Class 12 Maths Formulas

Class 12 maths formulas form the base for higher-level studies. These formulas also play a crucial role in preparing for various competitive exams like IIT-JEE. Class 12 maths syllabus is vast with many complex topics. Thus, memorizing class 12 math formulas is remarkably essential to score well in the class 12th board exam. Memorizing formulas enables students to solve all types of complex questions during exams. These formulas are majorly covered under most important math topics including calculus, three-dimensional geometry, vectors, algebra, matrices and trigonometry.

List of Important Class 12 Maths Formulas

A list of some basic Class 12 maths formulas related to most important topics covered under various school boards is given below:

• \(\overrightarrow {OP}\) = r = √x²+ y² + z²
• \(\overrightarrow {PQ}\) + \(\overrightarrow {QR}\) = \(\overrightarrow {PR}\)
• sin^-1(-x) = -sin^-1x 
• tan^-1x + cot^-1x = π / 2
• sin^-1x + cos^-1x = π / 2
• cos^-1(-x) = π  - cos^-1 x
• cot^-1(-x) = π - cot^-1x
• ∫ xⁿ dx = (x^{n + 1}) / (n + 1) + C
• ∫ e^x dx = e^x + C
• ∫ a^x dx = a^x / ln(a) + C
• ∫ ln(x) dx = x ln(x) - x + C
• P(A ∩ B) = P(A) P(B | A).
• P(A | B) = P(A ∩ B) / P(B), provided P(B) ≠ 0.

Class 12 Vector Formulas

Class 12 Vector formulas are an important part of the mathematics syllabus. Vector is a quantity that has both directions and magnitudes. These formulas hold great importance in mathematics and physics. Learning class 12 vector algebra formulas will help students in handling geometric transformations and it is very important in understanding Linear Algebra. Here are all important Class 12 vector algebra formulas:

• A + B = B + A (Commutative Law)
• A + (B + C) = (A + B) + C (Associative Law)
• (A • B )= |P| |Q| cos θ ( Dot Product )
• (A × B )= |P| |Q| sin θ (Cross Product)
• k (A + B )= kA + kB
• A + 0 = 0 + A (Additive Identity)

Class 12 Trigonometry Formulas

Class 12 Trigonometry formulas are based on inverse trigonometric functions. Memorizing these formulas will enable students to find angles with any of the trigonometry ratios. These formulas are derived from the properties of trigonometric functions and are applied in various engineering branches and other studies. Here are some important class 12 trigonometric formulas related to trigonometric ratios.

• sin^-1(-x) = - sin^-1x 

• tan^-1x + cot^-1x = π / 2
• sin^-1x + cos^-1 x = π / 2
• cos^-1(-x) = π - cos^-1x
• cot^-1(-x) = π - cot^-1x

Class 12 Calculus Formulas

Calculus is the branch of mathematics that has immense value in other subjects and studies like physics, biology, chemistry, and economics. Class 12 Calculus formulas are mainly based on the study of the change in a function’s value with respect to a change in the points in its domain. The formulas and concepts of derivatives are highly important as they are applied in many other math topics directly or indirectly. Here are some most important Class 12 Calculus Formulas that students must know and memorize:

• ∫ f(x) dx = F(x) + C
• Power Rule: ∫ xⁿ dx = (xⁿ⁺¹) / (n+1) + C. (Where n ≠ -1)
• Exponential Rules: ∫ e^x dx = e^x + C 
• ∫ a^x dx = a^x / ln(a) + C
• ∫ ln(x) dx = x ln(x) - x + C
• Constant Multiplication Rule: ∫ a dx = ax + C, where a is the constant. 
• Reciprocal Rule: ∫ (1/x) dx = ln(x)+ C 
• Sum Rules:  ∫ [f(x) + g(x)] dx = ∫f(x) dx + ∫g(x) dx
• Difference Rules:  ∫ [f(x) - g(x)] dx = ∫f(x) dx - ∫g(x) dx
• ∫k f(x) dx = k ∫f(x) dx, , where k is any real number.
• Integration by parts: ∫ f(x) g(x) dx = f(x) ∫ g(x) dx - ∫[d/dx f(x) ×  ∫ g(x) dx]dx
• ∫cos x dx = sin x + C
• ∫ sin x dx = -cos x + C
• ∫ sec² x dx = tan x + C
• ∫ cosec² x dx = -cot x + C
• ∫ sec x tan x dx = sec x + C
• ∫ cosec x cot x dx = - cosec x + C

