NMTC 2019 Stage 1 Sub junior Question 10 How many positive integers smaller than 400 can you get as a sum of eleven consecutive positive integers? NMTC 2019 Stage 1 Sub junior Question 11 Let $x, y$ and $z$ be positive real numbers and let $x \geq y \geq z$ so that $x+y+z=20.1$. Which of […]
NMTC 2010 Primary Stage 1 Question 1 $\mathrm{n}, \mathrm{a}$ are natural numbers each greater than 1 . If $a+a+a+a+\ldots+a=2010$, and there are $n$ terms on the left hand side, then the number of ordered pairs $(a, n)$ is NMTC 2019 Inter Stage 1 Question 17 The number of times the digit occurs in the result […]
NMTC 2019 Stage 1 Inter Question 5 The area of the curve enclosed by $|x-2 \sqrt{2}|+|y-\sqrt{5}|=2$ is : (A) 16(B) 12(C) 8(D) 4 NMTC 2019 Inter Stage 1 Question 11 In a rectangle $A B C D$, point $E$ lies on $B C$ such that $\frac{B E}{E C}=2$ and point $F$ lies on $C D$ […]
Try these AMC 10 Geometry Questions and check your knowledge! Two right circular cones with vertices facing down as shown in the figure below contains the same amount of liquid. The radii of the tops of the liquid surfaces are $3$ cm and $6$ cm. Into each cone is dropped a spherical marble of radius […]
Author: Kazi Abu Rousan C is hard but fast But you need to be on guard to last. Python is easy but slow But you can use it to glow. But if you have julia Beautiful rhythms will flow. ---Me Julia is a high-level, high-performance, dynamic programming language. Most of you guys have heard or […]
Dear student, In the past few years several Cheenta students reached the top 300 universities in the world. These universities include Oxford, UCLA, NUS, MIT and University of Edinburgh. We have gradually shaped a success pathway for students that works in the long run. This pathway can be useful for you as well.There two components of this success path: Component 1: Performance […]
Author: Kazi Abu Rousan There are some problems in number theory which are very important not only because they came in exams but also they hide much richer intuition inside them. Today, we will be seeing one of such problems. Sources: B.Stat. (Hons.) and B.Math. (Hons.) I.S.I Admission Test 2012 problem-2. B.Stat. (Hons.) and B.Math. […]
Author: Kazi Abu Rousan Where are the zeros of zeta of s? G.F.B. Riemann has made a good guess; They're all on the critical line, saith he, And their density's one over 2 p log t. Source https://www.physicsforums.com/threads/a-poem-on-the-zeta-function.16280/ If you are a person who loves to read maths related stuff then sure you have came […]
Problem If $\sum_{n=1}^{\infty} \frac{1}{n^2} =\frac{{\pi}^2}{6}$ then $\sum_{n=1}^{\infty} \frac{1}{(2n-1)^2}$ is equal to (A) $\frac{{\pi}^2}{24}$ (B) $\frac{{\pi}^2}{8}$ (C) $\frac{{\pi}^2}{6}$ (D) $\frac{{\pi}^2}{3}$ Hint Try to write the summation as sum of square of reciprocal of odd numbers and even numbers and take the advantage of the infinite sum Solution $\sum_{n=1}^{\infty} \frac{1}{n^2} =\frac{{\pi}^2}{6}$ $\Rightarrow \sum_{n=1}^{\infty} \frac{1}{(2n)^2} + \sum_{n=1}^{\infty} \frac{1}{(2n-1)^2}= […]
Probability theory is nothing but common sense reduced to calculation. Pierre-Simon Laplace Today we will be discussing a problem from the second chapter of A First Course in Probability(Eighth Edition) by Sheldon Ross. Let's see what the problem says: Describing the Problem The problem(prob-48) says: Given 20 people, what is the probability that among the […]
Have a look at the Questions and Solutions of Australian Mathematics Competition 2020 - Intermediate of Grade 9 and 10.
Solve beautiful Number Theory problem from IMO 1959 with the help of Euclidean Algorithm and Division Lemma.
Problem 1: How many \(1 \times 1\) squares are in this diagram? (A) 16(B) 18(C) 20(D) 24(E) 25 Problem 2: What is half of 2020?(A) 20(B) 101(C) 110(D) 1001(E) 1010 Problem 3: What is the perimeter of this triangle? (A) 33 m(B) 34 m(C) 35 m(D) 36 m(E) 37 m Problem 4: I stepped on […]
Problem 1: What is the perimeter of this rhombus? (A) 20 cm(B) 24 cm(C) 28 cm(D) 32 cm(E) 36 cm Problem 2: The temperature in the mountains was \(4^{\circ} \mathrm{C}\) but dropped overnight by \(7^{\circ} \mathrm{C}\). What was the temperature in the morning?(A) \(3{ }^{\circ} \mathrm{C}\)(B) \(11^{\circ} \mathrm{C}\)(C) \(-3^{\circ} \mathrm{C}\)(D) \(-4^{\circ} \mathrm{C}\)(E) \(-11^{\circ} \mathrm{C}\) Problem […]
Problem 1: Kurt paved his courtyard in the pattern shown. How many \(1 \times 1\) pavers are in his courtyard? (A) 28(B) 30(C) 32(D) 34(E) 36 Problem 2: Which of the following expressions has the smallest value?(A) (3+2)(B) (3-2)(C) \(3 \times 2\)(D) \(3 \div 2\)(E) 32 Problem 3: The numbers on the top corners of […]
Books play a significant role in the preparation for the Singapore Mathematics Olympiad. In Cheenta we recommend a few books based on their age and grades that suit them. Books for Preliminary AMC Books for Advanced AMC
Problem 1: \(2021-1202=\) (A) 719(B) 723(C) 819(D) 823(E) 3223 Problem 2: What is the perimeter of this figure? (A) 28 units(B) 26 units(C) 24 units(D) 20 units(E) 21 units Problem 3: The area of this triangle is (A) \(10\) \(cm^2\) (B) \(12\) \(cm^2\) (C) \(12.5\) \(cm^2\)(D) \(15\) \(cm^2\) (E) \(16\) \(cm^2\) Problem 4: On the […]
Schedule of the Test: Registration Fee: The registration fee is $8.00 per participant (from SMS institutional member schools) per competition category; and $10.00 per participant (from non-institutional member schools). The participants' names and fees should be forwarded by the Head of the Department of Mathematics (of the competing school) to the Chairman of the Competition Committee in the prescribed […]
Problem 1: How many dots are in this pattern? (A) 20(B) 21(C) 22(D) 23(E) 24 Problem 2: What number is one hundred more than \(465 \) ? (A) 365(B) 455(C) 475(D) 565(E) 1465 Problem 3: What fraction of this rectangle is shaded? (A) \(\frac{1}{2}\)(B) \(\frac{1}{4}\)(C) \(\frac{1}{6}\)(D) \(\frac{1}{8}\)(E) \(\frac{1}{10}\) Problem 4: There were 17 dogs and […]
Problem 1: How many eggs are in these cartons? (A) 12(B) 15(C) 16(D) 18(E) 21 Problem 2: Which one of the following is the largest number? (A) 401(B) 410(C) 14(D) 140(E) 44 Problem 3: Which of the following is equal to 3 m? (A) 3 cm(B) 30 cm(C) 300 cm(D) 3000 cm(E) 36 cm Problem […]