Bose Olympiad Intermediate is suitable for kids in Grade 5, 6, and 7. There are two levels of this olympiad:
- Prelims
- Mains
Curriculum
- Elementary Number Theory
- Counting Principles
- Algebra
- Geometry
Number Theory
The following topics in number theory are useful for the Intermediate round:
- Primes and Composites
- Arithmetic of Remainders
- Divisibility
- Number Theoretic Functions
Here is an example of a Number Theory problem that may appear in Bose Olympiad:
How many positive integer solutions are there of the equation $x^3 – y^3 = 121$ ?
Key idea: Primes
Geometry
The following topics in geometry are useful for the Intermediate round:
- Locus problems
- Geometry of lines (angles, parallels)
- Geometry of triangles (centroid, circumcenter, orthocenter)
- Geometry of circles (tangents, chords, cyclic quadrilaterals)
- Conic sections (ellipse, parabola, hyperbola).
- Triangular Inequality
Here is an example of an geometry problem that may appear in Bose Olympiad:
There are two trees A and B on a field such that distance between A and B is 5 meter. Ayesha is continuously running on the field such that sum of her distances from A and B is always 5 meters. How many times does she visit the midpoint of A and B?
Key idea: Locus
Algebra
The following topics in Algebra are useful for Intermediate Bose Olympiad:
- Factorization
- Linear equations
- Quadratic Equations
- Inequality
Here is an example of an algebra problem that may appear in Bose Olympiad:
Consider all rectangles of perimeter 40 cm. What is the largest area that can be enclosed by any such rectangle?
Key idea: inequality
Reference Books
- Mathematical Circles by Fomin
- Lines and Curves by Vasiliyev
- Challenges and Thrills of Pre College Mathematics
