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CBSE Maths Formulas Class 12

Last updated date: 27th Jun 2024
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CBSE Important Maths Formulas for Class 12 PDF Free Download

Class 12 is one of the most stressful academic years of every student’s life. In addition to this, the CBSE class 12 maths syllabus is vast. Thus, the prime step students must take while studying for their exam is to thoroughly learn the Class 12 Maths all formulas chapter wise. Class 12 acts as a pivotal bridge between higher education and school education. Due to this, students are often looking forward to acing their exams. However, this can be challenging when students grab hold of irrelevant study material. Learning maths formulas class 12 efficiently can help students improve their problem-solving skills. This is why the CBSE maths formulas for class 12 PDF free download is such a valuable learning tool.

Class 12 Maths all Formulas Chapter wise PDF

The Maths formulas Class 12 are rather vast. Every chapter of the class 12 mathematics subject boasts a significant number of formulas. Students can get access to individual class 12 maths formula sheet pdf as per the chapter. With these PDFs, students can easily refresh their knowledge on every chapter of class 12. Students can thus rely on these class 12 maths formulas PDF at the luxury of sitting at home. Download chapter-wise formula PDF from below.

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Competitive Exams after 12th Science

List of Important Maths Formula Class 12

In Class 12, there are numerous formulas across different chapters. Let's focus on some key formulas that are essential for understanding important math concepts. Regularly revisiting these maths formula sheet class 12 is crucial for a better grasp of mathematical concepts. You can easily access and download class 12 maths formulas PDF for significant chapters like trigonometry, vectors, three-dimensional geometry, matrices, and  algebra.

These Class 12 maths all formulas PDF play a vital role in helping students solve math problems more efficiently. By consistently reviewing them, students can build a strong foundation for their math skills. Formulas are the key to problem-solving; all you need to do is plug in the values of the entities into the respective formula to simplify the problem.

Let's quickly go over few important maths formulas class 12 from the syllabus:

Vectors and Three Dimensional Geometry Formulas for Class 12

  1. Position Vector - $ \overrightarrow{OP}=\vec{r}=\sqrt{x^{2}+y^{2}+z^{2}}$

  2. Direction Ratios - $ l=\dfrac{a}{r},m=\dfrac{b}{r},n=\dfrac{c}{r}$

  3. Vector Addition - $\vec{PQ}+\vec{QR}=\vec{PR}$

  4. Commutative Property - $ \vec{a}+\vec{b}=\vec{b}+\vec{a}$

  5. Associative Property - $\left (\vec{a}+\vec{b} \right )+\vec{c}=\vec{a}+\left (\vec{b}+\vec{c} \right )$

  6. Vector Joining Two Points - $\overrightarrow{P_{1}P_{2}} = \overrightarrow{OP_{2}} - \overrightarrow{OP_{1}}$

  7. Skew Lines - $\cos\theta = \left | \dfrac{a_{1}a_{2}+b_{1}b_{2}+c_{1}c_{2}}{\sqrt{a_{1}^{2}+b_{1}^{2}+c_{1}^{2}}\sqrt{a_{2}^{2}+b_{2}^{2}+c_{2}^{2}}} \right |$

  8. Equation of a Line - $\dfrac{x-x_{1}}{a}=\dfrac{y-y_{1}}{b}=\dfrac{z-z_{1}}{c}$

  9. Distance between two points in 3D: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}$

  10. Distance Formula: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

  11. Midpoint Formula: $(x_m, y_m) = \left( \dfrac{x_1 + x_2}{2},  \dfrac{y_1 + y_2}{2}\right)$

Algebra Formulas For Class 12

  1. If you have a vector $\vec{a}=x\hat{i}+y\hat{j}+z\hat{k}$, then you can find its length by using the formula $\left | \overrightarrow{a} \right | = a =\sqrt{x^{2}+y^{2}+z^{2}}$. This length is also called the magnitude, norm, or absolute value of the vector.

  2. A unit vector is a vector with a length of 1. If you have a vector $\vec{a}$  its unit vector is denoted as $\hat{a}$ is calculated as $\hat{a}=\dfrac{\vec{a}}{\left | \vec{a} \right |}$

  3. Some important unit vectors are $\hat{i}, \hat{j}, \hat{k}$, where $\hat{i} = [1,0,0],\: \hat{j} = [0,1,0],\: \hat{k} = [0,0,1]$

  4. If you have directional angles $\alpha, \beta, \gamma$ represented by $l=\cos \alpha, m=\cos \beta, n=\cos\gamma$, respectively, they are called directional angles of the vector $\overrightarrow{a} $. Additionally, the relationship $\cos^{2}\alpha + \cos^{2}\beta + \cos^{2}\gamma = 1$ holds for these directional angles.

  5. Quadratic Formula: $x =  \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

  6. Arithmetic Progression (AP):

  • $a_n = a + (n-1)d$

  • $S_n =  \dfrac{n}{2}[2a + (n-1)d]$

  • $S_n =  \dfrac{n}{2}[a + l]$

  1. Geometric Progression (GP):

  • $a_n = ar^{(n-1)}$

  • $S_n =  \dfrac{a(r^n - 1)}{r - 1}$

Vector Addition Formulas for Class 12

  1. $\vec{a}+\vec{b}=\vec{b}+\vec{a}$

  2. $\vec{a}+\left ( \vec{b}+ \vec{c} \right )=\left ( \vec{a}+ \vec{b} \right )+\vec{c}$

  3. $k\left ( \vec{a}+\vec{b} \right )=k\vec{a}+k\vec{b}$

  4. $\vec{a}+\vec{0}=\vec{0}+\vec{a}$,  therefore $\vec{0}$  is the additive identity in vector addition.

