosecant (cos), Secant (sec), and Cotangent (cot).

Let a right-angled triangle ABC is right-angled at point B and have \(\angle \theta\) is one of the other two angles.

sin θ = \(\frac{Side\, opposite\, to\, angle\, \theta}{Hypotenuse}\) = \(\frac{Perpendicular}{Hypotenuse}\) = P/H

cos θ = \(\frac{Adjacent\, side\, to\, angle\, \theta}{Hypotenuse}\) = \(\frac{Adjacent side}{Hypotenuse}\) = B/H

tan θ = \(\frac{Side\, opposite\, to\, angle\, \theta}{Adjacent\, side\, to\, angle\, \theta}\) = P/B

sec θ = \(\frac{1}{cos\, \theta }\)

cot θ = \(\frac{1}{tan\, \theta }\)

cosec θ = \(\frac{1}{sin\, \theta }\)

tan θ = \(\frac{Sin\, \theta }{Cos\, \theta }\)

The **Trigonometric Table** comprising the values of these trigonometric functions for standard angles is as under:

Angle | 0° | 30° | 45° | 60° | 90° |

sinθ | 0 | 1/2 | 1/√2 | √3/2 | 1 |

cosθ | 1 | √3/2 | 1/√2 | ½ | 0 |

tanθ | 0 | 1/√3 | 1 | √3 | Undefined |

cotθ | Undefined | √3 | 1 | 1/√3 | 0 |

secθ | 1 | 2/√3 | √2 | 2 | Undefined |

cosecθ | Undefined | 2 | √2 | 2/√3 | 1 |

Some other trigonometric formulas are given below:

- 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 - sin
^{2}θ + cos^{2}θ = 1 - sec
^{2 }θ = 1 + tan^{2}θ for 0**°**≤ θ < 90**°** - Cosec
^{2 }θ = 1 + cot^{2}θ for 0**°**≤ θ ≤ 90**°**

### Class 10 Maths Formulas For Algebra & Quadratic Equations

To know the algebra formulas for Class 10, first, you need to get familiar with Quadratic Equations.

The Quadratic Formula: For a quadratic equation px^{2} + qx + r = 0, the values of x which are the solutions of the equation are given by: |

\(x=-b\pm\frac{\sqrt{b^2-4ac}}{2a}\)

Now you know the basic quadratic equation.

Let us now go through the list of algebra formulas for Class 10:

- (a+b)
^{2 }= a^{2 }+ b^{2 }+ 2ab - (a-b)
^{2 }= a^{2 }+ b^{2 }– 2ab - (a+b) (a-b) = a
^{2 }– b^{2} - (x + a)(x + b) = x
^{2}+ (a + b)x + ab - (x + a)(x – b) = x
^{2}+ (a – b)x – ab - (a + b)
^{3}= a^{3}+ b^{3}+ 3ab(a + b) - (a – b)
^{3}= a^{3}– b^{3}– 3ab(a – b) - (x – a)(x + b) = x
^{2}+ (b – a)x – ab - (x – a)(x – b) = x
^{2}– (a + b)x + ab - (x + y + z)
^{2}= x^{2}+ y^{2}+ z^{2}+ 2xy + 2yz + 2xz - (x + y – z)
^{2}= x^{2}+ y^{2}+ z^{2}+ 2xy – 2yz – 2xz - (x – y + z)
^{2}= x^{2}+ y^{2}+ z^{2}– 2xy – 2yz + 2xz - (x – y – z)
^{2}= x^{2}+ y^{2}+ z^{2}– 2xy + 2yz – 2xz - x
^{3}+ y^{3}+ z^{3}– 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz -xz) - x
^{2 }+ y^{2}=½ [(x + y)^{2}+ (x – y)^{2}] - (x + a) (x + b) (x + c) = x
^{3}+ (a + b +c)x^{2}+ (ab + bc + ca)x + abc - x
^{3}+ y^{3}= (x + y) (x^{2}– xy + y^{2}) - x
^{3}– y^{3}= (x – y) (x^{2}+ xy + y^{2}) - x
^{2}+ y^{2}+ z^{2}-xy – yz – zx = ½ [(x-y)^{2}+ (y-z)^{2}+ (z-x)^{2}]

**Quick Note**: These formulas will be important in higher classes and various comeptitive examninations. So, memorize them and understand them well.

