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November 2, 2020

Bose Olympiad Intermediate - Resources

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

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