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Mathematics, JEE Main, Class 11, Class 12, Dropper

JEE Main Mathematics: Dropper Year

A dropper year of live JEE Main maths: all 14 units of NTA's 2027 syllabus, Class 11 and 12 together, in a group of up to 5 students or 1-on-1.

Course length
12 months (52 weeks)
Live classes
96
Batch size
Up to 5 students
Places left
5

Overview

This course follows the mathematics part of the official Syllabus for JEE (Main) - 2027, Paper 1 (B.E./B.Tech.), published by National Testing Agency (NTA). It takes the Class 11 and Class 12 part: 14 of the document's 14 units, 26 chapters and 81 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. A dropper year goes through both classes again in one year, Class 11's chapters of each unit before Class 12's. 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

  • Class 11 and Class 12 mathematics studied once: this year takes the whole syllabus again, unit by unit

What you will learn

  • Sets (Class 11)
  • Relations and Functions (Class 11)
  • Relations and Functions (Class 12)
  • Complex Numbers and Quadratic Equations (Class 11)
  • Matrices (Class 12)
  • Determinants (Class 12)
  • Permutations and Combinations (Class 11)
  • Binomial Theorem (Class 11)
  • Sequences and Series (Class 11)
  • Real functions and their graphs (Class 11)
  • Limits and Derivatives (Class 11)
  • Continuity and Differentiability (Class 12)
  • Application of Derivatives (Class 12)
  • Integrals (Class 12)
  • Application of Integrals (Class 12)
  • Differential Equations (Class 12)
  • Straight Lines (Class 11)
  • Conic Sections (Class 11)
  • Introduction to Three Dimensional Geometry (Class 11)
  • Three Dimensional Geometry (Class 12)
  • Vector Algebra (Class 12)
  • Statistics (Class 11)
  • Probability (Class 11)
  • Probability (Class 12)
  • Trigonometric Functions (Class 11)
  • Inverse Trigonometric Functions (Class 12)

Course curriculum

14 modules, 81 lessons

What you cover in 1 month

  1. Month 1
    • Module 1: Sets, relations and functions, lessons 1 to 7

The rest of the syllabus takes 11 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 18 lessons
  1. Lesson 1: Sets and their representation
  2. Lesson 2: Union, intersection and complement of sets and their algebraic properties
  3. Lesson 3: Power set
  4. Lesson 4: Relations
  5. Lesson 5: Functions
  6. Lesson 6: Types of relations, equivalence relations
  7. Lesson 7: One-one, into and onto functions
  8. Lesson 8: The composition of functions

Module 2: Complex numbers and quadratic equations

After this plan7 lessons
  1. Lesson 1: Complex numbers as ordered pairs of reals
  2. Lesson 2: Representation of complex numbers in the form a + ib and their representation in a plane, Argand diagram
  3. Lesson 3: Algebra of complex numbers
  4. Lesson 4: Modulus and argument (or amplitude) of a complex number
  5. Lesson 5: Quadratic equations in real and complex number systems and their solutions
  6. Lesson 6: Relations between roots and coefficients, nature of roots
  7. Lesson 7: The formation of quadratic equations with given roots

Module 3: Matrices and determinants

After this plan5 lessons
  1. Lesson 1: Matrices, algebra of matrices, types of matrices
  2. Lesson 2: Determinants and matrices of order two and three, evaluation of determinants
  3. Lesson 3: Area of triangles using determinants
  4. Lesson 4: Adjoint and inverse of a square matrix
  5. Lesson 5: Test of consistency and solution of simultaneous linear equations in two or three variables using matrices

Module 4: Permutations and combinations

After this plan4 lessons
  1. Lesson 1: The fundamental principle of counting
  2. Lesson 2: Permutations and combinations
  3. Lesson 3: Meaning of P(n, r) and C(n, r)
  4. Lesson 4: Simple applications

Module 5: Binomial theorem

After this plan3 lessons
  1. Lesson 1: Binomial theorem for a positive integral index
  2. Lesson 2: General term and middle term
  3. Lesson 3: Simple applications

Module 6: Sequences and series

After this plan3 lessons
  1. Lesson 1: Arithmetic and geometric progressions
  2. Lesson 2: Insertion of arithmetic and geometric means between two given numbers
  3. Lesson 3: Relation between A.M. and G.M.

