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December 25, 201539 Insightful Publications

**Maths Formulas for Class 10:** Memorising formulas in Class 10 Maths is difficult. Students tend to become nervous and forget the formulas. These formulae lay the mathematical foundation for high school and college entrance exams. Students who memorise formulas well tend to score better marks in Maths exams. Formulas in Class 10 help students solve mathematical problems with greater accuracy.

In addition to Maths, these formulae can also be applied in various fields. Students can also use the chapter-by-chapter Maths Formulas for Class 10 to prepare for the board exams. We advise students to download the PDF of these formulas to refer to them offline while studying for exams. Below we have provided all the necessary details related to Maths Formulas for Class 10.

Compiling all formulas of Class 10 Maths is not easy for the students. However, it is essential to score well in the Class 10 board exams, and Maths is one of the compulsory subjects in Class 10 in which students can score well. This exam is out of 100 marks and covers all the basic topics of Mathematics.

We at Embibe have covered all the formulas of Maths Class 10 NCERT PDF to help with your exam preparation. This exam is of 3 hours duration, and in order to manage this available time well during the examination, you must be aware of all the important concepts and their formulas.

Learning math is time-consuming because of the need for problem-solving and calculations. To learn these 10th Class Maths formulas, students can use PDFs created by Embibe. Before getting into the list of the formulas, let us check out the major chapters of Class 10 Maths for which formulas are needed:

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 a common difference, and **l** is the last term, is given as:

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

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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.

The **Trigonometric Formulas** for Class 10 cover 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**°**

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 competitive examinations. So, memorise them and understand them well.

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

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

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 |

Statistics in Class 10 is mostly about finding the given data’s Mean, Median, and Mode. 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+\(\frac{\frac{n}{2}-cf}{f}\times h\)

Mathematical formulas are the basic components needed to solve complicated Math problems, and these are highly beneficial in the below-mentioned ways:

- Maths formulas for Class 10 PDF covers all the important formulas of all chapters.
- Using PDF, candidates will have easy access to all chapters in one place.
- Formula PDF is prepared to cover the latest syllabus of CBSE according to chapters.
- With this, students can easily revise all-important things in one place.

**Ans: **For learning Maths formulas, students must practice the problems involving these formulas regularly.

**Ans:** Learning and memorising Maths formulas require a lot of effort and practice. Students must be familiar with the chapters and the concepts and then try to understand how a formula is derived.

**Ans: **The difficulty level of Maths is moderate, and topics and inflow from basic to advanced. The candidate must be acquainted with the formulas for making Maths easy to study and solve.

**Ans: **The important topics of NCERT Class 10 Maths syllabus includes statistics and probability, Geometry, and Algebra.

**Ans:** Students who are looking for the Maths formula for Surface area and volume can find them in this article.