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 […]
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.
The AMC 8 2021 past paper is one of the best practice resources for students aiming to excel in competitive mathematics. Use this official question paper to train your reasoning skills, learn smart shortcuts, and develop the speed needed for Olympiad-style exams like AMC 8.
Practice the official AMC 8 2021 past paper to build strong foundations in competitive Mathematics. This post provides the complete question paper PDF to help students improve problem-solving speed, accuracy, and reasoning for AMC 8 and Olympiad preparation.
Practice the official AMC 8 2020 past paper to sharpen your mathematical problem-solving skills. This post includes the complete question paper PDF for students preparing for AMC 8 and maths olympiads, helping improve accuracy, speed, and logical thinking.
The 2019 American Mathematics Contest 8 (AMC 8) was a 25-question, 40-minute multiple-choice math competition for middle school students (grades 8 and below).
Problem 1 Danica wants to arrange her model cars in rows with exactly 6 cars in each row. She now has 23 model cars. What is the smallest number of additional cars she must buy in order to be able to arrange her cars in this way?(A) 1(B) 2(C) 3(D) 4(E) 5 Answer : (A) […]
Problem 1 Susan had $\$ 50$ to spend at the carnival. She spent $\$ 12$ on food and twice as much on rides. How many dollars did she have left to spend?(A) 12(B) 14(C) 26(D) 38(E) 50 Answer : B Problem 2 The ten-letter code BEST OF LUCK represents the ten digits $0-9$, in order. […]
Problem 1 Harry and Terry are each told to calculate $8-(2+5)$. Harry gets the correct answer. Terry ignores the parentheses and calculates $8-2+5$. If Harry's answer is $H$ and Terry's answer is $T$, what is $H-T$ ?(A) -10(B) -6(C) 0(D) 6(E) 10 Answer (A) -10 Problem 2 Paul owes Paula 35 cents and has a […]