Module 7: Limits, continuity and differentiability

After this plan11 lessons
  1. Lesson 1: Real-valued functions, algebra of functions
  2. Lesson 2: Polynomial, rational, trigonometric, logarithmic and exponential functions; inverse functions
  3. Lesson 3: Graphs of simple functions
  4. Lesson 4: Limits
  5. Lesson 5: Differentiation of the sum, difference, product and quotient of two functions
  6. Lesson 6: Continuity and differentiability
  7. Lesson 7: Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions
  8. Lesson 8: Derivatives of order up to two
  9. Lesson 9: Rate of change of quantities
  10. Lesson 10: Monotonic (increasing and decreasing) functions
  11. Lesson 11: Maxima and minima of functions of one variable

Module 8: Integral calculus

After this plan8 lessons
  1. Lesson 1: Integral as an anti-derivative
  2. Lesson 2: Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions
  3. Lesson 3: Integration by substitution, by parts and by partial fractions
  4. Lesson 4: Integration using trigonometric identities
  5. Lesson 5: Simple integrals of the type ∫dx/(x² + a²), ∫dx/√(x² ± a²), ∫dx/(a² − x²), ∫dx/√(a² − x²), ∫dx/(ax² + bx + c), ∫dx/√(ax² + bx + c), ∫(px + q)dx/(ax² + bx + c), ∫(px + q)dx/√(ax² + bx + c), ∫√(a² ± x²)dx and ∫√(x² − a²)dx
  6. Lesson 6: The fundamental theorem of calculus
  7. Lesson 7: Properties of definite integrals, evaluation of definite integrals
  8. Lesson 8: Areas of the regions bounded by simple curves in standard forms

Module 9: Differential equations

After this plan4 lessons
  1. Lesson 1: Ordinary differential equations, their order and degree
  2. Lesson 2: Solution by the method of separation of variables
  3. Lesson 3: Solution of a homogeneous differential equation
  4. Lesson 4: Linear differential equations of the type dy/dx + p(x)y = q(x)

Module 10: Coordinate geometry

After this plan10 lessons
  1. Lesson 1: Cartesian system of rectangular coordinates in a plane, distance formula, section formula
  2. Lesson 2: Locus and its equation
  3. Lesson 3: The slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes
  4. Lesson 4: Various forms of equations of a line, intersection of lines, angles between two lines
  5. Lesson 5: Conditions for concurrence of three lines, the distance of a point from a line
  6. Lesson 6: Coordinates of the centroid, orthocentre and circumcentre of a triangle
  7. Lesson 7: Standard and general forms of the equation of a circle, its radius and centre
  8. Lesson 8: Equation of a circle when the endpoints of a diameter are given
  9. Lesson 9: Points of intersection of a line and a circle with the centre at the origin
  10. Lesson 10: Sections of conics; equations of the parabola, ellipse and hyperbola in standard forms

Module 11: Three-dimensional geometry

After this plan5 lessons
  1. Lesson 1: Coordinates of a point in space, the distance between two points, section formula
  2. Lesson 2: Direction ratios and direction cosines
  3. Lesson 3: The angle between two intersecting lines
  4. Lesson 4: Equation of a line
  5. Lesson 5: Skew lines, the shortest distance between them and its equation

Module 12: Vector algebra

After this plan3 lessons
  1. Lesson 1: Vectors and scalars, the addition of vectors
  2. Lesson 2: Components of a vector in two dimensions and three-dimensional space
  3. Lesson 3: Scalar and vector products

Module 13: Statistics and probability

After this plan8 lessons
  1. Lesson 1: Measures of dispersion
  2. Lesson 2: Mean, median and mode of grouped and ungrouped data
  3. Lesson 3: Standard deviation, variance and mean deviation for grouped and ungrouped data
  4. Lesson 4: Probability of an event
  5. Lesson 5: Addition theorem of probability
  6. Lesson 6: Multiplication theorem of probability
  7. Lesson 7: Bayes' theorem
  8. Lesson 8: Probability distribution of a random variable

Module 14: Trigonometry

After this plan2 lessons
  1. Lesson 1: Trigonometric identities and trigonometric functions
  2. Lesson 2: Inverse trigonometric functions and their properties
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