Junior Data Science Olympiad is suitable for students of grade 9 and above, interested in Data Science. Check out the resources for the Junior Data Science Olympiad in this post.
Mahalanobis Olympiad is suitable for College and University Students, interested in Statistics and Mathematics. Check out the resources for the Mahalanobis Olympiad in this post.
The following topics in number theory are useful for the Senior round:
Bezout’s Theorem and Euclidean Algorithm
Theory of congruence
Number Theoretic Functions
Theorems of Fermat, Euler, and Wilson
Pythagorean TriplesChinese Remainder Theorem
Here is an example of a Number Theory problem that may appear in Seinor Bose Olympiad:
Suppose $a, b, c$ are the side lengths of an integer sided right-angled triangle such that $GCD(a, b, c) = 1$. If $c$ is the length of the hypotenuse, then what is the largest value of the $GCD (b, c)$?
Key idea: Pythagorean Triples
Geometry
The following topics in geometry are useful for the Senior Bose Olympiad round:
Synthetic geometry of triangles, circles
Barycentric Coordinates
Miquel Point Configuration
Translation
Rotation
Screw Similarity
Here is an example of a geometry problem that may appear in the Senior Bose Olympiad:
Suppose the river Basumoti is 25 meters wide and its banks are parallel straight lines. Sudip's house 10 meters away from the bank of Basumoti. Apu's house is on the other side of the river, 15 meter away from the bank. If you are allowed to construct a bridge perpendicular to the banks of Basumoti, what is the shortest distance from Sudip to Apu's house.
Key idea: Reflection
Algebra
The following topics in Algebra are useful for Intermediate Bose Olympiad:
Screw similarity, Cyclotomic Polynomials using Complex Numbers
AM, GM, and Cauchy Schwarz Inequality
Rational Root Theorem, Remainder Theorem
Roots of a polynomial
Here is an example of an algebra problem that may appear in Senior Bose Olympiad:
The following sum is greater than which integer: $$ \frac{2}{3} + \frac{3}{4} \cdots + \frac{2019}{2020} + \frac{2020}{2} $$
(A) $2019$ (B) $2020$ (C) $2021$ (D) $2022$
Key idea: inequality
Bose Olympiad Previous Year Paper
Reference Books
Elementary Number Theory by David Burton
Principles and Techniques in Combinatorics by Chen Chuan Chong and Koh Khee Meng
Polynomials by Barbeau
Secrets in Inequalities by Pham Kim Hung
Complex Numbers from A to Z by Titu Andreescu
Challenges and Thrills of Pre College Mathematics
Lines and Curves by Vasiliyev (something else)
Geometric Transformation by Yaglom
Notes by Yufei Zhao
Trigonometric Delights by El Maor
Trigonometry by S.L. Loney
101 Problems in Trigonometry by Titu Andreescu
Bose Olympiad Intermediate - Resources
Bose Olympiad Intermediate is suitable for kids in Grade 5, 6, and 7.
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
Bose Olympiad Previous Year Paper
Reference Books
Mathematical Circles by Fomin
Lines and Curves by Vasiliyev
Challenges and Thrills of Pre College Mathematics
Bose Olympiad Junior Level: Resources
Bose Olympiad Junior is suitable for kids in Grade 1, 2, 3 and 4.
Basic skills of addition, subtraction and multiplication and division will be sufficient for attending arithmetic problems. Fundamental ideas about place-value system and ratios could be useful for Mains level.
Here is an example of an arithmetic problem that may appear in Bose Olympiad:
Suppose Ajit has 35 cheese sticks. Ajit makes Red Packs containing 3 sticks in each packet. Then Ajit makes Green packs containing 3 Red Packs each. Finally he makes Blue packs, each containing 3 Green Packs. How many unpacked sticks are there at the end of this process?
Key idea: Place Value System
Geometry
A basic understanding is of shapes like triangle, circle, square is sufficient for prelims. Locus (path traced out by a moving point) is another key geometry topic that may appear. At the Mains level, the student may need notions of Area and Perimeter.
Here is an example of an geometry problem that may appear in Bose Olympiad:
Ayesha is running on a field such that his distances from two trees A and B are always equal. That is the distance of the position of Manoj from tree A is equal to the distance of the position of Manoj from tree B at any point of time. Then what is the shape of the path along which Ayesha is running?
Key idea: Locus
Mathematical Puzzles
Mathematical puzzles may involve parallel channels, back tracking, greedy algorithm and recursive logic.
Here is an example of an puzzle problem that may appear in Bose Olympiad:
2019248 teams are playing in a knockout galactic football tournament. In this tournament no match ends in a draw and if you lose a match then you are out of the tournament. In the first round of the tournament the teams are paired up. In each subsequent round if even number of teams remain then they are again paired up, if odd number of teams remain then the highest scoring team is allowed to rest and directly go to the next round. How many matches are played in this tournament?