**Maths Formula for Class 12**

Phy can hardly wait to take the maths exam again!

I’ve been practicing maths every day for the past few weeks before my exam — a day that I really will hate ever again. I will give it three hours.

The maths curriculum of a class 12 board consists of the following syllabus:

1. Basic maths concepts and concepts

2. Mathematics for practical usage

3. Mathematical solutions

4. Mathematical Applications

5. Basic mathematics in applications

6. Mathematical operations

7. Basic mathematics in works

8. Maths of arithmetic and fraction

9. Basic math operations

10. Advanced math operations

The classes textbooks of a class 12 board are called Class-level general maths textbooks for maths-based (KAS-MATE) or practical purpose-based, or practical operations’ textbooks. Like most of the mathematics books, the basic definition of basic mathematics is: Mathematics is about numbers, whereas practical mathematical operations is based on knowing the names of numbers and other maths operations and operations. In these textbooks, mathematics and operations are basically the same, and the concepts of algebra and geometry, which are most of our theoretical knowledge in class 12, is not defined. Mathematics works are kind of tricky to conceptualize because it involves operations that are mathematical, but people can be unable to visualize the maths operations. For instance, Markov signals are mathematical operations, but I cannot actually imagine Markov signals (at least I can’t imagine a mathematical execution of a Markov signal). In other words, mathematicians never explicitly define what goes on inside the math operations, which is why we have a problem with logic, so you cannot pretend that math operations are only mathematical operations.

I used to have a particular hobby when I was younger. I was involved in national team-building activities, such as martial arts, computer programming, and welding. Unlike the technical skills of dynamical, classical, and logical operations, I was good at figuring out and understanding operations in theory. My critical problem with mathematicians was a lack of knowledge of operation concepts and operations. There is no definition of operations in the class 12 mathematics textbook and there are no operations concepts used in the textbook. The mathematics operations are used in specific use-casualty settings, and these operations in real situations are also non-committal. So it is with logical operations and time operations, I have even less understanding and understanding. I come up with the following ten basic mathematical operations for operations:

The first basic operation I will see in class 12 is equality: A divided state is the same after equilibrium (“equal plus one” ).

The second basic operation is the weighted sum, which means the value of some part of the sum has a fixed value (“zero + one” ).

The third basic operation is finite time operations.

The fourth basic operation is simple mathematical operations.

The fifth basic operation is coagulation operations, which looks like a mixture of most of the others.

The sixth basic operation is well controlled anti-disease operations.

The seventh basic operation is a simple multiplication operation (“one = 10”).

The eighth basic operation is a simple computation operation (“three = five”).

The ninth basic operation is real-time operations.

The tenth basic operation is simple statistics operations.

My list of operations for operations in class 12 is:

Ok, more operations in class 12 textbooks, but I think basic math operations can be easily described. Maybe I need to pay more attention to these operations after taking the examination exam. I will focus on operations and operations vocabulary in class 12 textbooks, rather than my theoretical understanding. Mathematics has always been my favorite subject. A math operation is what is described as a mathematical operation of operations or a mathematical operation of operations. Practical operations uses maths operations instead of mathematical operations and structure the functions that can work more efficiently. Maths operations are basically basic operations. A mathematics operation is a logical operation, only logical operations have a logical operation name. A mathematics operation works well by itself; other mathematical operations just work by themselves. Such operations are normally called functions, whereas a mathematical operation is a mathematical operation with a logical operation name (Class 10: Basic Functions; Class 12: Absolute Knowledge).

**Class 12 Maths Formula**

## Vectors and Three Dimensional Geometry Formulas for Class 12

Position Vector – OP = r = √ x² + y² + z²

Directions Ratios – l = a/r, m = b/r, n = c/r

Vector Addition = PQ→+QR→=PR→

Properties of Vector Addition :

Commutative Property – a⃗ + b⃗ = b⃗ + a⃗

Skew Lines –

Cos θ = | a₁ a₂ + b₁ b₂ + c₁ c₂ / √a₁² + b₂² + c₃² √a₁² + b₂² + c₃² |

Equation of a line –

x – x₁ / a = y – y₁ / b = z – z₁ / c

## Algebra Formulas for Class 12

If a⃗ =xi^+yj^+zk^then magnitude or length or norm or absolute value of a is

| a⃗ |=a= √ x² + y² + z²

A Vector of unit magnitude is unit vector. If a⃗ is a vector then unit vector of a⃗ is denoted by a⃗ and

a^=a⃗ ∣∣a⃗ ∣∣

Important unit vectors are i, j, k, where

i^=[1,0,0],j^=[0,1,0],k^=[0,0,1]

If l = cos α, m = cos β, n = cos γ, then α,β,γ, are called directional angles of the vectors and cos² α + cos² β + cos² γ = 1

## In Vector Addition

a⃗ + b⃗ = b⃗ + a⃗

(a⃗ +b⃗ ) + c⃗ =a⃗ + (b⃗ +c⃗ )

k (a⃗ +b⃗ ) = ka⃗ + kb⃗

a⃗ + 0 = 0 + a⃗ , therefore 0 is the additive identity in vector addition.

a⃗ + (-a⃗ ) = –a⃗ + a⃗ = 0, therefore, –a⃗ is the inverse in vector addition.

## Trigonometry Class 12 Formulas

**Definition**

θ = sin^{-1} (x) is equivalent to x = sin θ

θ = cos^{-1} (x) is equivalent to x = cos θ

θ = tan^{-1} (x) is equivalent to x = tan θ

**Inverse Properties**

sin(sin^{-1}(x)) = x

cos(cos^{-1}(x)) = x

tan(tan^{-1}(x)) = x

sin^{-1} (sin(θ)) = θ

cos^{-1} (cos(θ)) = θ

tan^{-1} (tan(θ)) = θ

**Double Angle and Half Angle Formulas**

sin(2x) = 2 sin x cos x

cos (2x) = cos² x – sin² x

tan (2x) = 2 tan x / 1 – tan² x

sin x/2 = ± √ 1 – cos x / 2

cos x/2 = ± √1 + cos x / 2

tan x/2 = 1 – cos x / sin x = sin x / 1 – cos x