Syllabus & Modality of the Olympiad

The time allotted for the Olympiad is 90 minutes. There will be two types of problems: broad & short. There will be 6 broad problems each carrying 10 marks and 8 short problems each carrying 5 marks. All questions are to be answered. Full marks of the Olympiad will be 100.

The problems will be set from among the topics comprising subject areas as listed below:-

1. Vector & Analytic Geometry:

Vectors in two and in three dimensions. Scalar product. Vector product. Applications to plane geometry. General equation of second degree: Conic section. Coordinates in three dimensions: Direction cosines. Planes and straight lines in three dimensions.

2. Algebra:

Complex numbers. De Moivre's theorem and applications. Polynomials and algebraic equations. Summation of algebraic and trigonometric series. Basic knowledge of groups, rings and fields. Elementary number theory. Vector spaces. Linear independence: Basis and Dimension. Linear transformations. Linear equations, Matrices and determinants.

3. Calculus of One Variable:

Functions and their graphs, limits, continuity, differentiation and application, integration and applications, fundamental theorems and applications. Convergence of infinite sequences and series.

4. Calculus of Several Variable:

Differentiation and integration of vector functions. Line, surface and volume integrals. Cylindrical polar and spherical polar coordinates. Theorems of Green, Gauss, Stokes and their applications.

5. Differential Equations:

Applications of 1st and 2nd order differential equations. Special functions.

N.B. Use of any type of calculator, mobile phone and laptop is not permitted during the exam period.