Logic

A statement, Negation, Implication, Converse, Contrapositive, Conjunction, Disjunction, Truth Table. Different methods of proof, Principle of Mathematical induction.

Algebra of sets

Set operation, Union, Intersection, Difference, Symmetric difference, Complement, Venn diagram, the Cartesian product of sets, Relation, and functions, Equivalence relation, Kinds of functions and their domain and range, Composite function, Inverse of a function.

Number system 

Real numbers (algebraic and order properties, rational and irrational numbers), Absolute value, Triangle inequality, AM≥ GM, Inequalities(simple cases), Complex numbers, Algebra of complex numbers, Conjugate and square root of a complex number, Cube roots of unity, De Moivre’s theorem with simple application. Permutations and Combinations - simple applications, Binomial theorem for the positive integral index, Identities involving binomial coefficients.

Determinants and matrices

Determinants of the third order, Minors and cofactors, Properties of determinants, Matrices up to third order, Types of matrices, algebra of matrix, adjoint and the inverse of a matrix, Application of determinants and matrices to the solution of linear equations (in three unknowns).

Trigonometry 

Compound angles, Multiple and Submultiple angles, Solution of trigonometric equations, Properties of triangles, Inverse circular function, Sum and product of sine and cosine functions.

Co-ordinate geometry of two dimensions

Straight lines, Pairs of straight lines, Circles, Equations of tangents and normals to a circle, Equations of the parabola, Ellipse and hyperbola in simple forms, their tangents and normals. A condition of tangency. Rectangular and Conjugate hyperbolas.

Coordinate geometry of three dimensions

Distance and Division formulae, Direction cosines and direction ratios, Projection, Angle between two planes, Angle between a line and a plane. The distance of a point from a line and a plane. The equation of a sphere – general equation, Equation of sphere when endpoints of a diameter are given.

Quadratic polynomials 

Roots of the quadratic polynomial, Factorisation of quadratic polynomials, Maximum and minimum values of quadratic polynomials for all real values of the variable, sign of the quadratic polynomial for all real values of the variable, Solution of quadratic inequations. Sequence and Series: Definition, Infinite geometric series, Arithmetic-geometric series, Exponential and Logarithmic series.

Vectors

Fundamentals, Dot and cross product of two vectors, Scalar triple product and vector triple product, Simple application of different products.

Differential calculus 

Concept of limit, Continuity of functions, Derivative of standard Algebraic and Transcendental functions, Derivative of composite functions, functions in parametric form, Implicit differentiation, Successive differentiation (simple cases), Leibnitz theorem, Partial differentiation, Application of Euler’s theorem, Derivative as a rate measure, Increasing and decreasing functions, Maxima and Minima, Indeterminate forms, Geometrical application of derivatives such as finding tangents and normals to plane curves. 

Integral calculus

Standard methods of integration (substitution, by parts, by partial fraction, etc), Integration of rational, irrational functions and trigonometric functions. Definite integrals and properties of definite integrals, Areas under plane curves.

Differential equations

Definition, order, the degree of a differential equation, General and particular solution of a differential equation, Formation of a differential equation, Solution of differential equations by the method of separation of variables, Homogeneous differential equations of first order

and first degree, Linear differential equations of the form dy/dx +p(x)y = q(x), Solutions of differential equations of the form d2y/dx2 =f(x)

Probability and statistics 

Average (mean, median and mode). Dispersion (standard deviation and variance), Definition of probability, Mutually exclusive events, Independent events, Compound events, Conditional probability, Addition theorem.

Number system 

Decimal, binary, octal, hexadecimal numbers and their conversion.