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: The domain of definition of $f(x)=-\log \left(x^{2}-2 x-3\right)$ is (a) $(0, \infty)$(b) $(-\infty,-1)$(c) $(-\infty,-1) \cup(3, \infty)$(d) $(-\infty,-3) \cup(1, \infty)$ Problem 2: $A B C$ is a right-angled triangle with the right angle at B. If $A B=7$ and $B C=24$, then the length of the perpendicular from $B$ to $A C$ is (a) […]
Let's discuss a problem from CMI Entrance Exam 2019 Problem that helps us to learn how to solve complex inequality problems using Geometry. The Problem: Count the number of roots $w$ of the equation $z^{2019} − 1 = 0$ over complex numbers that satisfy $|w + 1| ≥ 2 + √2$. The Solution: Some useful […]
Author: Kazi Abu Rousan Mathematics is the science of patterns, and nature exploits just about every pattern that there is. Ian Stewart Introduction If you are a math enthusiastic, then you must have seen many mysterious patterns of Prime numbers. They are really great but today, we will explore beautiful patterns of a special type […]
In this post, you will find ISI B.Stat B.Math 2021 Objective Paper with Problems and Solutions. This is a work in progress, so the solutions and discussions will be uploaded soon. You may share your solutions in the comments below. [Work in Progress] Problem 1 The number of ways one can express $2^{2} 3^{3} 5^{5} […]
In this post, you will find ISI B.Stat B.Math 2021 Subjective Paper with Problems and Solutions. This is a work in progress, so the solutions and discussions will be uploaded soon. You may share your solutions in the comments below. [Work in Progress] Problem 1: There are three cities each of which has exactly the […]
Let's discuss a problem from CMI Entrance Exam 2019 based on the Inscribed Angle Theorem or Central Angle Theorem and Transformation Geometry. The Problem: Let $A B C D$ be a parallelogram. Let 'O' be a point in its interior such that $\angle A D B+\angle D O C=180^{\circ}$. Show that $\angle O D C=\angle […]
In this post, we will be learning about the Rational Root Theorem Proof. It is a great tool from Algebra and is useful for the Math Olympiad Exams and ISI and CMI Entrance Exams. So, here is the starting point.... $a_{n} x^{n}+a_{n-1} x^{n-1}+\ldots+a_{2} x^{2}+a_{1} x+a_{0}$ This polynomial has certain properties. 1. The coefficients are all […]
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) […]
Problem 1 Mindy made three purchases for $\$ 1.98, \$ 5.04$ and $\$ 9.89$. What was her total, to the nearest dollar?(A) $\$ 10$(B) $\$ 15$(C) $\$ 16$(D) $\$ 17$(E) $\$ 18$ Answer: (D) $\$ 17$ Problem 2 On the AMC 8 contest Billy answers 13 questions correctly, answers 7 questions incorrectly and doesn't answer […]
Practise the AMC 8 2005 paper to sharpen your core math skills and contest thinking. This set of problems covers key topics like arithmetic, algebra, geometry, counting, and logical reasoning — perfect for Grades 6–8 students aiming for AMC 8 and other olympiad-style exams.
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.
Question 1 The instructions on a $350-$ gram bag of coffee beans say that proper brewing of a large mug of pour-over coffee requires 20 grams of coffee beans. What is the greatest number of properly brewed large mugs of coffee that can be made from the coffee beans in that bag? (a) 16 (b) […]
Question 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 […]
Question 1 In the year 2001, the United States will host the International Mathematical Olympiad. Let $I, M$, and $O$ be distinct positive integers such that the product $I \cdot M \cdot O=2001$. What's the largest possible value of the sum $I+M+O$ ? (a) 23 (b) 55 (c) 99 (d) 111 (e) 671 Question 2 […]
Question 1 The median of the list \[ n, n+3, n+4, n+5, n+6, n+8, n+10, n+12, n+15 \] is 10 . What is the mean? (a) 4 (b) 6 (c) 7 (d) 10 (e) 11 Question 2 A number \(x\) is 2 more than the product of its reciprocal and its additive inverse. In which […]
Question 1 The ratio \(\frac{10^{2000}+10^{2002}}{10^{2001}+10^{2001}}\) is closest to which of the following numbers? (a) 0.1 (b) 0.2 (c) 1 (d) 5 (e) 10 Question 2 For the nonzero numbers \(a, b, c\), define \((a, b, c)=\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\). Find \((2,12,9)\). (a) 4 (b) 5 (c) 6 (d) 7 (e) 8 Question 3 According to the standard convention […]
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 […]