The IIT-JEE (Indian Institutes of Technology Joint Entrance Examination) is a highly competitive entrance exam for admission to undergraduate programs in engineering and science at the prestigious Indian Institutes of Technology (IITs) in India. The exam tests candidates’ knowledge and problem-solving skills in physics, chemistry, and mathematics.

## Knowledge in Maths in the IIT-JEE Exam

In the mathematics section of the IIT-JEE exam, the questions are designed to assess a candidate’s understanding of various mathematical concepts and their ability to apply them to solve complex problems. The level of mathematics required for the IIT-JEE exam is relatively high, and it covers a wide range of topics.

Here are some of the key topics in mathematics that candidates should be well-versed in for the IIT-JEE exam:

### Algebra

This includes topics such as algebraic expressions, equations, inequalities, complex numbers, matrices, determinants, sequences, and series.

### Trigonometry

Candidates should have a strong understanding of trigonometric functions, identities, equations, properties of triangles, and heights and distances.

### Coordinate Geometry

This involves the study of lines, circles, conic sections, and various coordinate transformations.

### Differential Calculus

Candidates should be familiar with the concepts of limits, continuity, differentiation of functions, and applications of derivatives.

### Integral Calculus

This includes topics such as definite and indefinite integrals, integration methods, and integrals’ applications.

### Differential Equations

Candidates should have a good understanding of ordinary differential equations and their solutions.

### Vectors

This involves the study of vector algebra, scalar, and vector products, and their applications in geometry and physics.

### Probability and Statistics

Candidates should be familiar with concepts such as probability, random variables, probability distributions, mean, variance, and standard deviation.

### Mathematical Reasoning

This includes topics related to sets, relations, functions, mathematical induction, and logic.

Please note that the difficulty level of the IIT-JEE exam is high, and the questions can be challenging and require a deep understanding of the concepts. Candidates are advised to have a thorough understanding of these topics and practice solving various problems to perform well in the mathematics section of the IIT-JEE exam.

## What Is The Math Syllabus Of IIT-JEE?

The maths syllabus for the IIT-JEE exam (now known as JEE Advanced) covers a wide range of topics in algebra, calculus, coordinate geometry, trigonometry, vectors, and statistics. Here is a comprehensive list of the math topics included in the syllabus:

### Algebra:

- Complex numbers: Algebra of complex numbers, modulus, and argument representation, De Moivre’s theorem.

Quadratic equations and expressions: Roots of quadratic equations, relations between roots and coefficients, nature of roots, quadratic expressions.

- Progressions: Arithmetic, geometric, and harmonic progressions, arithmetic-geometric series, sums of finite arithmetic, and geometric progressions.

- Permutations and Combinations: Fundamental principle of counting, permutation as an arrangement, combination as selection, binomial theorem (positive integral index).

### Coordinate Geometry:

- Straight Lines: Equations of lines in different forms, the angle between two lines, distance of a point from a line, lines through the end of the intersection of two lines, and reflection of a point in a line.
- Circles: Standard form of the equation of a circle, general form of the equation of a circle, its radius and center, equation of a circle when endpoints of a diameter are given, points of intersection of a line and a circle with the center at the origin, equation of a tangent, equation of a family of circles.
- Conic Sections: Parabola, ellipse, and hyperbola (their standard equations and simple properties).

