Sine rule is an important rule relating to the sides and angles of any triangle. Here is a Subjective problem no. 120 from TOMATO. Try it. Problem: Sine Rule and Triangle (i) If $ A + B +C = n \pi $ and $ s=2 $, show that $ \sin 2A + \sin 2B + […]
Sine rule is an important rule relating to the sides and angles of any triangle. Here is a Subjective problem no. 120 from TOMATO. Try it. Problem: Sine Rule and Triangle (i) If $ A + B +C = n \pi $ and $ s=2 $, show that $ \sin 2A + \sin 2B + […]
This is a subjective problem from TOMATO based on Graphing integer value function. Problem: Graphing integer value function Let [x] denote the largest integer (positive, negative or zero) less than or equal to x. Let $ y= f(x) = [x] + \sqrt{x - [x]} $ and $ s=2 $ be defined for all real numbers […]
সংখ্যাতত্ত্ব লেখাটিতে আমরা Pythagorean triplet বা পিথাগোরীয়ান ত্রয়ী নিয়ে আলোচনা করা হয়েছে ।
Problem: Problem on Asteroid Let PQ be a line segment of a fixed length L with it's two ends P and Q sliding along the X axis and Y-axis respectively. Complete the rectangle OPRQ where O is the origin. Show that the locus of the foot of the perpendicular drawn from R on PQ is […]
This is a Test of Mathematics Solution Subjective 128 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Problem Draw the graph (on plain paper) of f(x)= min { |x| -1, |x-1| - […]
Try this Arithmetic Mean - Geometric Mean Subjective Problem number 82 from TOMATO. Problem: Arithmetic Mean - Geometric Mean Let $ {a, b, c, d}$ be positive real numbers such that $ {abcd = 1}$. Show that, $ {\displaystyle{(1 + a)(1 + b)(1 + c)(1 + d) {\ge} {16}}}$ Solution: $ {{\sum{a}} = a + […]
This is a subjective problem from TOMATO based on inequality. Problem: Inequality Problem If $ {\displaystyle{a}}$ and $latex {\displaystyle{b}}$ are positive real numbers such that, $ {\displaystyle{a + b = 1}}$, prove that,$ {\displaystyle{\left(a + {\frac{1}{a}}\right)^2 + \left(b + {\frac{1}{b}}\right)^2 {\ge} {\frac{25}{2}}}}$. Solution: $ {\displaystyle{\left(a + {\frac{1}{a}}\right)^2 + \left(b + {\frac{1}{b}}\right)^2 {\ge} {\frac{25}{2}}}}$$ {\displaystyle{\Leftrightarrow}}$ $ […]
This is a Test of Mathematics Solution Subjective 80 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem If $ {a, b, c}$ […]
This is a collection of some revision notes. They include topics discussed in first three sessions of Combinatorics Course at Cheenta (Faculty: Ashani Dasgupta). combinatorics 1(work sheet) Study of symmetry in geometry is greatly facilitated by combinatorial methods There are 6 symmetries of an equilateral triangle (=3! permutations of 3 things) There are 8 symmetries […]
Try this beautiful Geometry Problem on Equilateral Triangle from AMC-10A, 2010.You may use sequential hints to solve the problem.
Try this beautiful problem from PRMO, 2018 based on Geometry. You may use sequential hints to solve the problem.
Try this beautiful problem from TOMATO useful for ISI B.Stat Entrance based on Quadratic Equation. You may use sequential hints to solve the problem.
Try this beautiful problem from Geometry: Hexagon from AMC-10A, 2010. You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1992 based on Digits and Rationals.
Try this beautiful problem from the Pre-RMO, 2017 based on GP and 2-digit number. You may use sequential hints to solve the problem.
Try this beautiful problem from the Pre-RMO, 2017 based on Altitudes of triangle. You may use sequential hints to solve the problem.
Try this beautiful problem from Singapore Mathematics Olympiad, SMO, 2012 based on Probability. You may use sequential hints to solve the problem.
Try this beautiful problem from Algebra, based on Sum of digits from AMC-10A, 2020. You may use sequential hints to solve the problem
Try this beautiful problem from Number theory based on Integer from AMC-10A, 2020. You may use sequential hints to solve the problem.
Author: Kazi Abu Rousan Here there is $\pi$, there is circle. Today's blog will be a bit different. This will not discuss any formula or any proof, rather it will just contain a python program to compare a $\pi$ formula given by Leibniz and a one discovered by me (blush). How does Leibniz formula looks […]
Author: Kazi Abu Rousan Bottomless wonders spring from simple rules, which are repeated without end. Benoit Mandelbrot Today, we will be discussing the idea for making a simple Mandelbrot Set using python's Matplotlib. This blog will not show you some crazy color scheme or such. But rather the most simple thing you can make from […]
Try this beautiful problem from the Pre-RMO, 2019 based on Smallest Positive Integer. You may use sequential hints to solve the problem.
Author: Kazi Abu Rousan Mathematics is not yet ready for such problems. Paul Erdos Introduction A problem in maths which is too tempting and seems very easy but is actually a hidden demon is this Collatz Conjecture. This problems seems so easy that it you will be tempted, but remember it is infamous for eating […]
What is Mathcounts? MATHCOUNTS is a national middle school mathematics contest held in different places in the U.S. states and territories. It is established in 1983, which provides engaging mathematics programs to the US middle school students of different ability levels to grow their confidence and improve the attitudes about mathematics and problem solving. Who are the […]
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.