What should be the sequence to study maths for iit jee?

Studying mathematics for IIT-JEE requires a systematic approach that builds on foundational concepts and progressively tackles more complex topics. Here’s a suggested sequence to study mathematics effectively for IIT-JEE: ### 1. **Basics and Foundation:** Start with the fundamentals to build a strong base. Ensure you understand the basic concepts thoroughly before moving to advanced topics. - **Sets, Relations, and Functions:** Basic operations, types of relations, and functions. - **Complex Numbers and Quadratic Equations:** Algebra of complex numbers, polar form, quadratic equations, and their roots. ### 2. **Algebra:** Algebra forms a significant part of the IIT-JEE syllabus and involves various topics. - **Sequences and Series:** Arithmetic and geometric progressions, harmonic progression, and special series (e.g., sum of squares and cubes of first n natural numbers). - **Permutations and Combinations:** Fundamental principles, factorial notation, and applications. - **Binomial Theorem:** Expansion, general term, and middle term. - **Matrices and Determinants:** Matrix operations, determinants, and their properties. - **Probability:** Basic probability, conditional probability, Bayes' theorem, and random variables. ### 3. **Trigonometry:** Trigonometry is crucial and frequently tested. - **Trigonometric Ratios and Identities:** Basic identities, transformations, and trigonometric equations. - **Inverse Trigonometric Functions:** Their properties and graphs. - **Properties of Triangles:** Sine rule, cosine rule, area of a triangle, and solutions of triangles. ### 4. **Coordinate Geometry:** Geometry topics that blend algebra and geometry concepts. - **Straight Lines and Pair of Straight Lines:** Equations, distance formula, and angle between lines. - **Circles:** Standard equations, tangents, and normal lines. - **Conic Sections:** Parabola, ellipse, and hyperbola - equations and properties. ### 5. **Vectors and 3D Geometry:** - **Vectors:** Operations, dot and cross product, scalar triple product. - **Three-Dimensional Geometry:** Direction cosines, planes, lines, and the shortest distance between skew lines. ### 6. **Calculus:** A significant and complex part of the syllabus, calculus requires careful study and practice. - **Limits and Continuity:** Basic concepts, limits of functions, and continuity. - **Differentiation:** Derivatives, application of derivatives (tangents and normals, rate of change, maxima and minima). - **Integration:** Indefinite and definite integrals, properties, and applications (area under curves, differential equations). - **Differential Equations:** Formation, order and degree, solutions of first-order differential equations. ### 7. **Mathematical Reasoning and Statistics:** - **Mathematical Reasoning:** Statements, logical operations, and implications. - **Statistics:** Measures of central tendency and dispersion, probability distributions. ### Suggested Study Plan: 1. **Daily Schedule:** - Allocate dedicated time slots for mathematics daily. - Mix theoretical study with problem-solving practice. 2. **Practice Regularly:** - Solve problems from NCERT and reference books (e.g., "IIT Mathematics" by M.L. Khanna, "Problems in Calculus of One Variable" by I.A. Maron). - Practice previous years’ IIT-JEE papers and mock tests. 3. **Revision and Mock Tests:** - Regularly revise key concepts and formulas. - Take full-length mock tests to simulate exam conditions and improve time management. 4. **Focus on Weak Areas:** - Identify and spend extra time on weak topics. - Seek help from teachers, peers, or online resources to clarify doubts. ### Recommended Reference Books: - **"Mathematics for Class 11 & 12" by R.D. Sharma** - **"Higher Algebra" by Hall and Knight** - **"Problems in Calculus of One Variable" by I.A. Maron** - **"Coordinate Geometry" by S.L. Loney** - **"Trigonometry" by S.L. Loney** - **"IIT Mathematics" by M.L. Khanna** By following this sequence and maintaining a disciplined study routine, you can build a strong foundation in mathematics and be well-prepared for the IIT-JEE. read less