### Calculus:

- Functions: Definitions and notations, domain, range, modulus, and signum functions, greatest integer, and fractional part functions, and exponential and logarithmic functions.
- Limits, Continuity, and Differentiability: Limit of a function, continuity of functions, derivatives of composite functions, derivatives of inverse trigonometric functions, derivative of implicit functions, the concept of exponential and logarithmic functions.
- Methods of Differentiation: Differentiation of parametric, implicit, and logarithmic functions, higher-order derivatives, and derivatives as a rate measure.
- Applications of Derivatives: Rate of change, increasing and decreasing functions, tangents and normals, maxima and minima, Rolle’s and Lagrange’s mean value theorems.
- Indefinite Integrals: Integration by substitution, integration by parts, and integration by partial fractions.
- Definite Integrals: Fundamental theorem of calculus, evaluation of definite integrals, application of definite integrals to areas.
- Differential Equations: Formation of ordinary differential equations, solutions of homogeneous differential equations, solutions of linear differential equations of the type: dy/dx + py = q, where p and q are functions of x or constants.
- Vectors: Addition and subtraction of vectors, scalar and vector products, scalar and vector triple products, and their geometrical interpretations.
- Probability: Addition and multiplication rules of probability, conditional probability, Bayes’ theorem, independence of events, random variables, and probability distributions, Bernoulli trials, and binomial distribution.

### Trigonometry:

- Trigonometric Functions and Identities: Trigonometric functions, their periodicity, graphs, trigonometric identities, and equations.
- Trigonometric Equations: Inverse trigonometric functions and their properties, properties of triangles including the areas of triangles.
- Heights and Distances: Angle of elevation, angle of depression, simple problems on heights and distances.
- Statistics:

- Measures of Central Tendency and Dispersion: Calculation of mean, median, mode of grouped and ungrouped data, calculation of standard deviation, variance, and mean deviation for grouped and ungrouped data.
- Probability: Random experiments, outcomes, events, probability of an event, mutually exclusive events, addition theorem, conditional probability, multiplication theorem, independent events.

Please note that this is a general outline of the math syllabus for the IIT-JEE exam. Candidates are advised to refer to the official JEE Advanced Math syllabus website page or relevant study materials for a detailed and updated syllabus, as there may be occasional revisions or additions to the topics.

## How To Get Free Math Resources For the IIT-JEE Exam?

Preparing for the IIT-JEE exam requires access to quality study resources. While some resources may require a fee, there are also several free math resources available to help you in your preparation. Here are some ways to access free math resources for the IIT-JEE exam:

### Official Websites

Visit the official websites of exam-conducting bodies like the National Testing Agency (NTA) or the Indian Institutes of Technology (IIT). These websites often provide free sample papers, previous year question papers, and other study materials.

### Online Platforms and Forums

Explore online learning platforms and forums dedicated to IIT-JEE preparation. Websites like Khan Academy, Unacademy, and Toppr offer free video lectures, practice exercises, and study materials for math.

### YouTube Channels

Many educators and coaching institutes have YouTube channels that provide free video lessons on math topics for the IIT-JEE exam. Some popular channels include Mathongo, ExamFear Education, and Vedantu.

### Open Educational Resources

Look for open educational resources (OER) available online. Websites like OpenStax, MIT OpenCourseWare, and NPTEL provide free textbooks, lecture notes, and course materials on math and other relevant subjects.

### Mobile Apps

There are several mobile apps available for IIT-JEE math preparation. Apps like Doubtnut, Gradeup, and Toppr provide free study materials, practice questions, and mock tests.

### Online Communities and Discussion Forums

Join online communities and discussion forums focused on IIT-JEE preparation. Platforms like Quora, Stack Exchange, and Reddit have dedicated sections where you can ask questions, discuss math problems, and get guidance from experts and fellow aspirants.

### Libraries and Bookstores

Visit your local library or bookstore to find books and study materials specifically designed for IIT-JEE math preparation. While some books may require purchase, you can often find free resources or borrow books from libraries.

### Coaching Institute Websites

Several coaching institutes have websites where they offer free study materials, practice papers, and mock tests. Explore the websites of renowned JEE coaching institutes like Resonance, Allen Career Institute, and FIITJEE for free math resources.

Remember, while free resources can be valuable, it’s essential to ensure the quality and accuracy of the materials you use. Cross-check information from multiple sources and refer to trusted and reputable platforms to ensure that you are accessing reliable study materials for your IIT-JEE math preparation.