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JEE Advanced Mathematics Formula Sheet 2025: Important formulae for last minute preparation

Candidates can use JEE Advanced Mathematics Formula Sheet 2025 to enhance their last-minute preparation. The exam will be conducted on May 18, 2025, in two shifts.

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JEE Advanced Mathematics Formula Sheet 2025: For JEE Advanced to be held on May 18, 2025, aspirants to appear for the exams shall note JEE Advanced Mathematics Formula Sheet 2025 provided here. With the formula sheet, aspirants will be able to quickly access the list of the most important formulas for last-minute revisions before the exams. It is advisable to go through the formula sheet here to be able to remember all of the formulas at once. The key to mastering these formulas is repetitive reading and go through them thoroughly before the exam begins. Even the slightest change is the signs will change the final answers, so, it is useful to carefully place each signs while working on the questions.

JEE Advanced Mathematics Formula Sheet 2025

Aspirants shall refer to JEE Advanced Mathematics Formula Sheet 2025 for the most important formulas for last-minute revision:
Unit Name Formula
Complex Number
  • General form of Complex numbers: x + i, where ‘x’ is the Real part and ‘i is the Imaginary part.
  • Sum of nth root of unity = zero
  • Product of nth root of unity = (-1) n -1
  • Cube roots of unity 1, ω, ω 2
  • | z 1 + z 2 | ≤ | z 1 | + | z 2 |; | z 1 + z 2 | ≥ | z 1 | - | z 2 |; | z 1 - z 2 | ≥ | z 1 | - | z 2 |
  • If arg cos α = arg sin α = 0, arg cos 2 α = arg sin 2 α = 0.
  • arg cos 2n α = arg sin 2n α = 0
  • arg cos 2α = arg sin 2 α = 2/3
  • arg cos 3 α = 3 cos ( α + β + γ )
  • arg sin 3α = 3 sin ( α + β + γ )
  • arg cos (2α - β - γ ) = 3
  • arg sin (2α - β - γ ) = 0
  • a 3 + b 3 + c 3 - 3abc = (a + b + c)(a +bω + cω 2 )(a +bω 2 + cω)
Quadratic Equation
  • Standard form of Quadratic equation: ax2 + bx +c = 0
  • General equation: x = - b ± √(b 2 - 4ac)/ 2a
  • Sum of roots = -b/a
  • Product of roots discriminate = b 2 -4ac
  • If α , β are roots then Quadratic equation is: x 2 - x (α + β) + αβ = 0.
  • Number of terms in the expansion: (x + a) n is n + 1
  • Any three non coplanar vectors are linearly independent.
  • A system of vectors a 1 , a 2 , ......... a n are said to be linearly dependent, If there exist, x 1 a 1 + x 2 a 2 + ........x n a n = 0 at least one of x i ≠ 0, where i= 1,2,3 ...... n and determinant = 0.
  • a, b, c are coplanar then [abc] = 0
  • If i, j, k are unit vectors then [ijk] = 1
  • If a, b, c are vectors then [a + b, b + c, c + a] = 2 [abc]
  • (1 +x) n-1 is divisible by x and (1 + x) n - nx -1 is divisible by x 2 .
  • If n C r -1, n C r , n C r + 1 are in A.P, then (n - 2r) 2 = n +2
Trigonometric Identities
  • 1+ tan 2 (x)=sec 2 (x)
  • sin 2 (x)+cos 2 (x)=1
  • 1+cot 2 (x)=cosec 2 (x)
Limits
  • Limit of a constant function: lim c = c
  • Limit of a sum or difference: lim (f(x) ± g (x)) = lim f (x) ± lim g (x)
  • Limit of a product: lim(f(x)g(x)) = lim f(x) x lim g (x)
  • Limit of a quotient:  (f(x)/g(x)) = lim f (x) / lim g (x) if lim g (x) ≠ 0
Derivatives
  • Lower Rule: d/dx (x n ) =nx (n-1)
  • Sum/Difference Rule: d/dx (f(x) ± g(x)) = f (x) ±g (x)
  • Product Rule: d/dx (f(x)g(x)) = f (x)g(x) + f(x)g(x)
  • Quotient Rule: d/dx (f(x)/g(x)) = [g(x)f(x) - f(x)g(x)]/g 2 (x)
Integration
  • ∫ x n dx = x n+1 / n+1 + c where n ≠ -1
  • ∫ 1/x dx = log e | x| + c
  • ∫ e x dx = e z + c
  • ∫ a x dx = a z / log e a + c
  • ∫ sin xdx = - cosx + c
  • ∫ cos xdx = sin x + c
  • ∫ sec 2 xdx = tan x + c
  • ∫ cosec 2 sds = - cot x + c
  • ∫ sec xtan xdx = sec x + c
  • ∫ cosec x cot xdx = - cosec x+ c

JEE Advanced Subject-wise Formula Sheet 2025 |
Subject JEE Advanced Formula Sheet 2025 Links
Physics JEE Advanced Physics Formula Sheet 2025
Chemistry JEE Advanced Chemistry Formula Sheet 2025

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