Syllabus – JEE Mains – 2023 – Maths
| Unit No. | Unit Name | Topics |
| 1 | Sets, Relations and Functions | Sets and their representation |
| Union, intersection and complement of sets and their algebraic properties | ||
| Power set | ||
| Relation, Types of relations, equivalence relations, functions | ||
| One-one, into and onto functions, the composition of functions | ||
| 2 | Complex Number and Quadratic Equations | Complex numbers as ordered pairs of reals |
| Representation of complex numbers in the form (a+ib) and their representation in a plane, Argand diagram | ||
| Algebra of complex numbers, modulus and argument (or amplitude) of a complex number, square root of a complex number | ||
| Triangle inequality | ||
| Quadratic equations in real and complex number system and their solutions | ||
| The relation between roots and coefficients, nature of roots, the formation of quadratic equations with given roots | ||
| 3 | Matrices and Determinants | Matrices: Algebra of matrices, types of matrices, and matrices of order two and three |
| Determinants: Properties of determinants, evaluation of determinants, the area of triangles using determinants | ||
| Adjoint and evaluation of inverse of a square matrix using determinants and elementary transformations | ||
| Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices | ||
| 4 | Permutations and Combinations | The fundamental principle of counting |
| Permutation as an arrangement and combination as selection | ||
| The meaning of P (n,r) and C (n,r). Simple applications | ||
| 5 | Mathematical Induction | The principle of Mathematical Induction and its simple applications |
| 6 | Binomial Theorem | Binomial theorem for a positive integral index |
| General term and middle term | ||
| Properties of Binomial coefficients and simple applications | ||
| 7 | Sequences and Series | Arithmetic and Geometric progressions, insertion of arithmetic |
| Geometric means between two given numbers | ||
| The relation between A.M. and G.M | ||
| Sum up to n terms of special series: Sn, Sn2, Sn3 | ||
| Arithmetic – Geometric progression | ||
| 8 | Limit, Continuity and Differentiability | Real-valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic and exponential functions, inverse functions |
| Graphs of simple functions | ||
| Limits, continuity, and differentiability | ||
| Differentiation of the sum, difference, product, and quotient of two functions | ||
| Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions; derivatives of order up to two | ||
| Rolle’s and Lagrange’s Mean Value Theorems | ||
| Applications of derivatives: Rate of change of quantities, monotonic – increasing and decreasing functions, Maxima, and minima of functions of one variable, tangents, and normals. | ||
| 9 | Integral Calculus | Integral as an antiderivative |
| Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions | ||
| Integration by substitution, by parts, and by partial fractions | ||
| Integration using trigonometric identities | ||
| Integral as limit of a sum | ||
| Evaluation of simple integrals | ||
| Fundamental Theorem of Calculus | ||
| Properties of definite integrals, evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form | ||
| 10 | Differential Equations | Ordinary differential equations, their order, and degree. |
| Formation of differential equations | ||
| The solution of differential equations by the method of separation of variables | ||
| The solution of homogeneous and linear differential equations of the type | ||
| 11 | Coordinate Geometry | Cartesian system of rectangular coordinates in a plane, distance formula, section formula, locus and its equation, translation of axes, the slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes |
| Straight lines: Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines | ||
| The distance of a point from a line, equations of internal and external bisectors of angles between two lines, coordinates of centroid, orthocentre, and circumcentre of a triangle, equation of the family of lines passing through the point of intersection of two lines | ||
| Circles, conic sections: Standard form of equation of a circle, general form of the equation of a circle, its radius and centre, equation of a circle when the endpoints of a diameter are given, points of intersection of a line and a circle with the centre at the origin and condition for a line to be tangent to a circle, equation of the tangent | ||
| Sections of cones, equations of conic sections (parabola, ellipse, and hyperbola) in standard forms, condition for y = mx + c to be a tangent and point (s) of tangency | ||
| 12 | Three Dimensional Geometry | Coordinates of a point in space, the distance between two points |
| Section formula, direction ratios and direction cosines, the angle between two intersecting lines | ||
| Skew lines, the shortest distance between them and its equation | ||
| Equations of a line and a plane in different forms, the intersection of a line and a plane, coplanar lines | ||
| 13 | Vector Algebra | Vectors and scalars, the addition of vectors |
| Components of a vector in two dimensions and three-dimensional space | ||
| Scalar and vector products, scalar and vector triple product | ||
| 14 | Statistics and Probability | Measures of 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: Probability of an event, addition and multiplication theorems of probability, Bayes theorem, probability distribution of a random variate, Bernoulli trials and Binomial distribution. | ||
| 15 | Trigonometry | Trigonometric identities and equations. |
| Trigonometric functions. | ||
| Inverse trigonometric functions and their properties. | ||
| Heights and Distances | ||
| 16 | Mathematical Reasoning | Statements, logical operations and, or, implies, implied by, if and only if |
| Understanding of tautology, contradiction, converse, and Contrapositive | ||
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