 # 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 $$\overrightarrow{OP}=\vec{r}=\sqrt{x^{2}+y^{2}+z^{2}}$$ Direction Ratios $$l=\frac{a}{r},m=\frac{b}{r},n=\frac{c}{r}$$ Vector Addition $$\vec{PQ}+\vec{QR}=\vec{PR}$$ Properties of Vector Addition $$Commutative Property\ \vec{a}+\vec{b}=\vec{b}+\vec{a}$$ $$Associative Property \left (\vec{a}+\vec{b} \right )+\vec{c}=\vec{a}+\left (\vec{b}+\vec{c} \right )$$ Vector Joining Two Points $$\overrightarrow{P_{1}P_{2}}=\overrightarrow{OP_{2}}-\overrightarrow{OP_{1}}$$ Skew Lines $$Cos\theta = \left | \frac{a_{1}a_{2}+b_{1}b_{2}+c_{1}c_{2}}{\sqrt{a_{1}^{2}+b_{1}^{2}+c_{1}^{2}}\sqrt{a_{2}^{2}+b_{2}^{2}+c_{2}^{2}}} \right |$$ Equation of a Line $$\frac{x-x_{1}}{a}=\frac{y-y_{1}}{b}=\frac{z-z_{1}}{c}$$

### Algebra Formulas For Class 12

 If $$\vec{a}=x\hat{i}+y\hat{j}+z\hat{k}$$ then magnitude or length or norm or absolute value of $$\vec{a}$$ is $$\left | \overrightarrow{a} \right |=a=\sqrt{x^{2}+y^{2}+z^{2}}$$ A vector of unit magnitude is unit vector. If $$\vec{a}$$ is a vector then unit vector of $$\vec{a}$$ is denoted by $$\hat{a}$$ and $$\hat{a}=\frac{\vec{a}}{\left | \vec{a} \right |}$$ Important unit vectors are $$\hat{i}, \hat{j}, \hat{k}$$, where $$\hat{i} = [1,0,0],\: \hat{j} = [0,1,0],\: \hat{k} = [0,0,1]$$ If $$l=\cos \alpha, m=\cos \beta, n=\cos\gamma,$$ then $$\alpha, \beta, \gamma,$$ are called directional angles of the vectors$$\overrightarrow{a}$$ and $$\cos^{2}\alpha + \cos^{2}\beta + \cos^{2}\gamma = 1$$
 In Vector Addition $$\vec{a}+\vec{b}=\vec{b}+\vec{a}$$ $$\vec{a}+\left ( \vec{b}+ \vec{c} \right )=\left ( \vec{a}+ \vec{b} \right )+\vec{c}$$ $$k\left ( \vec{a}+\vec{b} \right )=k\vec{a}+k\vec{b}$$ $$\vec{a}+\vec{0}=\vec{0}+\vec{a}$$, therefore $$\vec{0}$$ is the additive identity in vector addition. $$\vec{a}+\left ( -\vec{a} \right )=-\vec{a}+\vec{a}=\vec{0}$$, therefore $$-\vec{a}$$  is the inverse in vector addition.

### Trigonometry Class 12 Formulas

 Definition $$\theta = \sin^{-1}\left ( x \right )\, is\, equivalent\, to\, x = \sin \theta$$ $$\theta = \cos^{-1}\left ( x \right )\, is\, equivalent\, to\, x = \cos \theta$$ $$\theta = \tan^{-1}\left ( x \right )\, is\, equivalent\, to\, x = \tan\theta$$ Inverse Properties $$\sin\left ( \sin^{-1}\left ( x \right ) \right ) = x$$ $$\cos\left ( \cos^{-1}\left ( x \right ) \right ) = x$$ $$\tan\left ( \tan^{-1}\left ( x \right ) \right ) = x$$ $$\sin^{-1}\left ( \sin\left ( \theta \right ) \right ) = \theta$$ $$\cos^{-1}\left ( \cos\left ( \theta \right ) \right ) = \theta$$ $$\tan^{-1}\left ( \tan\left ( \theta \right ) \right ) = \theta$$ Double Angle and Half Angle Formulas $$\sin\left ( 2x \right ) = 2\, \sin\, x\, \cos\, x$$ $$\cos\left ( 2x \right ) = \cos^{2}x – \sin^{2}x$$ $$\tan\left ( 2x \right ) = \frac{2\, \tan\, x}{1 – \tan^{2}x}$$ $$\sin\frac{x}{2} = \pm \sqrt{\frac{1 – \cos x}{2}}$$ $$\cos\frac{x}{2} = \pm \sqrt{\frac{1 + \cos x}{2}}$$ $$\tan\frac{x}{2} = \frac{1- \cos\, x}{\sin\, x} = \frac{\sin\, x}{1 – \cos\, x}$$

## 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?

The basic formulas that are introduced for class 12th students are for the topics:
Algebra
Geometry
Matrices
Calculus
Linear Programming
Probability

### How many formulas are there in Maths?

There are many formulas in Maths for which we cannot keep a record. Because for each and every concept there are formulas to find the solutions for mathematical problems. Also, for each grade the level of formulas are different.

### What is the importance of Maths formulas?

The importance of learning Maths formulas is that it helps us to solve problems easily. We should have to put the values of entities in the given formula and simplify them. For example, to find the average of a given set of values, we have to need to know first the sum of all those values and number of values. Hence, the average will be equal to the ratio of the sum of values and the number of values.

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

∫cos(a) da = Sin a + C
∫sin (a) da = -Cos a + C
∫sec^2a da = tan a + C

### What is the integration for exponential function?

The value of exponential function e^x remains the same with constant even after integration.
∫e^x dx = e^x + C