Skip to main content

Your first class is free: 45 minutes, 1-on-1, no card needed.

Book
SparklMind

Mathematics, JEE Advanced, Class 12

JEE Advanced Mathematics: Class 12

Live JEE Advanced maths for Class 12, on the official 2026 syllabus, from matrices to calculus and vectors, in a group of up to 5 or 1-on-1.

Course length
12 months (52 weeks)
Live classes
96

Overview

This course follows the mathematics part of the official JEE (Advanced) 2026 Syllabus, published by jeeadv.ac.in, the JEE (Advanced) 2026 site. It takes the Class 12 part: 8 of the document's 9 sections, 12 chapters and 43 topics, each topic a lesson in the document's own words. The document does not say which class a topic belongs to, so a chapter is placed in the class where the NCERT textbook teaches it. Classes are live and 60 minutes long: 8 a month in a group of up to 5 students, or 1-on-1 at times set with your family, over 52 weeks.

What to know first

  • The Class 11 part of the JEE Advanced syllabus: our Class 11 course, or the same chapters at school

What you will learn

  • Relations and Functions
  • Matrices
  • Determinants
  • Probability
  • Inverse Trigonometric Functions
  • Three Dimensional Geometry
  • Continuity and Differentiability
  • Application of Derivatives
  • Integrals
  • Application of Integrals
  • Differential Equations
  • Vector Algebra

Course curriculum

8 modules, 43 lessons

What you cover in 1 month

  1. Month 1
    • Module 1: Sets, Relations and Functions, all 4 lessons

The rest of the syllabus takes 10 months more. You can add months at any time.

This is the planned order at the plan's number of classes. Your teacher adjusts the pace to the student.

Module 1: Sets, Relations and Functions

Month 14 lessons
  1. Lesson 1: Equivalence relation
  2. Lesson 2: Invertible functions
  3. Lesson 3: Into, onto and one-to-one functions
  4. Lesson 4: Composition of functions

Module 2: Matrices

After this plan8 lessons
  1. Lesson 1: Matrices as a rectangular array of real numbers, equality of matrices
  2. Lesson 2: Addition, multiplication by a scalar and product of matrices, transpose of a matrix
  3. Lesson 3: Elementary row and column transformations
  4. Lesson 4: Properties of these matrix operations
  5. Lesson 5: Diagonal, symmetric and skew-symmetric matrices and their properties
  6. Lesson 6: Determinant of a square matrix of order up to three
  7. Lesson 7: Adjoint of a matrix, inverse of a square matrix of order up to three
  8. Lesson 8: Solutions of simultaneous linear equations in two or three variables

Module 3: Probability and Statistics

After this plan4 lessons
  1. Lesson 1: Multiplication rule of probability
  2. Lesson 2: Conditional probability, independence of events
  3. Lesson 3: Total probability, Bayes' theorem
  4. Lesson 4: Random variable, mean and variance of the random variable

Module 4: Trigonometry

After this plan1 lesson
  1. Lesson 1: Inverse trigonometric functions (principal value only) and their elementary properties

Module 5: Analytical Geometry

After this plan5 lessons
  1. Lesson 1: Direction cosines and direction ratios, equation of a straight line in space
  2. Lesson 2: Skew lines, shortest distance between two lines
  3. Lesson 3: Equation of a plane, distance of a point from a plane
  4. Lesson 4: Angle between two lines, angle between two planes, angle between a line and the plane
  5. Lesson 5: Coplanar lines

Module 6: Differential Calculus

After this plan10 lessons
  1. Lesson 1: Continuity of a function, limit and continuity of the sum, difference, product and quotient of two functions
  2. Lesson 2: L'Hospital rule of evaluation of limits of functions
  3. Lesson 3: Continuity of composite functions, intermediate value property of continuous functions
  4. Lesson 4: Chain rule, derivatives of polynomial, rational, trigonometric, inverse trigonometric, exponential and logarithmic functions
  5. Lesson 5: Derivatives of order two, derivatives up to order two of implicit functions
  6. Lesson 6: Rolle's theorem and Lagrange's mean value theorem, geometric interpretation of the two theorems
  7. Lesson 7: Tangents and normals
  8. Lesson 8: Increasing and decreasing functions
  9. Lesson 9: Maximum and minimum values of a function
  10. Lesson 10: Geometric interpretation of derivatives

Module 7: Integral Calculus

After this plan7 lessons
  1. Lesson 1: Integration as the inverse process of differentiation, indefinite integrals of standard functions
  2. Lesson 2: Definite integrals as the limit of sums, definite integrals and their properties, fundamental theorem of integral calculus
  3. Lesson 3: Integration by parts, integration by the methods of substitution and partial fractions
  4. Lesson 4: Application of definite integrals to the determination of areas bounded by simple curves
  5. Lesson 5: Formation of ordinary differential equations
  6. Lesson 6: Solution of homogeneous differential equations of first order and first degree
  7. Lesson 7: Separation of variables method, linear first order differential equations

Module 8: Vectors

After this plan4 lessons
  1. Lesson 1: Addition of vectors, scalar multiplication
  2. Lesson 2: Dot and cross products
  3. Lesson 3: Scalar and vector triple products
  4. Lesson 4: Their geometrical interpretations
From ₹3,999 a monthChoose a plan

Keep going with SparklMind