JEE Main Maths Formulas 2025

Trigonometry is an essential topic in JEE mains Mathematics and involves a lot of formulas. Some of the critical formulas in Trigonometry are:

• ${{\sin ^2}x + {\cos ^2}x = 1}$

• ${\tan x = \dfrac{{\sin x}}{{\cos x}}}$

• ${\sec x = \dfrac{1}{{\cos x}}}$

• ${\cot x = \dfrac{{\cos x}}{{\sin x}}}$

• ${\cos ecx = \dfrac{1}{{\sin x}}}$

Aspirants should first understand the concepts behind Trigonometry and then memorise these formulas. Regular practice and solving different types of problems will also help aspirants master Trigonometry.

Algebra Formulas

Algebra is another crucial topic in JEE Mathematics that involves several formulas. Some of the essential Algebra formulas are:

• ${{\left( {a + b} \right)^2} = {a^2} + 2ab + {b^2}}$

• ${{\left( {a - b} \right)^2} = {a^2} - 2ab + {b^2}}$

• ${{a^2} - {b^2} = \left( {a + b} \right)\left( {a - b} \right)}$

• ${{\left( {a + b} \right)^3} = {a^3} + 3{a^2}b + 3a{b^2} + {b^3}}$

• ${{\left( {a - b} \right)^3} = {a^3} - 3{a^2}b + 3a{b^2} - {b^3}}$

Aspirants should first understand the basic concepts of Algebra and then memorise these formulas. Regular practice and solving different types of problems will also help aspirants master Algebra.

Calculus Formulas

Calculus is an important topic in JEE mains Mathematics and involves several formulas. Some of the essential Calculus formulas are:

• ${\dfrac{d}{{dx}}\left( a \right) = 0}$

• ${\dfrac{d}{{dx}}\left( {ax} \right) = a}$

• ${\dfrac{d}{{dx}}\left( {{x^n}} \right) = n{x^{n - 1}}}$

• ${\dfrac{d}{{dx}}\left( {\sin x} \right) = \cos x}$

• ${\dfrac{d}{{dx}}\left( {\cos x} \right) =  - \sin x}$

• ${\dfrac{d}{{dx}}\left( {\tan x} \right) = {\sec ^2}x}$

• ${\dfrac{d}{{dx}}\left( {\cot x} \right) =  - \cos e{c^2}x}$

Aspirants should first understand the basic concepts of Calculus and then memorise these formulas. Regular practice and solving different types of problems will also help aspirants master Calculus.

Probability Formulas

Probability Formulas: Probability is an important topic in JEE mains Mathematics and involves several formulas. Some of the essential Probability formulas are:

• ${{{P}}\left( {{{A}} \cup {{B}}} \right) = {{P}}\left( {{A}} \right) + {{P}}\left( {{B}} \right) - {{P}}\left( {{{A}} \cap {{B}}} \right)}$

• ${{{P}}\left( {{{A}} \cap {{B}}} \right) = {{P}}\left( {{A}} \right) \times {{P}}\left( {\dfrac{{{B}}}{{{A}}}} \right)}$

• ${{{P}}\left( {\dfrac{{{A}}}{{{B}}}} \right) = \dfrac{{{{P}}\left( {{{A}} \cap {{B}}} \right)}}{{{{P}}\left( {{B}} \right)}}}$

Aspirants should first understand the basic concepts of Probability and then memorise these formulas. Regular practice and solving different types of problems will also help aspirants master Probability.

Geometry Formulas

Geometry is an important topic in JEEmains Mathematics and involves several formulas. Some of the essential Geometry formulas are:

• Area of a Triangle = $\left(\dfrac{1}{2}\right) { \times }$ base ${ \times }$ height

• Perimeter of a Square = 4 ${ \times }$ side

• Perimeter of a Rectangle = 2 ${ \times }$ (length + breadth)

• Area of a Circle = ${\pi {r^2}}$

• Circumference of a Circle = ${2\pi r}$

Aspirants should first understand the basic concepts of Geometry and then memorise these formulas. Regular practice

Basic Integration Formulas: 

The basic integration formulas are the ones that are used to find the integral of a function. Some of the essential basic integration formulas are:

• ${\int dx = x + c}$

• ${\int {x^n}dx = \dfrac{{\left( {{x^{\left( {n + 1} \right)}}} \right)}}{{\left( {n + 1} \right)}} + C}$

