# Math Formulas For Class 12

Many students of CBSE class 12 are phobic about math formulas, because of their negativity towards the subject and cannot focus or concentrate on math problems. Students have the most trouble before exams or even small class tests; that’s when nervousness kicks in. Due to the negativity and resentment towards math, most students fail in their exams. Also, check Trigonometry Formula For Class 12.

The only way students can get rid of the subject is by learning to get a strong grip on the maths formula. If students can do their best to be positive about maths formula, then they can achieve the kind of marks they desire. All those students need to do is to understand the concepts learn all the necessary math formulas and apply these formulas according to the problem and find the solution to a difficult question.

## List of Maths Formulas for 12th Class

Here is a list of Maths formulas for CBSE board class 12. Learning these formulas will help students of grade 12 to solve mathematical problems quickly.

Class 12th Maths concepts are very crucial and are to be understood by each student. These concepts are also further used for higher studies and hence, it is necessary to learn the related formulas as well.

To have a quick revision of all the formulas, we have gathered here the list of formulas as per standard 12 syllabi. The list of formulas are provided here for the following topics:

- Vectors
- Three Dimensional Geometry
- Algebra of Matrices
- Trigonometry

### Vectors and Three Dimensional Geometry Formulas for Class 12

Position Vector | [latex] \overrightarrow{OP}=\vec{r}=\sqrt{x^{2}+y^{2}+z^{2}}[/latex] |

Direction Ratios | [latex] l=\frac{a}{r},m=\frac{b}{r},n=\frac{c}{r}[/latex] |

Vector Addition | [latex]\vec{PQ}+\vec{QR}=\vec{PR}[/latex] |

Properties of Vector Addition | [latex]Commutative Property\ \vec{a}+\vec{b}=\vec{b}+\vec{a}[/latex]
[latex]Associative Property \left (\vec{a}+\vec{b} \right )+\vec{c}=\vec{a}+\left (\vec{b}+\vec{c} \right )[/latex] |

Vector Joining Two Points | [latex]\overrightarrow{P_{1}P_{2}}=\overrightarrow{OP_{2}}-\overrightarrow{OP_{1}}[/latex] |

Skew Lines | [latex]Cos\theta = \left | \frac{a_{1}a_{2}+b_{1}b_{2}+c_{1}c_{2}}{\sqrt{a_{1}^{2}+b_{1}^{2}+c_{1}^{2}}\sqrt{a_{2}^{2}+b_{2}^{2}+c_{2}^{2}}} \right |[/latex] |

Equation of a Line | [latex]\frac{x-x_{1}}{a}=\frac{y-y_{1}}{b}=\frac{z-z_{1}}{c}[/latex] |

### Algebra Formulas For Class 12

If [latex]\vec{a}=x\hat{i}+y\hat{j}+z\hat{k}[/latex] then magnitude or length or norm or absolute value of [latex]\vec{a} [/latex] is [latex] \left | \overrightarrow{a} \right |=a=\sqrt{x^{2}+y^{2}+z^{2}}[/latex] |

A vector of unit magnitude is unit vector. If [latex]\vec{a}[/latex] is a vector then unit vector of [latex]\vec{a}[/latex] is denoted by [latex]\hat{a}[/latex] and [latex]\hat{a}=\frac{\vec{a}}{\left | \vec{a} \right |}[/latex] |

Important unit vectors are [latex]\hat{i}, \hat{j}, \hat{k}[/latex], where [latex]\hat{i} = [1,0,0],\: \hat{j} = [0,1,0],\: \hat{k} = [0,0,1][/latex] |

If [latex] l=\cos \alpha, m=\cos \beta, n=\cos\gamma,[/latex] then [latex] \alpha, \beta, \gamma,[/latex] are called directional angles of the vectors[latex]\overrightarrow{a}[/latex] and [latex]\cos^{2}\alpha + \cos^{2}\beta + \cos^{2}\gamma = 1[/latex] |

