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 […]
Access Australian Mathematics Competition past year paper of 2013 year 5 - 6 Upper Primary to sharpen your problem-solving skills.
Access Australian Mathematics Competition past year paper of 2012 year 5 - 6 Senior to sharpen your problem-solving skills.
Access Australian Mathematics Competition past year paper of 2011 year 5 - 6 Upper Primary to sharpen your problem-solving skills.
Access Australian Mathematics Competition past year paper of 2010 year 5 - 6 Upper Primary to sharpen your problem-solving skills.
Access Australian Mathematics Competition past year paper of 2009 year 5 - 6 Upper Primary to sharpen your problem-solving skills.
Access Australian Mathematics Competition past year paper of 2008 year 5 - 6 Upper Primary to sharpen your problem-solving skills.
Dive into the discussion of the solution to Problem 17 from the 2023 AMC (Australian Mathematics Competition), Intermediate Year category.
Dive into the discussion of the solution to Problem 27 from the 2023 AMC (Australian Mathematics Competition), Junior Year category.
American Math Competition 8 (AMC 8) 2024 Problems, Solutions, Concepts and discussions.
Dive into the discussion of the solution to Problem 28
from the 2023 AMC (Australian Mathematics Competition), upper primary category.