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 […]
An interesting problem based on complex numbers and their inversion. This is a Subjective Problem 89 from the Test of Mathematics Book, highly recommended for the ISI and CMI Entrance Exams. Let's check out the problem and solutions in two episodes: Useful Resources Previous Year Problems for ISI and CMI How to use invariance in […]
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 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 […]
Question 1 What is the value of \[ 2^{\left(0^{\left(1^{9}\right)}\right)}+\left(\left(2^{0}\right)^{1}\right)^{9}? \] (a) 0 (b) 1 (c) 2 (d) 3 (e) 4 Question 2 What is the hundreds digit of \((20!-15!)\)? (a) 0 (b) 1 (c) 2 (d) 4 (e) 5 Question 3 Ana and Bonita were born on the same date in different years, \(n\) years […]
Question 1 What is the value of $$ \left(\left((2+1)^{-1}+1\right)^{-1}+1\right)^{-1}+1 ? $$ (a) $\frac{5}{8}$ (b) $\frac{11}{7}$ (c) $\frac{8}{5}$ (d) $\frac{18}{11}$ (e) $\frac{15}{8}$ Question 2 Liliane has $50 %$ more soda than Jacqueline, and Alice has $25 %$ more soda than Jacqueline. What is the relationship between the amounts of soda that Liliane and Alica have? (a) […]
Question 1 Mary's top book shelf holds five books with the following widths, in centimeters: \(6, \frac{1}{2}, 1,2.5\), and 10. What is the average book width, in centimeters? (a) 1 (b) 2 (c) 3 (d) 4 (e) 5 Question 2 Four identical squares and one rectangle are placed together to form one large square as […]