Sets, relations and functions - sets and their representation, union, intersection and complement of sets, algebraic properties, power sets, types of relations, equivalence relations, functions, one-one, into and onto functions, composition of functions

Complex number and quadratic equations - complex numbers as ordered pair of reals, a + ib representation, representation in a plane, Argand diagram, Algebra of complex numbers, Modulus, argument, square root, triangle inequality, quadratic equations and its roots, roots and co-efficients, nature of roots, formation of equation with given roots

Matrices and determinants - Algebra, types, order, properties of determinants, evaluation and area of triangles using determinants, adjoint and evaluation of inverse, elementary transformations, tests of consistency, solution of simultaneous equations in two or three variables

Permutations and Combinations - Principle of counting, Arrangement and selection, Meaning of P(N,r) and C(N, r)

Mathematical induction - Simple application of the principle

Binomial theorem - Positive integral index application. general and middle terms, properties of coefficients

Sequences and series - AP, GP, Insertion of arithmetic and geometric means, relations between AM and GM, Sum upto n terms, Arithmetico-geometric progression

Limit, continuity and differentiability - real-valued functions, algebra of functions, polynomials, rational, trigonometric, log and exponential functions, graphs of simple functions, limits, differentiation of sum, difference, product and quotient of two functions, differentiation of trigonometric, log, exponential functions, composite and implicit functions, Rolle’s and Lagrange’s mean value theorems, Applications of derivatives, Increasing and decreasing functions, maxima and minima, tangents and normals

Integral calculus - Fundamental integrals, integration by substitution, by parts and by partial fractions, using trigonometric identities, as limit of a sum, fundamental theorem of calculus, definite integrals, areas of regions bounded by simple curves

Differential equations - Ordinary DE, order and degree, formation and solution of DEs, Separation of variables, homogeneous and linear type of DEs.

Co-ordinate geometry - Cartesian system of rectangular co-ordinates in a plane, distance formula, section formula, locus and its equation, translation of axes, 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, 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 family of lines passing through the point of intersection of two lines, circles and 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 end points 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.

Three Dimensional Geometry - Coordinates of a point in space, distance between two points, section formula, direction ratios and direction cosines, 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, intersection of a line and a plane, coplanar lines.

Vector Algebra - Vectors and scalars, addition of vectors, components of a vector in two dimensions and three dimensional space, scalar and vector products, scalar and vector triple product.

Statistics and probability - Calculation of mean, median, mode of grouped and ungrouped data. Calculation of standard deviation, variance and mean deviation for grouped and ungrouped data, Probability of an event, addition and multiplication theorems of probability, Baye’s theorem, probability distribution of a random variate, Bernoulli trials and Binomial distribution.

Trigonometry - Trigonometrical identities and equations. Trigonometrical functions. Inverse trigonometrical functions and their properties. Heights and Distances.

Mathematical reasoning - Statements, logical operations and, or, implies, implied by, if and only if. Understanding of tautology, contradiction, converse and contrapositive

Out of both more important is coordinate geometry which includes an ellipse, hyperbola, parabola, circles, straight lines, etc. JEE asks a lot of questions on coordinate geometry out of which many are formula based.
Coordinate geometry and calculus together make up 50% of the paper.

Conic sections – Knowing the formulas well will help you. The parametric form is one of the most useful tools in solving problems of conics.

Vector Algebra – Knowing how to visualize the situation will be useful. The concepts of vector and scalar triple products are most scoring.

All the very best and good luck.