# Maths Formulas for Class 10

It’s obvious that students find Maths as a difficult subject and hard to master in it. But with the correct guidance and proper practice by using standard materials help students to grasp the concept easily and solve any kind of maths problems quickly with the help of **Maths Formulas**.

First and foremost, students should memorize all concepts formulas perfectly & apply those math formulas while solving the problems. CBSE Class 10 students have to get good on the maths concepts to decide the higher studies field. So, Maths formulas for Class 10 concepts are prevailing here in the form of lists with examples, formula sheets, or tables. Download or Get them offline & recall all those CBSE Class 10 Maths Formulas.

## Important Maths Formulas for Class 10 CBSE Students

Maths Formulas for Class 10 presented over here covers important formulas from the mathematics fundamentals of class 10. These Class 10 Maths Formulas helps you solve your homework or assignment problems easier and quicker.

- Area Related to Circles Class 10 Formulas
- Surface Areas and Volumes Class 10 Formulas
- Constructions Class 10 Formulas
- Circles Class 10 Formulas
- Introduction to Trigonometry Class 10 Formulas
- Coordinate Geometry Class 10 Formulas
- Arithmetic Progression Class 10 Formulas
- Quadratic Equations Class 10 Formulas
- Pair Of Linear Equations in Two Variables Class 10 Formulas
- Polynomials Class 10 Formulas
- Real Numbers Class 10 Formulas
- Triangles Class 10 Formulas
- Some Applications of Trigonometry Class 10 Formulas
- Statistics Class 10 Formulas
- Probability Class 10 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}h
r = radius, |

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

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

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+\(\frac{\frac{n}{2}-cf}{f}\times h\)