I.S.I. & C.M.I. Entrance 2019 – Mock Tests and Review Classes

From advanced Number Theory to beautiful geometry and combinatorics. Prepare for some seriously interesting mathematics!

Our Classes for I.S.I. & C.M.I. Entrance 2019

Beautiful Mathematics for brilliant minds.

I.S.I. and C.M.I. Entrance program review classes

Take five full-length I.S.I. Entrance Model Test (B.Stat – B.Math)

  1. Attend the model tests online or at Calcutta Offline Center (near Tollygunge)
  2. Attend review sessions on Number Theory, Geometry, Algebra and Combinatorics.
  3. Mock Interview access (if the student qualifies the actual I.S.I. Entrance written test in May)

Access Fee: ₹ 5750

Alternatively you may join Online Classroom Program for I.S.I. Entrance 2020, and 2021.

RMO 2019 Maharashtra and Goa Problem 2 Geometry

RMO 2019 Maharashtra and Goa Problem 2 Geometry

Understand the problemGiven a circle $latex \Gamma$, let $latex P$ be a point in its interior, and let $latex l$ be a line passing through $latex P$. Construct with proof using a ruler and compass, all circles which pass through $latex P$, are tangent to $latex...

Algebra, Austria MO 2016, Problem 4

Algebra, Austria MO 2016, Problem 4

This algebra problem is an elegant application of culminating the ideas of polynomials to give a simple proof of an inequality. Try with our sequential hints.

Inequality, Israel MO 2018, Problem 3

Inequality, Israel MO 2018, Problem 3

This problem is a basic application of triangle inequality along with getting to manipulate the modulus function efficently. Try with our sequential hints.

Algebra, Germany MO 2019, Problem 6

Algebra, Germany MO 2019, Problem 6

This problem is a beautiful application of algebraic manipulations, ideas of symmetry, and vieta’s formula in polynomials. Try with our sequential hints.

Combinatorics, Israel MO 2014, Problem 4

Combinatorics, Israel MO 2014, Problem 4

This is a bashing problem of combinatorics that will require the idea of patiently solving out the cases with intricate details and patience. Try with our sequential hints.

Number Theory – Germany MO 2019, Problem 4

Number Theory – Germany MO 2019, Problem 4

This problem is a very basic, tricky and intuitive application resulting in the solutions of a diophantine equation and unique representation of a number. Try with our sequential hints.

Polynomial, Vietnam MO 2014 Problem 2

Polynomial, Vietnam MO 2014 Problem 2

This problem is an intermediate application of the polynomials and invoking a cute number theoritic argument to make it a good problem to try with our sequential hints.

An Hour of Beautiful Proofs

Every week we dedicate an hour to Beautiful Mathematics - the Mathematics that shows us how Beautiful is our Intellect. This week, I decided to do three beautiful proofs in this one-hour session... Proof of Fermat's Little Theorem ( via Combinatorics )It uses...

Inequality – In Equality

Inequality – In Equality

This article aims to give you a brief overview of Inequality, which can be served as an introduction to this beautiful sub-topic of Algebra. This article doesn't aim to give a list of formulas and methodologies stuffed in single baggage, rather it is specifically...

AM GM inequality in ISI Entrance

AM GM inequality in ISI Entrance

Arithmetic Mean and Geometric Mean inequality form a foundational principle. This problem from I.S.I. Entrance is an application of that.

How to solve an Olympiad Problem (Number Theory)?

Suppose you are given a Number Theory Olympiad Problem. You have no idea how to proceed. Totally stuck! What to do? This post will help you to atleast start with something. You have something to proceed. But as we share in our classes, how to proceed towards any...

The best exponent for an inequality

The best exponent for an inequality

Understand the problemLet be positive real numbers such that .Find with proof that is the minimal value for which the following inequality holds:Albania IMO TST 2013 Inequalities Medium Inequalities by BJ Venkatachala Start with hintsDo you really need a hint? Try...

A functional inequation

A functional inequation

Understand the problemFind all functions such thatholds for all . Benelux MO 2013 Functional Equations Easy Functional Equations by BJ Venkatachala Start with hintsDo you really need a hint? Try it first!Note that the RHS does not contain $latex y$. Thus it should be...

Mathematical Circles Inequality Problem

Mathematical Circles Inequality Problem

A beautiful inequality problem from Mathematical Circles Russian Experience . we provide sequential hints . key idea is to use arithmetic mean , geometric mean inequality.