### Class 10 Maths Formulas For Circle

Circle formulas act as a base for Mensuration. The Class 10 Maths Circle formulas for a circle of radius **r** are given below:

- 1. Circumference of the circle = 2 π r
- 2. Area of the circle = π r
^{2} - 3. Area of the sector of angle θ = (θ/360) × π r
^{2} - 4. Length of an arc of a sector of angle θ = (θ/360) × 2 π r

### Class 10 Maths Formulas For Surface Area & Volume

These formulas are very important for successfully solving mensuration questions. Find below the formulas in a tabulated form for your convenience.

Here, LSA = Lateral Surface Area,

TSA = Total Surface Area.

Sphere | Diameter: 2rCircumference: 2 π rTSA: 4πr^{2} Volume: \(\frac{4}{3}\pi r^2\)r = radius |

Cylinder | Circumference: 2πrLSA: 2πrhTSA: 2πr (r + h)Volume: πr^{2}hr = radius, h = height |

Cone | Slant height: \(l=\sqrt{h^2+r^2}\)LSA: πrlTSA: πr(r + l)Volume: \(\frac{1}{3}\pi r^2h\) r = radius, l = slant height, h = height |

Cuboid | LSA: 2h(l + b)TSA: 2(lb + bh + hl)Volume: lbhl = length, b = breadth, h = height |

Cube | LSA: 4a^{2}TSA: 6a^{2}Volume: a^{3}a = sides of a cube |

### Class 10 Maths Formulas For Statistics

Statistics in Class 10 is majorly about finding the Mean, Median, and Mode of the given data. The statistic formulas are given below:

**(I) The Mean of Grouped Data** can be found by 3 methods.

**Direct Method: x̅**= \(\frac{\sum_{i=1}^{n}f_{i}x_{i}}{\sum_{i=1}^{n}f_{i}}\), where f_{i }x_{i }is the sum of observations for i = 1 to n And f_{i }is the number of observations for i = 1 to n**Assumed Mean Method**:**x̅**= a+\(\frac{\sum_{i=1}^{n}f_{i}d_{i}}{\sum_{i=1}^{n}f_{i}}\)**Step Deviation Method : x̅**= a+\(\frac{\sum_{i=1}^{n}f_{i}u_{i}}{\sum_{i=1}^{n}f_{i}}\times h\)

**(II) The Mode of Grouped Data:** Mode = l +\(\frac{f_{i}-f_{0}}{2f_{1}-f_{0}-f_{2}}\times h\)

**(III) The median for a grouped data:** Median = l+\(\frac{\frac{n}{2}-cf}{f}\times h\)

### Some FAQs On Maths Formulas Class 10

Here are some frequently asked questions that students ask regarding Class 10 Maths Formulas.

**Ques 1: How do you memorize math formulas?**

Ans: Learning or memorizing maths formulas requires a lot of practice. First, familiarize yourself with the chapter and concepts, then try to understand how a formula is derived and then memorize it.

**Quest 2: What is the difference between formula and equation?**

Ans: A formal is a set of instructions that produces the desired result whereas an equation contains numerical operators. For and equation the LHS should be equal to RHS.

**Ques 3: How can I learn maths formulas for Class 10 easily?**

Ans: To learn maths formulas easily you can take the help of formulas provided in this article. You can learn them directly from the article or you can take a printout.

**Ques 4: Where can I get maths formulas for Surface Areas and volume?**

Ans: Students looking for Surface Areas and Volume formulas can view them through this article.

**SOLVE CLASS 10 MATHS PRACTICE QUESTIONS NOW**

These are some of the important formulas for Class 10 Maths. These Maths formulas for Class 10 will prove to be helpful in your learning process. You will find them useful while revising the CBSE Class 10 Maths syllabus.

Solve the free **Class 10 Maths questions** and refer to these formulas to score better in Class 10 board exams:

Maths Formulas For Class 8 | Mensuration Formulas |

Trigonometry Table | Trigonometric Ratios |

*If you have any queries regarding this article on *Maths formulas for class 1*0 , feel free to ask in the comment section below. We will get back to you at the earliest.*

*Embibe wishes you all the best!*

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