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 their exams.

The only way students can get rid of the subject is by learning to get a strong grip on maths formula. If students can do their best to be positive about maths formula 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.

Here is a list of Maths formulas for CBSE class 12.

Vectors and Three Dimensional Geometry Formulas for Class 12

Position Vector \( \overrightarrow{OP}=\vec{r}=\sqrt{x^{2}+y^{2}+z^{2}}\)
Direction Ratios \( l=\frac{a}{r},m=\frac{m}{r},n=\frac{c}{r}\)
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

\(\overrightarrow{P_{1}P_{2}}=\overrightarrow{OP_{1}}-\overrightarrow{OP_{1}}\)
Skew Lines \(Cos\theta = \left | \frac{a_{1}a_{2}+b_{1}b_{2}+c_{1}c_{2}}{\sqrt{a_{1}^{2}+a_{1}^{2}+c_{1}^{2}}\sqrt{a_{2}^{2}+a_{2}^{2}+c_{2}^{2}}} \right |\)
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 \(\hat{a}=\frac{\hat{a}}{\left | \hat{a} \right |}\) Therefore \( \hat{a}=\frac{\hat{a}}{\left | \hat{a} \right |}\hat{a}\)
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

\(\sin\left ( 2x \right ) = 2\,  \sin\, x\, \cos\, x\)
\(\cos\left ( 2x \right ) = \cos^{2}x – \sin^{2}x\)
\(\tan\left ( 2x \right ) = \frac{2\, \tan\, x}{1 – \tan^{2}x}\)
\(\sin\frac{x}{2} = \pm \sqrt{\frac{1 – \cos x}{2}}\)
\(\cos\frac{x}{2} = \pm \sqrt{\frac{1 + \cos x}{2}}\)
\(\tan\frac{x}{2} = \frac{1- \cos\, x}{\sin\, x} = \frac{\sin\, x}{1 – \cos\, x}\)<


Practise This Question

A horse runs along a circle with a speed of 20 km/hr. A lantern is at the centre of the circle. A fence is along the tangent to the circle at the point at which the horse starts. The speed with which the shadow of the horse move along the fence at the moment when it covers 18 of the circle in km/hr is