JEE Advanced 2025 Maths Revision Notes - PDF Download

JEE Advanced Maths Notes are given on this page in the form of a link you can go to the link and click on it. You can find the topic-wise Maths notes for the JEE Advanced exam. These JEE Advanced Maths notes revision notes are also recommended to download in PDF so that they can use it for offline use. It is very important for JEE aspirants to remember all the formulas which are used in problem solving in Maths. so, the JEE Advanced Maths notes are the perfect material for learning the formulas and important theorems.

The JEE Advanced notes prepared by our subject teacher expert help students with a quick revision of important topics. One preparing for the JEE Advanced must have a proper plan to crack the exam. Practicing previous years’ i.e pyqs JEE Advanced Maths questions is essential to understand the exam pattern and difficulty level.

Students are advised to download and learn the JEE Advanced Maths previous year’s questions with solutions and you should also understand the JEE Advanced syllabus.

Chapter-wise Revision Notes for Maths

Make the most of our extensive review notes to help you prepare for the Math subject of JEE Advanced 2025 and get the PDF, incorporate it into your study schedule, and improve your math readiness.

Students may also click on the following table's links to view JEE Advanced Maths notes per chapter: 

Important Formulas Covered in JEE Advanced

Complex Number:

• General form of Complex numbers: $x+i$, where ‘$x$' is Real part and ‘i’ is an Imaginary part.

• Sum of nth root of unit: zero

• Product of nth root of unity = $(-1) n-1$

• Cube roots of unity: $1, \omega, \omega^2$

• $\left|z_1+z_2\right| \leq\left|z_1\right|+\left|z_2\right| ;\left|z_1+z_2\right| \geq\left|z_1\right|-\left|z_2\right| ;\left|z_1-z_2\right| \geq\left|z_1\right|-\left|z_2\right|$

• If three complex numbers $z_1, z_2, z_3$ are collinear then,

• $\left|\begin{array}{lll}z_1 & \overline{z_1} & 1 \\ z_2 & \overline{z_2} & 1 \\ z_3 & \overline{z_3} & 1\end{array}\right|=0$

• If $\arg \cos \alpha=\arg \sin \alpha=0, \arg \cos 2 \alpha=\arg \sin 2 \alpha=0$

• $\arg \cos 2 n \alpha=\arg \sin 2 n \alpha=0$

• $\arg \cos 2 \alpha=\arg \sin 2 \alpha=\frac{3}{2}$

• $\arg \cos 3 \alpha=3 \cos (\alpha+\beta+\gamma)$

• $\arg \sin 3 \alpha=3 \sin (\alpha+\beta+\gamma)$

• $\arg \cos (2 \alpha-\beta-\gamma)=3$

• $\arg \sin (2 \alpha-\beta-\gamma)=0$

• $a^3+b^3+c^3-3 a b c=(a+b+c)\left(a+b \omega+c \omega^2\right)\left(a+b \omega^2+c \omega\right)$

Quadratic Equation:

• Standard form of Quadratic equation:$a x^2+b x+c=0$

• General equation: $x=\frac{-b \pm \sqrt{\left(b^2-4 a c\right)}}{2 a}$

• Sum of roots $=-\frac{b}{a}$

• Product of roots discriminate $=b^2-4 a c$

• If $\alpha, \beta$ are roots then Quadratic equation is $x^2-x(\alpha+\beta)+\alpha \beta=0$

• Number of terms in the expansion: $(x+a)^n$ is $n+1$

• Any three non coplanar vectors are linearly independent

• A system of vectors $\overline{a_1}, \overline{a_2}, \ldots \overline{a_n}$ are said to be linearly dependent, If there exist,$x_1 \overline{a_1}+x_2 \overline{a_2}+\ldots+x_n a_n=0$ at least one of $x_i \neq 0$ where $i=1,2,3 \ldots n$ and determinant = 0 

• a, b, c are coplanar then $[a b c]=0$

• If i, j, k are unit vectors then $[i j k]=1$

• If a, b, c are vectors then $[a+b, b+c, c+a]=2[a b c]$

• $(1+x)^{n-1}$ is divisible by x and $(1+x)^n-n x-1$ is divisible by $x^2$

• If ${ }^n C_r-1,{ }^n C_r,{ }^n C_r+1$ are in A.P, then $(n-2 r)^2=n+2$

Trigonometric Identities:

• $\sin ^2(x)+\cos ^2(x)=1$

• $1+\tan ^2(x)=\sec ^2(x)$

• $1+\cot ^2(x)=\operatorname{cosec}^2(x)$

Limits:

• Limit of a constant function: $\lim c=c$

• Limit of a sum or difference: $\lim (f(x) \pm g(x))=\lim f(x) \pm \lim g(x)$

• Limit of a product: $\lim (f(x) g(x))=\lim f(x) \times \lim g(x)$

• Limit of a quotient: $\lim \left(\frac{f(x)}{g(x)}\right)=\frac{\lim f(x)}{\lim g(x)}$ if $\lim g(x) \neq 0$

Derivatives:

• Power Rule: $\frac{d}{d x}\left(x^n\right)=n x^{(n-1)}$

• Sum/difference Rule: $\frac{d}{d x}(f(x) \pm g(x))=f^{\prime}(x) \pm g^{\prime}(x)$

