American Math Competition 8 (AMC 8) 2024 Problems, Solutions, Concepts and discussions.
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 $\mathbb{N}$ be the set of all positive integers and $S=\left\{(a, b, c, d) \in \mathbb{N}^4: a^2+b^2+c^2=d^2\right\}$. Find the largest positive integer $m$ such that $m$ divides $a b c d$ for all $(a, b, c, d) \in S$. Solution Notice that $(2, 2, 1, 3)\in S\Rightarrow m$ is a divisor of $12 […]
Try this ISI BStat - BMath Entrance 2023, Problem no. 2 with hints and final solution.
In the math world, a unique challenge emerges, combining algebra and number theory. The goal: show that specific equation solutions aren't simple fractions. We reveal a key insight about b² - 4ac: it's always a distinct odd perfect square. Using "parity check," No matter the numbers, the left side remains even, while the right side stays odd. The result: these solutions differ from simple fractions, highlighting math's power in problem-solving.
In 2023, the following Cheenta students are successful for Indian Statistical Institute's B.Stat Entrance and Chennai Mathematical Institute's B.Sc. Math Entrance. They ranked within the first 100 in the entire country in these entrances. Most of these students attended the problem solving workshops regularly, which happen 5 times every week. CMI B.Sc. Math Entrance I.S.I. […]
Dive into the discussion of the solution to Problem 22 from the 2021 AMC (Australian Mathematics Competition), Middle Primary category.
Dive into the discussion of the solution to Problem 28 from the 2022 AMC (Australian Mathematics Competition), Middle Primary category.
Dive into the discussion of the solution to Problem 14 from the 2021 AMC (Australian Mathematics Competition), Middle Primary category.
Dive into the discussion of the solution to Problem 26 from the 2021 AMC (Australian Mathematics Competition), Middle Primary category.
Dive into the discussion of the solution to Problem 20 from the 2022 AMC (Australian Mathematics Competition), Junior Year category.
Access Australian Mathematics Competition past year paper of 2015 year 7 - 8 Junior to sharpen your problem-solving skills.
Access Australian Mathematics Competition past year paper of 2016 year 5 - 6 Upper Primary to sharpen your problem-solving skills.
Access Australian Mathematics Competition past year paper of 2015 year 5 - 6 Upper Primary to sharpen your problem-solving skills.
Access Australian Mathematics Competition past year paper of 2014 year 5 - 6 Upper Primary to sharpen your problem-solving skills.
Access Australian Mathematics Competition past year paper of 2013 year 5 - 6 Upper Primary to sharpen your problem-solving skills.