There are some important formulas and identities in vector Mathematics.
A vector of unit magnitude is called a unit vector. The most common unit vectors used in Class 12 are i, j and k given by i = [0 0 1], j = [0 1 0] and k = [0 0 1].
If l = cos a, m = cos b and n = cos c, then a, b and c are called the directional angles of the vector ‘a’ and cos2a + cos2b + cos2c = 1.
Vector addition obeys commutative and associative law.
A zero vector is the additive identity of a vector.
The negative of a vector is the additive inverse of a vector.
Trigonometry is a branch of mathematics that deals with the study of sides and angles of a three-sided closed geometrical shape (triangle). Trigonometry in class 12 has a wide list of formulas. A few important formulas of class 12 trigonometry are quoted below.
x = sin θ is also equivalent to θ = sin-1 x
x = cos θ is also equivalent to θ = cos-1 x
x = tan θ is also equivalent to θ = tan-1 x
Inverse Trigonometric Properties:
sin (sin-1 p) = p
cos (cos-1 p) = p
tan (tan-1 p) = p
sin-1 (sin A) = A
cos-1 (cos A) = A
tan-1 (tan A) = A
Half Angle and Double Angle Trigonometric Formulae:
Mathematics is one of the most difficult subjects for the student community. Many students have a false notion that the subject is more tough because of the formulas and identities in it. More than 70% of the student community finds it difficult to practice and memorize class 12 formulas because of the ambiguity and dilemma of choosing a suitable identity. Students who wonder ‘how to memorize class 12 maths formulas?’ should practice the following tips to memorize the class 12 formula.
Tip 1: Concentration
For the first time, when a new identity is studied, analyze each and every variable used in the formula with utmost concentration. This helps in retaining the formula for a longer duration in our brains.
Tip 2: Relax Mind and Brain
Do not learn or memorize the formulas with a stressed mindset. This will retard the will power of the brain and in turn, will result in forgetfulness and confusion between the variables used in Class 12 formula.
Tip 3: Use 3 r’s
When a 12th math formula or any other formula, in general, is to be remembered for a long duration, the secret of 3 r’s should be followed. The 3 r’s that help in storing a formula in human memory unit for a lengthier time duration are:
Revise: Learn the formula for a certain number of times visualizing it.
Repeat: Repeat the formulas in written form by applying it in the mathematical problems.
Recall: Without looking into the formula, stir up the brain to recollect the formula and variables used in it.
Tip 4: Periodic Revision
Following the tips 1, 2, and 3 may help an individual remember the formula for a short time duration. However, if the class 12 maths formulas are to be remembered for the longest time period, the practice of tip 3 should be repeated on a regular basis. Repeat the tip 3 in a sequence of 1, 3, 5 7 15, 30, 90 days.
Important 12th maths formulas list pdf can be accessed from various websites that provide study materials and other resources for exam preparation.
What is the inverse sine function of the sine of an angle ‘T’ equal to?
Cosine of angle T
Inverse tangent of angle T
Which of the following indicates the representation of unit vector ‘j’?
[ 0 0 1 ]
[ 0 1 0 ]
[ 1 0 1 ]
1. What are Mathematical Formulas? How are They Important to Class 12 Students?
Ans. Mathematical formulas are generalized equality statements representing the relationship between any of the quantities bound to a specific concept in Mathematics.
Mathematical formulas are generally a short form of representing the long relationship equality statements in a symbolic manner. When analyzed at a closer look, these identities or formulas are very helpful in remembering a complex Mathematical concept effortlessly. For class 12 students, these formulas assist as a guide to crack their urge of flourishing with excellent scores in Mathematics. Though students consider memorizing formulas as a tedious task, it eventually becomes their cup of tea by regular practice and follow-ups. Students are usually recommended to download 12th Maths formulas list pdf on their smartphones or tablets to gain maximum exposure to the list of formulas.
2. How can the Mathematical Formulas be Remembered Easily?
The 12th Math formula list, though it looks to be lengthy and hard to understand, is very easy and effective in making the Mathematical concepts more clear.
Students can reduce the complexity of a Mathematical problem with the aid of formulas.
To learn the formulas, students need to analyze each and every formula with a calm mindset free from negative thoughts. Positivity is the main key to learn and memorize class 12 formulas.
It is very important for the students to revise, repeat, and recall the formulas at regular time breaks so that they do not vanish completely from the brain.
Students are also recommended to create formula charts and hang in their study rooms or download the Maths formula for class 12 pdf on their smartphones and just have a glance at the formulas every day so that they remain fresh in the human memory unit.