• Product Rule: $\frac{d}{d x}(f(x) g(x))=f^{\prime}(x) g(x)+f(x) g^{\prime}(x)$

• Quotient Rule: $\frac{d}{d x}\left(\frac{f(x)}{g(x)}\right)=\frac{\left[g(x) f^{\prime}(x)-f(x) g^{\prime}(x)\right]}{g^2(x)}$

Integration:

• $\int x^n d x=\frac{x^{n+1}}{n+1}+c$ where $n \neq-1$

• $\int \frac{1}{x} d x=\log _e|x|+c$

• $\int e^x d x=e^x+c$

• $\int a^x d x=\frac{a^x}{\log _e a}+c$

• $\int \sin x d x=-\cos x+c$

• $\int \cos x d x=\sin x+c$

• $\int \sec ^2 x d x=\tan x+c$

• $\int \operatorname{cosec}^2 x d x=-\cot x+c$

• $\int \sec x \tan x d x=\sec x+c$

• $\int \operatorname{cosec} x \cot x d x=-\operatorname{cosec} x+c$

• $\int \cot x d x=\log |\sin x|+c$

• $\int \tan x d x=-\log |\cos x|+c$

• $\int \sec x d x=\log |\sec x+\tan x|+c$

• $\int \operatorname{cosec} x d x=\log |\operatorname{cosec} x-\cot x|+c$

• $\int \frac{1}{\sqrt{a^2-x^2}} d x=\sin ^{-1}\left(\frac{x}{a}\right)+c$.

• $\int \frac{1}{a^2+x^2} d x=\frac{1}{a} \tan ^{-1}\left(\frac{x}{a}\right)+c$

• $\int-\frac{1}{a^2+x^2} d x=\frac{1}{a} \cot ^{-1}\left(\frac{x}{a}\right)+c$

• $\int \frac{1}{x \sqrt{x^2-a^2}} d x=\frac{1}{a} \sec ^{-1}\left(\frac{x}{a}\right)+c$

• $\int-\frac{1}{x \sqrt{x^2-a^2}} d x=\frac{1}{a} \operatorname{cosec}^{-1}\left(\frac{x}{a}\right)+c$

Important Topics Covered in JEE Advanced

Mathematics chapters demand a clear understanding of the concepts & formulas of any chapter. The following are the most important Math chapters for JEE Advanced 2025 mentioned down below Have a look:

1.  3 Dimensional Geometry

2. Integrals

3. Conic section

4. Functions

5. Complex Number

6. Vector Algebra

7. Continuity and Derivability

8. Limits

9. Matrices and Determinants

10. Parabola

11. Differential Equation

12. Circle

13. Probability 

14. Area under curves

15. Sequences and series

16. Application of Derivatives

17. Permutations and combination

18. Calculus

19. Straight Lines

20. Quadratic Equation

21. Binomial Theorem & M. I

22. Set & Relation

23. Properties of Triangle

Mathematics Chapter-wise Weightage in JEE Advanced 2025

To help students prepare smartly, here we have organized the JEE Advanced 2025 Math Topic–wise weightage. The table below will give you a brief idea of the important topics that you need to focus on for the Math exam.

Students can practice other study materials with the JEE Advanced Maths notes

Having JEE Advance Previous Year Question Papers PDF Download option is a boon for JEE Advance aspirants. It facilitates convenient storage, allowing students to compile a comprehensive study resource. The benefits of having JEE Advance Previous Year Question Papers PDF include easy portability across devices, offline accessibility, and the ability to create a personalized collection of question banks. 

Aspirants can efficiently organize their study materials, making revision seamless. Additionally, JEE Advance Question Paper PDF Download provides an opportunity for students to go deeper into specific topics, and create a focused and structured approach to their JEE Advance 2025 preparation.

JEE Advanced Maths Important Questions

• Sets Relations and Functions

• Complex Numbers

• Quadratic Equations

• Arithmetic and Geometric Progressions

• Logarithms

• Straight Line

• Circle

• Parabola

• Ellipse

• Hyperbola

• Permutations and Combinations

• Binomial Theorem

• Probability

• Matrix and Determinants

• Limits Continuity and Differentiability

• Differentiations

• Applications of Derivatives

• Integrals

• Application of Integrals

• Differential Equations

• Vectors Algebra

• Three Dimensions Geometry

How useful are Revision Notes for the JEE Advanced Exam?

This Maths revision notes provides a perfect picture of important mathematical concepts and formulas which allows you to quickly review and revise important topics before the JEE Advanced exam.  Notes usually include step-by-step solutions to various types of problems, offering insights into effective problem-solving strategies that you can apply during the exam. Make sure that you will Well-organize your JEE Advanced revision notes and break down the complex mathematical concepts into easy ones which helps you grasp difficult topics with clarity and these notes will help you save time during revision by focusing on the most important concepts, allowing you to allocate more time to practice problems.

You can refer to these revision notes to quickly recall formulas, theorems, and concepts, which can be especially helpful when faced with time constraints, during your exam. These well designed revision notes will help in your exam and it will reduce your exam fear.