  5. $\vec{a}+\left ( -\vec{a} \right )=-\vec{a}+\vec{a}=\vec{0}$, therefore $-\vec{a}$  is the inverse in vector addition.

Calculus Formulas for Class 12

  1. Limits: $\lim_{{x \to a}} f(x) = L$


  1. $ \dfrac{d}{dx}(x^n) = nx^{(n-1)}$

  2. $ \dfrac{d}{dx}(e^x) = e^x$

  3. $ \dfrac{d}{dx}(\ln(x)) =  \dfrac{1}{x}$

  4. $ \dfrac{d}{dx}(\sin(x)) = \cos(x)$

  5. $ \dfrac{d}{dx}(\cos(x)) = -\sin(x)$


  1. $\int x^n \,dx =  \dfrac{x^{(n+1)}}{(n+1)}$

  2. $\int e^x \,dx = e^x$

  3. $\int  \dfrac{1}{x} \,dx = \ln|x|$

  4. $\int \sin(x) \,dx = -\cos(x)$

  5. $\int \cos(x) \,dx = \sin(x)$

Trigonometry Class 12 Formulas for Class 12

  1. $\theta = \sin^{-1}\left ( x \right )\, is\, equivalent\, to\, x = \sin \theta$

  2. $\theta = \cos^{-1}\left ( x \right )\, is\, equivalent\, to\, x = \cos \theta$

  3. $\theta = \tan^{-1}\left ( x \right )\, is\, equivalent\, to\, x = \tan\theta$

Inverse Properties

  1. $\sin\left ( \sin^{-1}\left ( x \right ) \right ) = x$

  2. $\cos\left ( \cos^{-1}\left ( x \right ) \right ) = x$

  3. $\tan\left ( \tan^{-1}\left ( x \right ) \right ) = x$

  4. $\sin^{-1}\left ( \sin\left ( \theta \right ) \right ) = \theta$

  5. $\cos^{-1}\left ( \cos\left ( \theta \right ) \right ) = \theta$

  6. $\tan^{-1}\left ( \tan\left ( \theta \right ) \right ) = \theta$

Double Angle and Half Angle Formulas

  1. $\sin\left ( 2x \right ) = 2\, \sin\, x\, \cos\, x$

  2. $\cos\left ( 2x \right ) = \cos^{2}x – \sin^{2}x$

  3. $\tan\left ( 2x \right ) = \dfrac{2\, \tan\, x}{1 – \tan^{2}x}$

  4. $\sin\dfrac{x}{2} = \pm \sqrt{\dfrac{1 – \cos x}{2}}$

  5. $\cos\dfrac{x}{2} = \pm \sqrt{\dfrac{1 + \cos x}{2}}$

  6. $\tan\dfrac{x}{2} = \dfrac{1- \cos\, x}{\sin\, x} = \dfrac{\sin\, x}{1 – \cos\, x}$

Probability Formulas for Class 12

  1. Probability of an event A: $P(A) =  \dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$


Vedantu offers a valuable resource with its comprehensive collection of maths formulas for class 12 PDF Free download for CBSE students ensuring easy accessibility. The inclusive class 12 maths formula sheet pdf aids students in mastering concepts systematically. This resource serves as a handy guide for quick reference, facilitating a better understanding of complex mathematical principles. With Vedantu's commitment to accessible education, the Class 12 Maths All Formulas Chapter Wise sheet in PDF format becomes an essential tool for students aiming for success in their exams.

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FAQs on CBSE Maths Formulas Class 12

1. Why do Students Find it Difficult to Recite Maths Formulas?

Maths formulas can be extremely difficult to understand and revise. However, there’s no shortcut to revising maths formulas. Students have to regularly jot down the formulas and memorize them to ensure that they don’t forget the formulas before their exams. Students must avoid mugging up these formulas right before exams as they may not only forget the formulas but also jumble up the formulas. Thus, students must take time out to understand how formulas are created. This can sound illogical but can help students learn how to derive the formulas.

2. Why Should You Refer to Class 12 Maths Formulas?

The prime perk of referring to the class 12 maths formula PDF is eliminating the need to recite problems and learn how to solve them instead. Students can directly refer to these formulas instead of going through the textbooks to save time to prepare well for their exams. Writing down each one of these formulas can be a tedious task. However, referring to them online can help you encounter a fun-loving and inspiring learning experience.

3. How many formulas do I need to remember for the Class 12 Maths exam?

There isn't a specific number of formulas you need to memorize. It's more important to understand the concepts behind the formulas and how to apply them in different situations. However, remembering key formulas will definitely save you time and effort during the exam.

4. What are some tips for memorizing maths formulas class 12 effectively?

Here are some tips for memorizing formulas effectively:

  • Don't just memorize the formula, try to understand the logic and derivation behind it. This will help you recall the formula more easily and apply it correctly.

  • Solve problems from your textbook or other resources that involve the formulas you want to learn. This will help solidify your understanding and build confidence in using them.

  • Organize the formulas in a way that works for you, like flashcards or mind maps. This can help visualize the relationships between different formulas and make them easier to remember.

  • Don't try to cram all the formulas the night before the exam. Regularly revise them throughout your preparation to ensure they stay fresh in your memory.

5. Are there any maths formulas class 12 that are more important than others?

While every formula has its place, some formulas are used more frequently or are crucial for specific topics. Focus on understanding formulas in these areas:

  • Algebra: Quadratic equations, complex numbers, permutations and combinations.

  • Calculus: Differentiation and integration rules, applications of derivatives and integrals.

  • Vectors and 3D Geometry: Dot product, cross product, distance formula, direction cosines.

  • Probability: Conditional probability, Bayes' theorem.