• ${\int {e^x}dx = {e^x} + C}$

• ${\int \sin xdx =  - \cos x + C}$

• ${\int \cos xdx = \sin x + C}$

Integration Formulas

Integration by substitution is a common technique used to solve integrals. This technique involves substituting a part of the integral with a new variable. The formula for Integration by substitution is:

• ${\int f\left( {g\left( x \right)} \right)g'\left( x \right)dx = \int f\left( u \right)du}$

Integration by Parts: Integration by parts is another technique used to solve integrals. This technique involves selecting two parts of the integral and applying a specific formula. The formula for Integration by Parts is:

• $\int udv = uv - \int vdu$

Straight Line Formulas

Equation of a Straight Line: The equation of a straight line is y = mx + c, where m is the slope of the line, and c is the y-intercept. The slope of a line is given by:

• ${m = \dfrac{{\left( {{y_2} - {y_1}} \right)}}{{\left( {{x_2} - {x_1}} \right)}}}$

• Point-Slope Form: The Point-Slope Form of a straight line is $y - y_1 = m(x - x_1)$. This form is used to find the equation of a straight line when the slope and one point on the line are given.

• Intercept Form: The Intercept Form of a straight line is ${\dfrac{x}{a} + \dfrac{y}{b} = 1}$, where a and b are the x-intercept and y-intercept, respectively. This form is used to find the equation of a straight line when the intercepts are given.

• Slope-Intercept Form: The Slope-Intercept Form of a straight line is $y = mx + c$. This form is used to find the equation of a straight line when the slope and y-intercept are given.

• Two-Point Form: The Two-Point Form of a straight line is ${\dfrac{{\left( {y - {y_1}} \right)}}{{\left( {{y_2} - {y_1}} \right)}} = \dfrac{{\left( {x - {x_1}} \right)}}{{\left( {{x_2} - {x_1}} \right)}}}$. This form is used to find the equation of a straight line when two points on the line are given.

• Perpendicular Distance Formula: The Perpendicular Distance Formula is used to find the perpendicular distance between a point and a line. The formula is:

• Distance = {\dfrac{{\left| {ax + by + c} \right|}}{{\sqrt {\left( {{a^2} + {b^2}} \right)} }}}

• Distance Formula: The Distance Formula is used to find the distance between two points. The formula is:

• Distance = ${\sqrt {\left[ {{{\left( {x2 - x1} \right)}^2} + {{\left( {y2 - y1} \right)}^2}} \right]} }$

• A Parabola is a U-shaped curve that is symmetric around a line called the axis of the parabola. The standard equation of a parabola is ${{y^2} = 4ax}$, where a is a constant and the axis of the parabola is parallel to the x-axis.

• Vertex Form: The Vertex Form of a parabola is given as ${y - k = a{\left( {x - h} \right)^2}}$, where (h, k) is the vertex of the parabola. This form is used to find the equation of a parabola when the vertex and the value of a are given.

• Standard Form: The Standard Form of a parabola is given as ${{\left( {x - h} \right)^2} = 4a\left( {y - k} \right)}$, where (h, k) is the vertex of the parabola. This form is used to find the equation of a parabola when the vertex and the value of a are given.

• Focus-Directrix Form: The Focus-Directrix Form of a parabola is given as ${{\left( {x - h} \right)^2} = 4a\left( {y - k} \right)}$, where the focus of the parabola is ${\left( {h,k + \dfrac{1}{{4a}}} \right)}$, and the directrix of the parabola is ${y = k - \dfrac{1}{{4a}}}$. This form is used to find the equation of a parabola when the focus and the directrix are given.

• Latus Rectum Form: The Latus Rectum Form of a parabola is given as ${y = mx + \dfrac{a}{m}}$, where m is the slope of the tangent to the parabola at any point on it. This form is used to find the equation of the latus rectum of the parabola.

Matrices and Determinants Formulas

1. Matrix Multiplication: If A is an $m \times n$ matrix and B is an $n \times p$ matrix, the resultant matrix AB will be $m \times p$.

