# 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)

- Attend the model tests
**online or at Calcutta**Offline Center (near Tollygunge) - Attend review sessions on Number Theory, Geometry, Algebra and Combinatorics.
**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

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...

## What are some mind-blowing facts about mathematics?

Mathematics is all about visualisation and how to imply them in you day to day life. Maths is something that we all will need at every step of your life

## Number Theory, Ireland MO 2018, Problem 9

This problem in number theory is an elegant applications of the ideas of quadratic and cubic residues of a number. Try with our sequential hints.

## Number Theory, France IMO TST 2012, Problem 3

This problem is an advanced number theory problem using the ideas of lifting the exponents. Try with our sequential hints.

## 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.

## Number Theory, Cyprus IMO TST 2018, Problem 1

This problem is a beautiful and simple application of the ideas of inequality and bounds in number theory. Try with our sequential hints.

## Number Theory, South Africa 2019, Problem 6

This problem in number theory is an elegant applciations of the modulo technique used in the diophantine equations. Try with our sequential hints

## Who was the best mathematician in the initial era?

Well comparision between mathematicians was and is and will never be possible. I personally think that Gauss is the best mathematician of the initial era.

## Number Theory, Korea Junior MO 2015, Problem 7

This problem in number theory is an elegant application of the ideas of the proof of infinitude of primes from Korea. Try with our sequential hints.

## 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.

## Number Theory, Greece MO 2019, Problem 3

This problem is a beautiful application of prime factorization theorem, and reveal how important it is. Try with our sequential hints.

## Why is the number zero most important in mathematics?

The number 0, looks very ordinary but has a huge role in every field of mathematics. Here is the reason why it has a huge role in mathematics.

## How did Aryabhatta invent zero? How did he get this idea? Why did he give zero an oval shape?

We all know about the famous number 0. Our Indian mathematician Aryabhatta has a mind cracking contribution in the inversion of 0.

## 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.

## Geometry, Israel MO 2019, Problem 3

This problem is cute and intermediate application of the basic geometry principles. Try out this problem with our sequential hints.

## What are some facts about Leonardo Fibonacci and the Fibonacci sequence that everyone wants to know?

So we all know about the famous Fibanacci Sequence but , I found some really interesting facts about this sequence about it’s application.

## 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

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

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.

## What are the first three Ramanujan numbers?

So we all know about Hardy-Ramanujan Number 1729. I found some extensions of these type of number we are really mind cracking and amazing.

## Number Theory – Italy MO 2019, Problem 2

This problem is an intermediate application of basic number theoritical principles. from Italy MO Solve this problem with the help of Sequential Hints.

## Number Theory – Dutch MO 2015, Problem 4

This problem is a very simple application of the principle of parity and divisibilty in elementary number theory. Try out with our sequential hints.

## Who was the first woman mathematician in India?

Shuakuntala Devi the first Indian woman mathematician who was also known as human calculator has given us mind cracking quick multiplication.

## Who is/was the most mysterious mathematician?

I found this question in Quora , so I started research on Srinivasa Ramanujan. Came across his mind cracking results and his other works.

## What is the 30th term in the Fibonacci series?

We all know about this sequence , but is this really possible to find the 30th term with just adding the previous trems in order to get such large terms?

## What’s the speciality of the number ‘5040’?

I have posted the answer on quora of this question. The number 5040 has many special number theoretic aspects and I have listed all of this one by one.

## Inequality Module for I.S.I. Entrance and Math Olympiad

Inequality module for I.S.I. Entrance and Math Olympiad Program begins on 13th October, 2019. Taught by Srijit Mukherjee (I.S.I. Kolkata)

## 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...

## Polynomial Functional Equation – Random Olympiad Problem

This beautiful application of Functional Equation is related to the concepts of Polynomials. Sequential hints are given to work out the problem and to revisit the concepts accordingly.

## Number Theory – Croatia MO 2005 Problem 11.1

This beautiful application from Croatia MO 2005, Problem 11.1 is based on the concepts of Number Theory. Sequential hints are given to work the problem accordingly.

## 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...

## Sum based on Probability – ISI MMA 2018 Question 24

This is an interesting and cute sum based on the concept of Arithematic and Geometric series .The problem is to find a solution of a probability sum.

## System of the linear equation: ISI MMA 2018 Question 11

This is a cute and interesting problem based on System of the linear equation in linear algebra. Here we are finding the determinant value .

## 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...

## How are Bezout’s Theorem and Inverse related? – Number Theory

The inverse of a number (modulo some specific integer) is inherently related to GCD (Greatest Common Divisor). Euclidean Algorithm and Bezout’s Theorem forms the bridge between these ideas. We explore these beautiful ideas.

## How to use Invariance in Combinatorics – ISI Entrance Problem

Invariance is a fundamental phenomenon in mathematics. In this combinatorics problem from ISI Entrance, we discuss how to use invariance.

## 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

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

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