Class 12 Geometry Formulas

Class 12 three-dimensional geometry formulas are important to implement understanding of the connection between algebra and geometry. Class 12 three-dimensional geometry formulas are also significant for various competitive examinations. Thus, it is very important to study these formulas with utmost focus and diligence. 

•  Cartesian equation of a plane: lx + my + nz = d 
• Distance between two points P(x1, y1, z1) and Q(x2, y2, z2): PQ = √ ((x₁ - x₂)² + (y₁ - y₂)² + (z₁ - z₂)²) 

Applications of Class 12 Maths Formulas 

Class 12 Maths formulas are the cornerstone of numeracy skills. They hold a great significance in our lives. Class 12 maths formulas are applied in various calculations of insurance risks, analysis of statistical data taken by a census, and so on. Below are some of the common applications of Class 12 maths formulas.

• Class 12 Calculus formulas are needed in Physics to determine various components like the center of mass or mass moment of Inertia of a sports utility vehicle.
• Formulas based on integration are also important to calculate an object's velocity or trajectory. Additionally, the use of these formulas is also prominent in monitoring the location of planets and explaining electromagnetism.
• Class 12 trigonometry formulas are employed to estimate various dimensions of architectural designs, buildings, slopes, etc. 
• Class 12 vector algebra formulas are used in the calculation of the magnitude of various quantities in Physics and so on.

Tips to Memorize Class 12 Maths formulas 

Students can follow some useful memorization tips to remember Class 12 math formulas that will help them in their exam preparation.

• The most efficient means of memorizing class 12 math formulas is to apply them in solving multiple questions. Solving questions by employing Class 12 math formulas is an excellent approach to memorizing them. 
• Writing down class 12 formulas will help students in memorizing them faster. Therefore, students should write down complex formulas several times as well as try to solve as many problems by applying them.
• Incorporating visual illustrations with math formulas and practice will help in remembering them quickly. This approach will also benefit students to recollect terms and concepts easily. Since visual representation helps our brains to process information better. 
• It is necessary to comprehend formulas and concepts to memorize them better. When students will understand the entire reason or process behind a certain formula, it will be easier for them to remember it as it will make more sense then.
• Apply all the formulas as much as possible, understanding the application of the formula which will help to retain the information better. Try solving and practicing problems using the formulas.
• Learning and memorizing math formulas requires a lot of effort and practice. Students must be familiarized with the chapters and the concepts and must then try to understand how a formula is derived.

Class 12 Maths Formulas Examples

Example 1: A circular disc of radius 3 cm is being heated. Due to expansion, its radius increases at a rate of 0.05 cm per second. Find the rate at which its area is increasing if the radius is 3.2 cm.

Solution:

Let us assume that “r” be the radius of the given disc and “A” be the area, then the area is given as:

A = π x r²

By using the chain rule,

Then dA/dt = 2 π r(dr/dt)

Thus, the approximate rate of increase of radius = dr = (dr/dt) ∆t = 0.05 cm per second

Hence, the approximate rate of increase in area is:

dA = (dA/dt)(∆t) = 2πr[(dr/dt) ∆t ]

= 2π (3.2) (0.05)

= 0.320π cm² per second.

Therefore, when r = 3.2 cm, then the area is increasing at a rate of 0.320π cm²/second.

Example 2 Find the number of all one-one functions from set A = {1, 2, 3} to itself.

Solution:

One-one function from {1, 2, 3} to itself is simply a permutation on three

symbols 1, 2, 3. 

Therefore, the total number of one-one maps from {1, 2, 3} to itself is

same as a total number of permutations on three symbols 1, 2, 3. 

That is 3! = 6.

You can download the printable Maths Formulas Class 12 sheet from below