2. Determinant of a 2x2 Matrix: $|A| = \begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad - bc$

3. The inverse of a Matrix: $A^{-1} = \frac{1}{|A|} \text{adj}(A)$

Vectors Formulas

1. Dot Product: $vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| \cos \theta$

2. Cross Product: $\vec{a} \times \vec{b} = |\vec{a}||\vec{b}|\sin\theta \hat{n}$

3. Scalar Triple Product: $\vec{a} \cdot (\vec{b} \times \vec{c})$

Complex Numbers Formulas

1. Polar Form: $z = r (\cos \theta + i \sin \theta)$

2. Euler’s Form: $z = r e^{i\theta}$

3. De Moivre's Theorem: $(\cos \theta + i \sin \theta)^n = \cos (n\theta) + i \sin (n\theta)$

Permutations and Combinations Formulas

1. Permutation: $P(n, r) = \frac{n!}{(n-r)!}$

2. Combination: $C(n, r) = \frac{n!}{r!(n-r)!}$

Binomial Theorem Formulas

1. Expansion: $(a + b)^n = \sum_{k=0}^n C(n, k) a^{n-k} b^k$

2. General Term: $T_{k+1} = C(n, k) a^{n-k} b^k$

Three-Dimensional Geometry Formulas

1. Distance Between Two Points: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}$

2. Equation of a Line: $\frac{x - x_1}{l} = \frac{y - y_1}{m} = \frac{z - z_1}{n}$

3. Equation of a Plane: $ax + by + cz + d = 0$

Differential Equations Formulas

1. General Form: $\frac{dy}{dx} + P(x)y = Q(x)$

2. Solution Using Integrating Factor (IF): $y \cdot IF = \int Q(x) \cdot IF \, dx$ where $IF = e^{\int P(x) dx}$

Statistics Formulas

1. Mean (Arithmetic Mean): $\text{Mean} = \frac{\sum x_i}{n}$

2. Variance: $\sigma^2 = \frac{\sum (x_i - \bar{x})^2}{n}$

3. Standard Deviation: $\sigma = \sqrt{\sigma^2}$​

Logarithms Formulas

1. Basic Properties:
   $\log(ab) = \log a + \log b$
   $\log \frac{a}{b} = \log a - \log b$
   $\log a^n = n \log a$

2. Change of Base Formula:$\log_b a = \frac{\log a}{\log b}$

Circle Formulas

1. Standard Equation: $(x-h)^2 + (y-k)^2 = r^2$

2. Parametric Form: $x = h + r \cos \theta, \, y = k + r \sin \theta$

Study Tips and Techniques to Learn Maths Formulas for JEE Main 2025

• Understand the Syllabus: Familiarise yourself with the JEE mains Math syllabus to identify the different topics and subtopics you need to cover. This will help you organise your study plan and prioritise your efforts.

• Categorise the Formulas: Divide the formulas into different categories such as Algebra, Calculus, Trigonometry, Coordinate Geometry, and Statistics. This will help you focus on one category at a time and prevent confusion between different topics.

• Create a Formula Sheet: Develop a personalised formula sheet or notebook where you can compile all the important formulas. Include the formulas along with their variables, units, and any special conditions or exceptions. Keep this sheet handy for quick reference and regular revision.

• Understand the Concepts: Merely memorising formulas is not enough; strive to understand the underlying concepts and principles behind each formula. Mathematics is a subject that builds upon logical reasoning and problem-solving skills. Focus on understanding the derivations and logic behind the formulas.

• Practice Problem Solving: Mathematics is best learned through practice. Solve a variety of problems related to each formula you learn. Start with basic problems and gradually move on to more complex ones. Regular practice will help you become familiar with the formulas and improve your problem-solving skills.

• Create Visual Aids: Utilise diagrams, graphs, and visual representations to understand geometric and graphical concepts. Visual aids can enhance your understanding and help you visualise how the formulas apply to different situations.

• Solve Previous Years' Question Papers: Practice solving previous years' JEE mains Math question papers. This will help you become familiar with the types of questions asked and the application of formulas in different contexts. It will also help you manage your time effectively during the exam.

• Review and Revise Regularly: Regularly revise the formulas and concepts you have learned. Set aside dedicated time for revision, solve practice problems, and test yourself using mock tests or quizzes. Regular revision will reinforce your knowledge and ensure better retention of the formulas.

Conclusion 

Mathematics is an essential subject for JEE Main and Advanced, and it plays a crucial role in determining a candidate's rank and score. To excel in JEE Mathematics, aspirants must understand and memorise the essential formulas related to Algebra, Trigonometry, Calculus, and Geometry. The integration formula, straight line formula, and parabola formula are some of the essential formulas that aspirants need to master. Moreover, aspirants must know how to apply these Maths Formulas for JEE Mains PDF in solving problems and be quick in calculations to score well in JEE Mathematics.

JEE Main Other Subject-wise Important Formulas

Start your JEE Main journey with confidence, equipped with our Subject-wise important formulas that encompass the crucial concepts from Physics, Chemistry, and Mathematics. The table below will prove to be an invaluable asset in your JEE Main preparation.

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