Watch the video to learn more about opportunities after Mathematical Olympiads in India, the United States and other countries.
Watch the video to learn more about opportunities after Mathematical Olympiads in India, the United States and other countries.
reading a book written by a true master is like learning from him or her directly. It is an outstanding opportunity that none of us should miss. Here are some of those walks with the masters, that has transformed my life and the way I do mathematics. You may use this list of beautiful mathematics books to stay inspired.
If you are preparing for Mathematics Olympiads, ISI-CMI Entrances or challenging College level entrances then this article is for you. We will describe the no short-cut approach of Cheenta Programs and how you can use them.
Dear parent, One of the key contributions of modern mathematics is its tryst with infinity. As parents and teachers we can initiate thought provoking communication with our children using infinity. Consider the following set: N = {1, 2, 3, … } Notice that N contains infinitely many elements. Take a subset of N that consists […]
‘Teachers for Tomorrow’ is a unique program for parents and teachers who wish to take their kids / students an extra mile in mathematical training. Cheenta uses modern tools (such as Latex, GeoGebra, STACK etc.) to deliver its courses. It also uses carefully experimented teaching methods developed in USSR, United States, and India. We firmly believe that these tools and methods are very valuable in stimulating creativity in young mind.
Philosophical Remarks When did we first fall in love with mathematics? For me, it was in class 6. My father exposed me to a problem from Euclidean geometry. We were traveling in Kausani. After days of frustration and failed attempts, I could put together the ‘reason’ that made ‘everything fit together perfectly’. The problem was […]
In this instructional video from Math Olympiad Geometry of AMC, IOQM, ISI-CMI , we delve into the intriguing concept of maximizing area while constrained by a fixed perimeter, employing rectangles and squares as our illustrative models. We explore how subtle adjustments in a rectangle's dimensions can yield substantial variations in its enclosed area, offering a tangible understanding of this fundamental geometric principle.
A problem and solution from ISI BStat BMath Entrance 2015, using the concept of AM - GM Inequality from Algebra
In the world of fake olympiads and thousands of contests, it is important to select the right ones and focus on them. Children take hundreds of tests these days under peer pressure. No good comes out this rat race. We urge kids to learn deep mathematical science and prepare for 1 or 2 real contests […]
Try this Algebra challenge for Math Olympiad and ISI-CMI entrance
American Math Competition 8 (AMC 8) 2024 Problems, Solutions, Concepts and discussions.
PART - I Problem 1 In a convex polygon, the number of diagonals is 23 times the number of its sides. How many sides does it have?(a) 46(b) 49(c) 66(d) 69Answer: B Problem 2 What is the smallest real number a for which the function \(f(x)=4 x^2-12 x-5+2a\) will always be nonnegative for all real […]
PART I Problem 1 The measures of the angles of a pentagon form an arithmetic sequence with common difference \(15^{\circ}\). Find the measure of the largest angle. (a) \(78^{\circ}\)(b) \(103^{\circ}\)(c) \(138^{\circ}\)(d) \(153^{\circ}\) Answer : C Problem 2 If \(x-y=4\) and \(x^2+y^2=5\), find the value of \(x^3-y^3\). (a) -24(b) -2(c) 2(d) 8 Answer : B Problem […]
High school research projects and journals that accept papers from high school students in mathematical science.
Part I Problem 1 Let \(XZ\) be a diameter of circle \(\omega\). Let Y be a point on \(XZ\) such that \(XY=7\) and \(YZ=1\). Let W be a point on \(\omega\) such that \(WY\) is perpendicular to \(XZ\). What is the square of the length of the line segment \(WY\) ? (a) 7(b) 8(c) 10(d) […]
PART I Problem 1 Answer: A Problem 2 Answer: D Problem 3 Answer: D Problem 4 Answer: A Problem 5 Answer: D Problem 6 Answer: D Problem 7 Answer: D Problem 8 Answer: C Problem 9 Answer: B Problem 10 For positive real numbers a and b, the minimum value of\( \left18 a+\frac{1}{3 b}\right\left3 b+\frac{1}{8 […]
