JEE Main Maths Important Formulas 2025 - Download PDF

JEE Main Maths important formulas 2025 according to JEE Main 2025 math syllabus are Complex numbers, Algebraic Operations, important properties of Conjugate, Amplitude, Vectorial Representation of a Complex Number, Cube Root, Square Root, Sum of Series, Straight Lines and many more. 

It is advised to read all the topics and make quick short notes of all the formulas associated. Making a study note of all the theorems, formulas, and sticky notes will help students save time. It will reduce the risk of mistakes, leading to an excellent performance in the JEE Main 2025 exam.

JEE Main Maths Important Formulas 2025 - Download PDF

JEE main math important formulas chapter-wise are mentioned in the below PDF. Students can directly download the PDF by clicking on the link below:

Also Read: JEE Main Important Formulas 2025

Chapter Wise JEE Main Maths Important Formulas 2025

JEE Main Maths Important Formulas 2025 are from these topics: Exponential and Logarithmic Series and Mathematical Induction, Functions and Relations, Trigonometry, Properties and Solution of a Triangle, Height and Distances and many more chapters.

Complex Numbers

• The general form of Complex numbers: x+i, where 'x' is the Real part and 'i' is an Imaginary part.
• The sum of the nth root of unity = zero
• Product of nth root of unity =(–1)n–1
• Cube roots of unity: 1,ω,ω2
• |z1+z2| ≤ |z1| + |z2|,|z1 + z2| ≥ |z1| −|z2|;|z1−z2|≥|z1|−|z2|
• If arg cosα= arg sinα= 0, arg cos2α=arg sin2α=0
• Arg cos2nα= arg sin2nα= 0
• Arg cos2α= argsin2α= 32
• Arg cos3α= 3cos(α+β+γ)
• Arg sin3α= 3sin(α+β+γ)
• Arg cos(2α–β–γ)= 3
• argsin(2α–β–γ)= 0
• a3+b3+c3–3abc= (a+b+c)(a+bω+cω2)(a+bω2+cω)

Quadratic Equation

• The standard form of Quadratic equation: ax2+bx+c=0
• General equation: x=−b±(b2−4ac)−−−−−−−−√2a
• Sum of roots =−ba
• Product of roots discriminant =b2–4ac
• If α and β are roots, then the Quadratic equation is x2–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 a1¯,a2¯,….an¯ are said to be linearly dependent; if there exist, x1a1¯+x2a2¯+….+xnan=0 at least one of xi≠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 x2 
• If nCr−1,nCr,nCr+1 are in A.P, then (n–2r)2=n+2

Also Read: Important Chapters for JEE Main 2025

Trigonometric Identities

• sin2(x)+cos2(x)=1
• 1+tan2(x)=sec2(x)
• 1+cot2(x)=cosec2(x)

Limits

• Limit of a constant function: limc=c
• Limit of a sum or difference: lim(f(x)±g(x))=limf(x)±limg(x)
• Limit of a product: lim(f(x)g(x))=limf(x)×limg(x)
• Limit of a quotient: lim(f(x)g(x))=limf(x)log(x) if limg(x)≠0

Also Read: Tips to Prepare Mathematics for JEE Main 2025

Derivatives

• Power Rule: ddx(xn)=nx(n−1)
• Sum/Difference Rule: ddx(f(x)±g(x))=f′(x)±g′(x)
• Product Rule: ddx(f(x)g(x))=f′(x)g(x)+f(x)g′(x)
• Quotient Rule: ddx(f(x)g(x))=[g(x)f′(x)−f(x)g′(x)]g2(x)

Integration

• ∫xndx=xn+1n+1+c where n≠−1
• ∫1xdx=loge|x|+c
• ∫exdx=ex+c
• ∫axdx=axlogea+c
• ∫sinxdx=−cosx+c
• ∫cosxdx=sinx+c
• ∫sec2xdx=tanx+c
• ∫cosec2xdx=−cotx+c
• ∫secxtanxdx=secx+c
• ∫cosec xcotxdx=–cosecx+c
• ∫cotxdx=log|sinx|+c
• ∫tanxdx=−log∣cosx∣+c
• ∫secxdx=log∣secx+tanx∣+c
• ∫cosec xdx=log∣cosec x–cotx∣+c
• ∫1a2−x2−−−−−−√dx=sin−1(xa)+c
• ∫−1a2−x2−−−−−−√dx=cos−1(xa)+c
• ∫1a2+x2dx=1atan−1(xa)+c
• ∫−1a2+x2dx=1acot−1(xa)+c
• ∫1xx2−a2−−−−−−√dx=1asec−1(xa)+c
• ∫−1xx2−a2−−−−−−√dx=1acosec−1(xa)+c

Also Read: JEE Main Mathematics Syllabus 2025

After referring to the given formulas, candidates should start preparing the numericals based out of these formulas. For practicing numericals, one should refer to Previous Year Question Papers, Mock tests, and Reference books. This will help the candidates to perform well and get good rank in JEE Main Exam.