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 […]
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 […]
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.
Question 1 What is the value of \(2-(-2)^{-2}\)? (a) \(-2\) (b) \(\frac{1}{16}\) (c) \(\frac{7}{4}\) (d) \(\frac{9}{4}\) (e) \(6\) Question 2 Marie does three equally time-consuming tasks in a row without taking breaks. She begins the first task at 1:00 PM and finishes the second task at 2:40 PM. When does she finish the third task? […]
Question 1 Mary thought of a positive two-digit number. She multiplied it by 3 and added 11. Then she switched the digits of the result, obtaining a number between 71 and 75, inclusive. What was Mary's number? (a) 11 (b) 12 (c) 13 (d) 14 (e) 15 Question 2 Sofia ran 5 laps around the […]
Question 1 Kate bakes 20 -inch by 18 -inch pan of cornbread. The cornbread is cut into pieces that measure 2 inches by 2 inches. How many pieces of cornbread does the pan contain? (a) 90 (b) 100 (c) 180 (d) 200 (e) 360 Question 2 Sam drove 96 miles in 90 minutes. His average […]
The session opened with the Literacy module, in which all learners were assessed using a structured oral and written reading tool to determine their current levels, which were duly recorded in the assessment tick sheet. The group responded to the activity with genuine enthusiasm, and the facilitators noted that every learner showed a willingness to […]
Question 1 What is the value of $$ 1-(-2)-3-(-4)-5-(-6) ? $$ (a) -20 (b) -3 (c) 3 (d) 5 (e) 21 Question 2 Carl has 5 cubes each having side length 1 , and Kate has 5 cubes each having side length 2 . What is the total volume of these 10 cubes? (a) 24 […]
Question 1 How many integer values of $x$ satisfy $|x|<3 \pi$ ? (a) 9 (b) 10 (c) 18 (d) 19 (e) 20 Question 2 What is the value of $\sqrt{(3-2 \sqrt{3})^{2}}+\sqrt{(3+2 \sqrt{3})^{2}}$ ? (a) 0 (b) $4 \sqrt{3}-6$ (c) 6 (d) $4 \sqrt{3}$ (e) $4 \sqrt{3}+6$ Question 3 In an after-school program for juniors and […]
Question 1 What is the value of $1234+2341+3412+4123$ ? (a) 10,000 (b) 10,010 (c) 10,110 (d) 11,000 (e) 11,110 Question 2 What is the area of the shaded figure shown below? (a) 4 (b) 6 (c) 8 (d) 10 (e) 12 Question 3 The expression $\frac{2021}{2020}-\frac{2020}{2021}$ is equal to the fraction $\frac{p}{q}$ in which $p$ […]
Question 1 Define $x \diamond y$ to be $|x-y|$ for all real numbers $x$ and $y$. What is the value of $$ (1 \diamond(2 \diamond 3))-((1 \diamond 2) \diamond 3) ? $$ (a) -2 (b) -1 (c) 0 (d) 1 (e) 2 Question 2 In rhombus $A B C D$, point $P$ lies on segment […]
Question 1 Mrs. Jones is pouring orange juice into four identical glasses for her four sons. She fills the first three glasses completely full but runs out of juice when the fourth glass is only $\frac{1}{3}$ full. What fraction of a glass must Mrs. Jones pour from each of the first three glasses into the […]
Question 1 In a long line of people arranged left to right, the $1013^{\text {th }}$ person from the left is also the $1010^{\text {th }}$ person from the right. How many people are in the line? (a) 2021 (b) 2022 (c) 2023 (d) 2024 (e) 2025 Question 2 What is $10!-7!\cdot 6!$ ? (a) […]