In Vector Addition |

[latex]\vec{a}+\vec{b}=\vec{b}+\vec{a}[/latex] |

[latex]\vec{a}+\left ( \vec{b}+ \vec{c} \right )=\left ( \vec{a}+ \vec{b} \right )+\vec{c}[/latex] |

[latex]k\left ( \vec{a}+\vec{b} \right )=k\vec{a}+k\vec{b}[/latex] |

[latex]\vec{a}+\vec{0}=\vec{0}+\vec{a}[/latex], therefore [latex] \vec{0}[/latex] is the additive identity in vector addition. |

[latex]\vec{a}+\left ( -\vec{a} \right )=-\vec{a}+\vec{a}=\vec{0}[/latex], therefore [latex]-\vec{a}[/latex] is the inverse in vector addition. |

### Trigonometry Class 12 Formulas

Definition |

[latex]\theta = \sin^{-1}\left ( x \right )\, is\, equivalent\, to\, x = \sin \theta[/latex] |

[latex]\theta = \cos^{-1}\left ( x \right )\, is\, equivalent\, to\, x = \cos \theta[/latex] |

[latex]\theta = \tan^{-1}\left ( x \right )\, is\, equivalent\, to\, x = \tan\theta[/latex] |

Inverse Properties |

[latex]\sin\left ( \sin^{-1}\left ( x \right ) \right ) = x[/latex] |

[latex]\cos\left ( \cos^{-1}\left ( x \right ) \right ) = x[/latex] |

[latex]\tan\left ( \tan^{-1}\left ( x \right ) \right ) = x[/latex] |

[latex]\sin^{-1}\left ( \sin\left ( \theta \right ) \right ) = \theta[/latex] |

[latex]\cos^{-1}\left ( \cos\left ( \theta \right ) \right ) = \theta[/latex] |

[latex]\tan^{-1}\left ( \tan\left ( \theta \right ) \right ) = \theta[/latex] |

Double Angle and Half Angle Formulas |

[latex]\sin\left ( 2x \right ) = 2\, \sin\, x\, \cos\, x[/latex] |

[latex]\cos\left ( 2x \right ) = \cos^{2}x – \sin^{2}x[/latex] |

[latex]\tan\left ( 2x \right ) = \frac{2\, \tan\, x}{1 – \tan^{2}x}[/latex] |

[latex]\sin\frac{x}{2} = \pm \sqrt{\frac{1 – \cos x}{2}}[/latex] |

[latex]\cos\frac{x}{2} = \pm \sqrt{\frac{1 + \cos x}{2}}[/latex] |

[latex]\tan\frac{x}{2} = \frac{1- \cos\, x}{\sin\, x} = \frac{\sin\, x}{1 – \cos\, x}[/latex] |

## 12th Maths Formulas

The mathematical formulas for grade 12 are based on the chapters introduced to 12th students under NCERT curriculum as per the CBSE board. Here is the name of the chapters listed for all the formulas.

Chapter 1 – Relations and Functions formula
Chapter 2 – Inverse Trigonometric Functions Chapter 3 – Matrices Chapter 4 – Determinants Chapter 5 – Continuity and Differentiability Chapter 6 – Applications of Derivatives Chapter 7 – Integrals Chapter 8 – Applications of the Integrals Chapter 9 – Differential Equations Chapter 10 – Vectors Chapter 11 – Three dimensional Geometry Chapter 12 – Linear Programming Chapter 13 – Probability |

## Frequently Asked Questions – FAQs

### What are the basic maths formulas for class 12th?

Algebra

Geometry

Matrices

Calculus

Linear Programming

Probability

### How many formulas are there in Maths?

### What is the importance of Maths formulas?

### What is the formula for integrating trigonometry ratio?

∫sin (a) da = -Cos a + C

∫sec^2a da = tan a + C

### What is the integration for exponential function?

∫e^x dx = e^x + C