Essential Formulas And Theorems For 12th Class Mathematics Board Exams

The 12th class Mathematics board exams in India cover a wide range of topics. Here are some essential formulas and theorems that you should be familiar with for the exam:

Algebra:

Quadratic Formula: For a quadratic equation of the form ax^2 + bx + c = 0, the solutions can be found using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

Factorization Formulas:

• (a + b)^2 = a^2 + 2ab + b^2
• (a - b)^2 = a^2 - 2ab + b^2
• a^2 - b^2 = (a + b)(a - b)
• a^3 + b^3 = (a + b)(a^2 - ab + b^2)
• a^3 - b^3 = (a - b)(a^2 + ab + b^2)

Binomial Theorem: The expansion of (a + b)^n can be found using the binomial theorem: (a + b)^n = C(n, 0) * a^n * b^0 + C(n, 1) * a^(n-1) * b^1 + ... + C(n, n) * a^0 * b^n where C(n, r) denotes the binomial coefficient.

Trigonometry:

Pythagorean Identities:

• sin^2θ + cos^2θ = 1
• 1 + tan^2θ = sec^2θ
• 1 + cot^2θ = csc^2θ

Trigonometric Ratios:

• sinθ = Opposite / Hypotenuse
• cosθ = Adjacent / Hypotenuse
• tanθ = Opposite / Adjacent
• cscθ = 1 / sinθ
• secθ = 1 / cosθ
• cotθ = 1 / tanθ

Addition and Subtraction Formulas:

• sin(A ± B) = sinA * cosB ± cosA * sinB
• cos(A ± B) = cosA * cosB ∓ sinA * sinB
• tan(A ± B) = (tanA ± tanB) / (1 ∓ tanA * tanB)

Calculus:

Derivative Formulas:

• d/dx (k) = 0 (where k is a constant)
• d/dx (xn) = nx^(n-1)
• d/dx (sinx) = cosx
• d/dx (cosx) = -sinx
• d/dx (tanx) = sec^2x
• d/dx (ex) = ex

Integration Formulas:

• ∫ k dx = kx + C (where k is a constant)
• ∫ x^n dx = (x^(n+1))/(n+1) + C (where n ≠ -1)
• ∫ sinx dx = -cosx + C
• ∫ cosx dx = sinx + C
• ∫ sec^2x dx = tanx + C
• ∫ ex dx = ex + C

Coordinate Geometry:

Distance Formula: The distance between two points (x1, y1) and (x2, y2) in a coordinate plane is given by: d = √((x2 - x1)^2 + (y2 - y1)^2)

Slope Formula: The slope (m) of a line passing through two points (x1, y1) and (x2, y2) is given by: m = (y2 - y1) / (x2 - x1)

Equation of a Line: The equation of a line with slope (m) and passing through a point (x1, y1) is given by: y - y1 = m(x - x1)

These are just a few essential formulas and theorems from different topics. It's important to review and practice all the concepts and formulas covered in your syllabus to perform well in the 12th class Mathematics board exam.