Maths is considered to be one of the most important and difficult subjects because of its practical nature. This is a subject that consists of a variety of formulas, theories and concepts that are used for problem-solving and that too requires rigorous practice to become a master in Maths concepts and their formulas.

If you think of a question related to the area or volume of any object, it would not be possible to find the answer without having knowledge of its formulas. Thus, it becomes necessary to learn and revise these formulas regularly if we even talk about basic Maths for class 10.

CREST Champs knows this requirement and therefore we have brought you **Math formulas for Class 10** of each chapter to ease the preparation of the students which will help you do regular practice and score better.

CREST Champs makes sure that all the formulas mentioned are accurate according to the updated syllabus, the latest for the present academic year.

Here’s the list of important formulas for Maths class 10 CBSE chapter-wise. You can find the formulas for the below-mentioned chapters:

**Real Numbers**

**Polynomials**

**Pair of Linear Equations in Two Variables**

**Quadratic Equations**

**Arithmetic Progression**

**Trigonometry**

**Area of Circle**

**Surface Area and Volume**

**Algebraic Formulas**

- Natural Numbers

N ={ 1, 2,3,4,5 … }

- Whole Numbers

W = { 0, 1, 2, 3, 4, 5… }

**Rational Numbers**- Numbers that can be presented in the a/b form.

Polynomials |
General Form |
Formula |

Linear | ax + b = 0, a ≠ 0 | k = {- constant}/{coefficient(x)} |

Quadratic | ax2 + bx + c = 0, a ≠ 0 | k1 + k2 = {coefficient(x)}/{coefficient(x^{2})} |

Cubic | ax3 + bx2 + c = 0, a ≠ 0 | k1 + k2 + k3 = {coefficient(x^{2})}/{coefficient(x^{3})} |

- a
_{1}x+b_{1}y+c_{1}=0 - a
_{2}x+b_{2}y+c_{2}=0

Where

- a
_{1}, b_{1}, c_{1}, a_{2}, b_{2}, and c_{2}are real numbers and - a
_{1}^{2}+b_{1}^{2}≠ 0 & a_{2}^{2}+ b_{2}^{2}≠ 0

The standard form of a Quadratic Equation is:

ax^{2}+bx+c=0 where a ≠ 0 & x = [-b ± √(b^{2} – 4ac)]/2a

If a_{1}, a_{2}, a_{3}….. 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 n^{th} 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 1^{st} term, d is a 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 Trigonometric formulas 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).**

**sinθ** = (Side opposite to angle θ)/(Hypotenuse) = Perpendicular/Hypotenuse = P/H

**cosθ** = (Adjacent side to angle θ)/(Hypotenuse) = Adjacent side/Hypotenuse = B/H

**tanθ** = (Side opposite to angle θ)/(Adjacent side to angle θ) = P/B

Angle |
0° |
30° |
45° |
60° |
90° |

Sinθ |
0 | 1/2 | 1/√2 | √3/2 | 0 |

Cosθ |
1 | √3/2 | 1/√2 | 1/2 | 1 |

Tanθ |
0 | 1/√3 | 1 | √3 | 0 |

Cotθ |
Undefined | √3 | 1 | 1/√3 | Undefined |

Secθ |
1 | 2/√3 | √2 | 2 | 1 |

Cosecθ |
Undefined | 2 | √2 | 2/√3 | Undefined |

- sin(90° – θ) = cosθ
- cos(90° – θ) = sinθ
- tan(90° – θ) = cotθ
- cot(90° – θ) = tanθ
- sec(90° – θ) = cosecθ
- cosec(90° – θ) = secθ
- sin2θ + cos2θ = 1
- sec2θ = 1 + tan2θ for 0° ≤ θ < 90°
- Cosec2θ = 1 + cot2θ for 0° ≤ θ ≤ 90°

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

Where the radius is denoted by **r.**

Here, **LSA = Lateral Surface Area & TSA = Total Surface Area**

**Sphere**- Diameter: 2r
- Circumference: 2πr
- TSA: 4πr
^{2} - Volume: 4/3πr
^{3}

**Cylinder**- Circumference: 2πr
- LSA: 2πrh
- TSA: 2πr(r + h)
- Volume: πr
^{2}h - r = radius
- h = height
- r = radius

**Cone**- Slant height: l = √(r
^{2}+ h^{2}) - LSA: πrl
- TSA: πr(r + l)
- Volume: 1/3πr
^{2}h - r = radius
- l = slant height
- h = height

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

**Cube**- LSA: 4a
^{2} - TSA: 6a
^{2} - Volume: a
^{3} - a = side of a cube

- (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 - (x – a)(x + b) = x
^{2}+ (b – a)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 + 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)(x^{2}+ y^{2}+ z^{2}– 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}]

Formulas are always considered to be the basic requirement for solving any question in Mathematics. Let's go through a few benefits of the Math formulas.

- The formulas collection works best to revise the chapters & also when the last few days are left before the exam.

- Students can revise all the important things in one place before any test or exam.

Hope you’ve gained some knowledge through this useful article. These formulas will surely help you in your preparation for the **class 10 Maths CBSE** **exam. **At CREST Champs, you can also explore **Maths CBSE class 10 courses**. These courses are available by many tutors. If you like to take online coaching for Maths, then CREST Champs is the most preferred platform.

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