Author: Kazi Abu Rousan The pure mathematician, like the musician, is a free creator of his world of ordered beauty. Bertrand Russell Today we will be discussing one of the most fascinating idea of number theory, which is very simple to understand but very complex to get into. Today we will see how to find […]
Problem Let $f$:$\mathbb{R} \rightarrow \mathbb{R}$ be a continous function such that for all$x \in \mathbb{R}$ and all $t\geq 0$ f(x)=f(ktx) where $k>1$ is a fixed constant Hint Case-1 choose any 2 arbitary nos $x,y$ using the functional relationship prove that $f(x)=f(y)$ Case-2 when $x,y$ are of opposite signs then show that $$f(x)=f(\frac{x}{2})=f(\frac{x}{4})\dots$$ use continuity to […]
PROBLEM Let $f (0,\infty)\rightarrow \mathbb{R}$ be a continous function such that for all $x \in (0,\infty)$ $f(x)=f(3x)$ Define $g(x)= \int_{x}^{3x} \frac{f(t)}{t}dt$ for $x \in (0,\infty)$ is a constant function HINT Use leibniz rule for differentiation under integral sign SOLUTION using leibniz rule for differentiation under integral sign we get $g'(x)=f(3x)-f(x)$ $\Rightarrow g'(x)=0$ [ Because f(3x)=f(x)] […]
PROBLEM Show that there are exactly $2$ numbers $a$ in the set $\{1,2,3\dots9400\}$ such that $a^2-a$ is divisible by $10000$ HINT Use Modular arithmetic and concepts of coprime numbers SOLUTION we know $10000=2^4*5^4$ In order for $10000$ to divide $a^2-a$ both $2^4$ and $5^4$ must divide $ a^2-a $ Write $a^2-a=a(a-1)$ Note that $a$ and […]
Author: Kazi Abu Rousan $\pi$ is not just a collection of random digits. $\pi$ is a journey; an experience; unless you try to see the natural poetry that exists in $\pi$, you will find it very difficult to learn. Today we will see a python code to find the value of $\pi $ up to […]
Author: Kazi Abu Rousan Pi is not merely the ubiquitous factor in high school geometry problems; it is stitched across the whole tapestry of mathematics, not just geometry’s little corner of it. $\pi$ is truly one of the most fascinating things exist in mathematics. It's not just there in geometry, but it's also there in pendulum, […]
To some extent the beauty of number theory seems to be related to the contradiction between the simplicity of the integers and the complicated structure of the primes, their building blocks. This has always attracted people. A. Knauf from "Number theory, dynamical systems and statistical mechanics" This quote is indeed true. If you just think about the […]
The 2015 American Mathematics Contest 8 (AMC 8) was a 25-question, 40-minute multiple-choice exam for students in Grade 8 and below, conducted by the MAA.
It focused on strong middle-school problem solving—covering algebra basics, geometry, number theory, and counting/probability—with an emphasis on logic and speed (no calculators).
The 2016 American Mathematics Contest 8 (AMC 8) was a 25-question, 40-minute multiple-choice mathematics competition for students in Grade 8 and below, conducted by the MAA.
It tested middle-school level problem-solving and logical reasoning across topics like algebra, geometry, number theory, and counting & probability, with no calculators allowed.
Access the complete AMC 8 - 2001 paper with carefully arranged questions for practice. Ideal for students in Grades 6–8 preparing for AMC 8, math olympiads, and competitive problem-solving.
Problem 1 Rachelle uses 3 pounds of meat to make 8 hamburgers for her family. How many pounds of meat does she need to make 24 hamburgers for a neighborhood picnic? Answer: (E) 9. Problem 2 In the country of East Westmore, statisticians estimate there is a baby born every 8 hours and a death […]
Problem 1 Margie bought 3 apples at a cost of 50 cents each. She paid with a 5 -dollar bill. How much change did Margie receive? Answer: (E) Is the correct answer. Problem 2 Karl's rectangular vegetable garden is 20 by 45 feet, and Makenna's is 25 by 40 feet. Which garden is larger in […]
The 2018 American Mathematics Contest 8 (AMC 8) was a 25-question, 40-minute multiple-choice exam for students, focused on core middle-school problem solving.
It tested logical reasoning and fundamentals from areas like algebra, geometry, number theory, and counting/probability
The 2017 American Mathematics Competition 8 (AMC 8) was a 25-question, 40-minute multiple-choice exam for students in Grade 8 and below, organised by the MAA.
It focused on middle-school problem solving across arithmetic, algebra basics, geometry, and counting/probability, testing speed + reasoning without advanced mathematics.
The AMC 8 2025 past paper is a perfect benchmark for serious preparation. Use this latest official paper to understand the current difficulty level, identify important topic patterns, and practise solving questions efficiently under timed conditions.
The AMC 8 2021 past paper is one of the best practice resources for students aiming to excel in competitive mathematics. Use this official question paper to train your reasoning skills, learn smart shortcuts, and develop the speed needed for Olympiad-style exams like AMC 8.
Practice the official AMC 8 2021 past paper to build strong foundations in competitive Mathematics. This post provides the complete question paper PDF to help students improve problem-solving speed, accuracy, and reasoning for AMC 8 and Olympiad preparation.