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 […]
9 Cheenta students ranked with top 100 in India and qualified for ISI and CMI Entrance. How did they achieve this? More importantly how Cheenta can help them next?
About KVPY 2021 The Kishore Vaigyanik Protsahan Yojana 2021 is a National Program of Fellowship on Basic Sciences, conducted and funded by the Department of Science and Technology, Government of India. This fellowship aims to assist the students in realizing their potential at the national level and to make sure that the best scientific talent […]
Bernoulli Random Variable Story A trial is performed with probability $p$ of "success", and $X$ counts the number of successes: 1 means success (one success), 0 means failure (zero success). Definition $$X= \begin{cases}1 & \text {with probability } p \\ 0 & \text {with probability } 1-p \end{cases}$$ Example (Indicator Random Variable): Indicator Random Variable […]
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).
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 […]
Problem 1 What is the ones digit of $$222,222-22,222-2,222-222-22-2 ?$$ (A) 0(B) 2(C) 4(D) 6(E) 8 Answer: (B) 2 Problem 2 What is the value of this expression in decimal form? $$\frac{44}{11}+\frac{110}{44}+\frac{44}{1100}$$ (A) 6.4(B) 6.504(C) 6.54(D) 6.9(E) 6.94 Answer: (C) 6.54 Problem 3 Four squares of side length $4,7,9$, and 10 units are arranged in […]
AMC 8 2004 is a classic middle-school math contest featuring 25 engaging problems in algebra, geometry, counting, probability, and logical reasoning. It tests speed, accuracy, and smart problem-solving strategies in a fun competitive format.
Problem 1Theresa's parents have agreed to buy her tickets to see her favorite band if she spends an average of 10 hours per week helping around the house for 6 weeks. For the first 5 weeks, she helps around the house for $8,11,7,12$ and 10 hours. How many hours must she work during the final […]
Get the official AMC 8 - 2003 paper with all questions. This exam from the Mathematical Association of America helps young students practice analytical thinking and prepare effectively for upcoming competitions.
The AMC 8 - 2002 paper is a middle-school level mathematics contest featuring engaging problems that test logical reasoning, number sense, and problem-solving skills. This paper is ideal for students preparing for Math Oympiads and competitive exams.
Problem 1 At Euclid High School, the mathematics teachers are Mrs. Germain, Mr. Newton, and Mrs. Young. There are 11 students in Mrs. Germain's class, 8 in Mr. Newton, and 9 in Mrs. Young's class are taking the AMC 8 this year. How many mathematics students at Euclid High School are taking the contest?(A) 26(B) […]
Question 1 What is the difference between the sum of the first 2003 even counting numbers and the sum of the first 2003 odd counting numbers? (a) 0 (b) 1 (c) 2 (d) 2003 (e) 4006 Question 2 Members of the Rockham Soccer League buy socks and T-shirts. Socks cost \($ 4\) per pair and […]
Question 1 You and five friends need to raise \($ 1500\) in donations for a charity, dividing the fundraising equally. How many dollars will each of you need to raise? (a) 250 (b) 300 (c) 1500 (d) 7500 (e) 9000 Question 2 For any three real numbers \(a, b\), and \(c\), with \(b \neq c\), […]
Question 1 While eating out, Mike and Joe each tipped their server 2 dollars. Mike tipped \(10 %\) of his bill and Joe tipped \(20 %\) of his bill. What was the difference, in dollars between their bills? (a) 2 (b) 4 (c) 5 (d) 10 (e) 20 Question 2 For each pair of real […]
Question 1 Sandwiches at Joe's Fast Food cost \($3\) each and sodas cost \($ 2\) each. How many dollars will it cost to purchase 5 sandwiches and 8 sodas? (a) 31 (b) 32 (c) 33 (d) 34 (e) 35 Question 2 Define \(x \otimes y=x^{3}-y\). What is \(h \otimes(h \otimes h)\) ? (a) \(-h\) (b) […]
Question 1 What is $10 \cdot\left(\frac{1}{2}+\frac{1}{5}+\frac{1}{10}\right)^{-1}$ ? (a) 3 (b) 8 (c) $\frac{25}{2}$ (d) $\frac{170}{3}$ (e) 170 Question 2 Roy's cat eats $\frac{1}{3}$ of a can of cat food every morning and $\frac{1}{4}$ of a can of cat food every evening. Before feeding his cat on Monday morning, Roy opened a box containing 6 cans […]
Question 1 What is the value of $9901 \cdot 101-99 \cdot 10101$ ? (a) 1 (b) 20 (c) 200 (d) 202 (e) 2020 Question 2 A 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 $a$ […]
Question 1 What is the value of $$ 3+\frac{1}{3+\frac{1}{3+\frac{1}{3}} ?} $$ (a) $\frac{31}{10}$ (b) $\frac{49}{15}$ (c) $\frac{33}{10}$ (d) $\frac{109}{33}$ (e) $\frac{15}{4}$ Question 2 Mike cycled 15 laps in 57 minutes. Assume he cycled at a constant speed throughout. Approximately how many laps did he complete in the first 27 minutes? (a) 5 (b) 7 (c) […]
Question 1 What is the value of $$ \left(2^{2}-2\right)-\left(3^{2}-3\right)+\left(4^{2}-4\right) ? $$ (a) 1 (b) 2 (c) 5 (d) 8 (e) 12 Question 2 Portia's high school has 3 times as many students as Lara's high school. The two high schools have a total of 2600 students. How many students does Portia's high school have? (a) […]
Question 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) $\frac{5}{6}$ Question 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) […]
Question 1 Cities $A$ and $B$ are 45 miles apart. Alice and Barbara start biking from $A$ and $B$ at speeds of 18 mph and 12 mph , respectively. How far away from city $A$ will they be when they meet? (a) 20 (b) 24 (c) 25 (d) 26 (e) 27 Question 2 The weight […]