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The Comprehensive Guide to Class 12 Mathematics Formula for CBSE Board and Competitive Exams
From algebraic equations to trigonometry, Class 12 Mathematics is a subject that requires students to grasp various concepts and their corresponding formulas. These formulas are not only important for the CBSE board exams but also play a crucial role in various competitive exams like JEE Main, NEET, and AIIMS. In this comprehensive guide, we will explore the essential formulas that every Class 12 student should know to excel in their exams.
Algebraic Formulas
Algebra is the foundation of higherlevel mathematics, and having a strong grasp of its formulas is crucial. Some of the important algebraic formulas for Class 12 Mathematics include:
Quadratic Equation Formula:
4.5 out of 5
Language  :  English 
File size  :  2607 KB 
TexttoSpeech  :  Enabled 
Enhanced typesetting  :  Enabled 
Lending  :  Enabled 
Screen Reader  :  Supported 
Print length  :  93 pages 
Paperback  :  148 pages 
Item Weight  :  12.3 ounces 
Dimensions  :  7 x 0.34 x 10 inches 
The quadratic equation formula is one of the fundamental formulas that students come across in their Class 12 Mathematics syllabus. It is represented as:
ax^{2} + bx + c = 0
Where a, b, and c are coefficients and x represents the unknown variable.
Using the quadratic formula, students can solve for the value of x by substituting the corresponding coefficients.
Binomial Theorem:
The binomial theorem is another important concept in algebra that deals with expanding powers of a binomial. The formula is given by:
(a + b)^{n} = Σ C(n, r) a^{nr} b^{r}
Where n is a positive integer, a and b are real numbers, and C(n, r) represents the binomial coefficient.
Understanding and applying these algebraic formulas can help students solve complex algebraic expressions effectively and accurately.
Trigonometric Formulas
Trigonometry involves the study of relationships between angles and sides of triangles. Knowing the trigonometric formulas is essential for solving trigonometry problems in Class 12 Mathematics. Some of the commonly used trigonometric formulas include:
Pythagorean Identities:
The Pythagorean identities are a set of three trigonometric equations that relate the three basic trigonometric functions: sine, cosine, and tangent. These identities are:
sin^{2}(θ) + cos^{2}(θ) = 1
1 + tan^{2}(θ) = sec^{2}(θ)
1 + cot^{2}(θ) = cosec^{2}(θ)
Understanding and applying these identities can help simplify trigonometric expressions and solve intricate trigonometric equations.
Sum and Difference Formulas:
The sum and difference formulas for trigonometric functions are used to find the sine, cosine, and tangent of a sum or difference of two angles. These formulas are:
sin(A ± B) = sin(A)cos(B) ± cos(A)sin(B)
cos(A ± B) = cos(A)cos(B) ∓ sin(A)sin(B)
tan(A ± B) = (tan(A) ± tan(B)) / (1 ∓ tan(A)tan(B))
Mastering these trigonometric formulas can help students tackle complex trigonometric problems with ease.
Calculus Formulas
Calculus is a branch of mathematics that focuses on change and motion. It involves the study of limits, derivatives, and integrals. Some of the essential calculus formulas for Class 12 Mathematics are:
Limits Formulas:
Limits play a crucial role in calculus, and understanding their formulas is essential. Some important limit formulas include:
lim(x→a) k = k (Constant Rule)
lim(x→a) x = a (Identity Rule)
lim(x→a) [f(x) ± g(x)] = lim(x→a) f(x) ± lim(x→a) g(x) (Sum/Difference Rule)
These formulas help in simplifying limits and evaluating the behavior of functions as they approach a certain value.
Derivative Formulas:
Derivatives are used to determine the rates of change of functions. Some of the derivative formulas include:
d/dx (k) = 0 (Constant Rule)
d/dx (x^{n}) = nx^{n1} (Power Rule)
d/dx (sin(x)) = cos(x) (Derivative of Sine)
These formulas enable students to find the instantaneous rates of change of functions and solve optimization problems.
Integral Formulas:
Integrals are used to find the area under curves and solve problems related to accumulation. Some of the integral formulas include:
∫ k dx = kx + C (Constant Rule)
∫ x^{n} dx = (x^{n+1})/(n+1) + C (Power Rule)
∫ sin(x) dx = cos(x) + C (Integral of Sine)
Understanding and applying these integral formulas can help students solve problems involving area and accumulation effectively.
Class 12 Mathematics Formula for CBSE board and competitive exams are crucial for students to excel in the exams. From algebraic formulas to trigonometric, calculus, and more, mastering these formulas will help students solve complex problems accurately and efficiently. By understanding the concepts behind these formulas and practicing their application, students can build a strong foundation in mathematics and increase their chances of success in both board exams and competitive entrance tests.
4.5 out of 5
Language  :  English 
File size  :  2607 KB 
TexttoSpeech  :  Enabled 
Enhanced typesetting  :  Enabled 
Lending  :  Enabled 
Screen Reader  :  Supported 
Print length  :  93 pages 
Paperback  :  148 pages 
Item Weight  :  12.3 ounces 
Dimensions  :  7 x 0.34 x 10 inches 
This is an outstanding book for class 12 students who want to get all formulas of Mathematics at one place. This ebook is designed to help all CBSE Board as well as competitive aspirants to learn all the formulas in easy way. Once you get the formulas of this book your Class 12 mathematics paper will be very easy to solve and appears a piece a cake. This will immensely help you in solving questions of your future competitive exams like JEE/Olympiads/IBPS etc. This is a must have book for all Mathematics students.
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