Problem 1. Let $x_1, x_2, x_3, \ldots$ be a sequence of positive integers defined as follows: $x_1=1$ and for each $n \geqslant 1$ we have $$x_{n+1}=x_n+\left\lfloor\sqrt{x_n}\right\rfloor$$ Determine all positive integers $m$ for which $x_n=m^2$ for some $n \geqslant 1$. (Here $\lfloor x\rfloor$ denotes the greatest integer less or equal to $x$ for every real number […]
1 What is the value of the following expression? 1+2-3+4+5-6+7+8-9+10+11-12 A. 18 B. 21 C. 24 D. 27 E. 30 Answer - A 2 In the array shown below, three 3 s are surrounded by 2 s, which are in turn surrounded by a border of 1 s . What is the sum of the […]
Problem 1What is the value of $\frac{(2112-2021)^{2}}{169}$ ?(A) 7(B) 21(C) 49(D) 64(E) 91 Answer: (C) 49 Problem 2Menkara has a $4 \times 6$ index card. If she shortens the length of one side of this card by 1 inch, the card would have area 18 square inches. What would the area of the card be […]
Problem 1 What value of $\boldsymbol{x}$ satisfies $$x-\frac{3}{4}=\frac{5}{12}-\frac{1}{3} ?$$ (A) $-\frac{2}{3}$(B) $\frac{7}{36}$(C) $\frac{7}{12}$(D) $\frac{2}{3}$(E) $\frac{5}{6}$ Answer: (E) $\frac{5}{6}$ Problem 2 The numbers $3,5,7, a$ and $b$ have an average (arithmetic mean) of 15 . What is the average of $a$ and $b$ ?(A) 0(B) 15(C) 30(D) 45(E) 60 Answer: (C) 30 Problem 3 Assuming $a […]
Problem 1 (A) 0(B) 1(C) 2(D) 3(E) 4 Answer: (C) 2 Problem 2What is the hundreds digit of $(20!-15!)$ ?(A) 0(B) 1(C) 2(D) 4(E) 5 Answer: (A) 0 Problem 3Ana and Bonita were born on the same date in different years, $n$ years apart. Last year Ana was 5 times as old as Bonita. This […]
Problem 1What is the value of $9901 \cdot 101-99 \cdot 10101$ ?(A) 2(B) 20(C) 200(D) 202(E) 2020 Answer: (A) 2 Problem 2A model used to estimate the time it will take to hike to the top of the mountain on a trail is of the form $T=a L+b G$, where $a$ and $b$ are constants, […]
Problem 1 What is the value of $\frac{(2112-2021)^{2}}{169}$ ?(A) 7(B) 21(C) 49(D) 64(E) 91 Answer: (C) 49 Problem 2 Menkara has a $4 \times 6$ index card. If she shortens the length of one side of this card by 1 inch, the card would have area 18 square inches. What would the area of the […]
Problem 1 Andy and Betsy both live in Mathville. Andy leaves Mathville on his bicycle at $1: 30$, traveling due north at a steady 8 miles per hour. Betsy leaves on her bicycle from the same point at $2: 30$, traveling due east at a steady 12 miles per hour. At what time will they […]
The AMC 8 (2005) is a 40-minute, 25-question multiple-choice contest for middle-school students (Grade 8 and below).
It tests problem-solving in arithmetic, algebra, geometry, counting, and probability (not complex calculus).
মানচিত্র আঁকছিলাম। রাস্তা গুলো সোজা সোজা। উত্তর, দক্ষিণ, পুব, পশ্চিমে যাওয়া যায়। এক ধাপ ডাইনে গেলে, সঙ্গে সঙ্গে এক ধাপ বাঁয়ে ফেরার নিয়ম নেই। (তাহলে আর ডাইনে গেলাম কেন!) তেমনি একধাপ উত্তরে গেলে, সঙ্গে সঙ্গে একধাপ দক্ষিণে ফেরাও মানা।
মানচিত্র আঁকতে আঁকতে দেখলাম এক উদ্ভট দেশ তৈরি হচ্ছে। সে দেশের প্রতি চৌমাথায় অসীম সব রাস্তা। সে সব রাস্তা আবার একে অপরের সঙ্গে তেমন দেখা সাক্ষাৎ করে না। এ হেন দেশের সীমান্ত নিয়ে আমাদের যত মাথা ব্যাথা। খুঁজতে খুঁজতে বেড়িয়ে পড়ল এক আজব কিস্যা!
সীমান্তে একলা দাঁড়িয়ে আছেন ক্যান্টর।
বাকি আড্ডা ভিডিও তে।
লিনিয়ার বীজগণিত নিয়ে আমরা একটি ভিডিও সিরিজ তৈরী করছি। 'চিন্তা'-র কলেজ গণিত প্রোগ্রামে যদিও প্রধানত ইংলিশে আলোচনা হয়, আমরা চেষ্টা করি বিভিন্ন আঞ্চলিক ভাষা গুলোতে কিছু আলোচনা করতে। পরবর্তী আলোচনা গুলো খুব আসছে এই পাতায়।
গ্রুপ থিয়োরি নিয়ে বাংলায় একটা কোর্স তৈরি করার ইচ্ছা বহুদিনের। এই ভিডিও সিরিজটা তারই শুরুয়াদ। আমরা প্রচুর ইংরেজি শব্দ ব্যাবহার করব। তারই সাথে চলতি বাংলা থেকে কিছু ছবি, কিছু কথা, কিছু ধ্বনি আনিত হবে। গ্রুপ কয় কাহারে? আমরা 'ডেফিনেশন' দিয়ে শুরু করতে পারি। কিন্তু তার বদলে শুরু করছি একটা বেশ কৌতূহলোদ্দীপক উদাহরণ দিয়ে। ভিডিওটা দেখার […]
সংখ্যাতত্ত্ব লেখাটিতে আমরা Pythagorean triplet বা পিথাগোরীয়ান ত্রয়ী নিয়ে আলোচনা করা হয়েছে ।
দৈনন্দিন জীবনে বস্তু গোনবার পদ্ধতি খুব কাজের জিনিস । এই পোস্ট থেকে একটি পদ্ধতি সম্বন্ধে জানব যা ডিরিশিলিটের বাক্স নীতি বা ইংরেজিতে Pigeonhole principle বলে।
A post on homological triangles... topic of our math camp August 2014 (in Scotland)