- Types of relations: reflexive, symmetric, transitive and equivalence relations.
- One to one and onto functions, composite functions, inverse of a function and Binary operations

- Definition, range, domain, principal value branch
- Graphs of inverse trigonometric functions
- Elementary properties of inverse trigonometric functions

- Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices
- Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication
- Noncommutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2).Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries)

- Division of a line segment in a given ratio (internally).
- Tangent to a circle from a point outside it.
- Construction of a triangle similar to a given triangle.

- Simple and believable problems on heights and distances.
- Problems should not involve more than two right triangles.
- Angles of elevation / depression should be only 30°, 45°, 60°.

- Simple and believable problems on heights and distances.
- Problems should not involve more than two right triangles.
- Angles of elevation / depression should be only 30°, 45°, 60°.

- Integration as inverse process of differentiation
- Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them
- Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof)
- Basic properties of definite integrals and evaluation of definite integrals

- Applications in finding the area under simple curves, especially lines, circles/parabolas/ellipses (in standard form only)
- Area between any of the two above said curves (the region should be clearly identifiable)

- Definition, order and degree, general and particular solutions of a differential equation
- Formation of differential equation whose general solution is given
- Solution of differential equations by method of separation of variables solutions of homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type:
- dy/dx + py = q, where p and q are functions of x or constants
- dx/dy + px = q, where p and q are functions of y or constants

- Vectors and scalars, magnitude and direction of a vector
- Direction cosines and direction ratios of a vector
- Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio
- Definition, Geometrical Interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors, scalar triple product of vectors

- Direction cosines and direction ratios of a line joining two points.
- Cartesian equation and vector equation of a line, coplanar and skew lines, shortest distance between two lines. Cartesian and vector equation of a plane
- Angle between (i) two lines, (ii) two planes, (iii) a line and a plane
- Distance of a point from a plane

- Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, mathematical formulation of L.P. problems
- Graphical method of solution for problems in two variables, feasible and infeasible regions (bounded and unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints)

- Conditional probability, multiplication theorem on probability
- Independent events, total probability, Baye’s theorem
- Random variable and its probability distribution, mean and variance of random variable
- Repeated independent (Bernoulli) trials and Binomial distribution