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 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.
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.
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 […]
Question 1 One can holds 12 ounces of soda. What is the minimum number of cans to provide a gallon (128 ounces) of soda? (a) 7 (b) 8 (c) 9 (d) 10 (e) 11 Question 2 Four coins are picked out of a piggy bank that contains a collection of pennies, nickels, dimes, and quarters. […]
Question 1 A bakery owner turns on his doughnut machine at 8:30 AM. At 11:10 AM the machine has completed one third of the day's job. At what time will the doughnut machine complete the job? (a) 1:50 PM (b) 3:00 PM (c) 3:30 PM (d) 4:30 PM (e) 5:50 PM Question 2 A square […]
Question 1 What is the value of \(\left(2^{0}-1+5^{2}+0\right)^{-1}\times 5\)? (a) \(-125\) (b) \(-120\) (c) \(\frac{1}{5}\) (d) \(\frac{5}{24}\) (e) \(25\) Question 2 A box contains a collection of triangular and square tiles. There are 25 tiles in the box, containing 84 edges total. How many square tiles are there in the box? (a) 3 (b) 5 […]
Question 1 What is the value of \(\frac{11!-10!}{9!}\)? (a) 99 (b) 100 (c) 110 (d) 121 (e) 132 Question 2 For what value of \(x\) does \(10^{x}\cdot 100^{2x}=1000^{5}\)? (a) 1 (b) 2 (c) 3 (d) 4 (e) 5 Question 3 For every dollar Ben spent on bagels, David spent 25 cents less. Ben paid \($12.50\) […]
Question 1 A taxi ride costs \($1.50\) plus \($0.25\) per mile traveled. How much does a 5-mile taxi ride cost? (a) \($2.25\) (b) \($2.50\) (c) \($2.75\) (d) \($3.00\) (e) \($3.25\) Question 2 Alice is making a batch of cookies and needs \(2\frac{1}{2}\) cups of sugar. Unfortunately, her measuring cup holds only \(\frac{1}{4}\) cup of sugar. […]
Question 1 Cagney can frost a cupcake every 20 seconds and Lacey can frost a cupcake every 30 seconds. Working together, how many cupcakes can they frost in 5 minutes? (a) 10 (b) 15 (c) 20 (d) 25 (e) 30 Question 2 A square with side length 8 is cut in half, creating two congruent […]
Question 1 A cell phone plan costs \($20\) each month, plus \($0.05\) per text message sent, plus \($0.10\) for each minute used over 30 hours. In January Michelle sent 100 text messages and talked for 30.5 hours. How much did she have to pay? (a) \($24.00\) (b) \($24.50\) (c) \($25.50\) (d) \($28.00\) (e) \($30.00\) Question […]