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IOA American Mathematics Olympiad (AMO) Sample Paper :

Organisation : International Olympiad Academy (IOA)
Exam : American Mathematics Olympiad (AMO)
Document Type : Sample Paper
Class : Primary 2 (Grade 2)
Website :

What is American Mathematics Olympiad (AMO)?

The American Mathematics Olympiad (AMO) is an affiliate of Math Olympiads for Elementary and Middle Schools, USA (MOEMS) and is one of the oldest and most established primary and secondary school math competition in America that helps to nurture mathematics talent. Singapore International Math Contests Centre (SIMCC) is the main organiser of AMO in ASEAN and Greater China (China, Hong Kong, Macau and Taiwan).

American Mathematics Olympiad Sample Paper

Primary 2 (Grade 2):
1. On Saturday, Elise bought a furniture from a shop. The furniture will be sent to Elise’s house in 30 days. On what day of the week will the furniture reach Elise’s house?
2. The numbers in each row, column, and diagonal of the table below add up to 30. What is the value of X?
3. Alan has an old grandfather clock. The grandfather clock is moving slower than the normal clock. Every day at 9 am, Alan corrects it from 8:30 am to 9:00 am. One day, Alan went on vacation for 4 days. He left his house at 9:00 am after resetting the clock. When Alan returned after vacation to correct the clock to 9:00 am, what time did the clock show?
4. In the addition shown, different letters represent different digits. What is the sum of A, B and C?

Primary 3 (Grade 3):
1. In the pattern below, what will be the 78th letter written? A B B C C D A B B C C D A … and so on
2. In a magic square, the sum of the numbers in each row and each column is the same. If exactly one number is changed in this picture, the result is a magic square. Which number must be changed?
3. The digits 1 through 9 are placed in the boxes shown, one per box. In each corner box is a prime number. In each box in the middle column is a square number. In the 3 boxes of the middle row is the least 3-digit number possible. What is that 3-digit number?
4.How many numbers between 10 and 99 have digits that differ by 3?
5. Judy has two more sisters that she has brothers. Her brother, Mark, has twice as many sisters as he has brothers. How many children are in their family?

Primary 4 (Grade 4):
1. How many 2-digit odd numbers are greater than 18?
2. The sum of the page numbers of Chapter 2 (of a certain book) is 75. If there are 6 pages in Chapter 2, on what page does Chapter 2 begin?
3. How many different three-digit numbers of the form 5 are divisible by 5?
4. E is one‐quarter of the way from A to B. F is one‐quarter of the way from B to C. ABCD is a square with an area of 64 and has center X. What is the area of the shaded region (EXFB)?
5. In the figure shown, the numbers 1, 2, 3, 5, 6, and 7 are to be placed one in each empty square. The following 4 sums are the same: the numbers in the left column, the numbers in the right column, and the numbers in each diagonal. What is the greatest possible product of the 3 numbers across the grey row?

Primary 5 (Grade 5):
1. Madison has five stickers in a row on a piece of paper. The star is one to the left of the puppy. The rainbow is to the right of the heart. The puppy is three to the left of the kitten. Which sticker is in the middle of the row?

2. For a certain 3-digit number:
** the digits are in increasing order
** the difference of the greatest and least digits is 7
** it is a multiple of 9 and greater than 200.
Find the 3-digit number.

3. In the Marble Club, the average number of marbles the members have is 100. When Person X joins the club with his 80 marbles, the average number of marbles per member becomes 96. How many people, including Person X, are in the Marble Club?

4. Each student in an art class has 48 identical 1 cm cubes. Each student glues all of his or her cubes together to make a rectangular solid. No two solids are identical. What is the maximum number of students in that art class?

5. Emily plays a game that uses a marker, a coin and a number line. Her marker begins at zero on the number line. She flips the coin. If the coin lands heads up, she moves her marker 3 units to the right. If the coin lands tails up, she moves her marker 10 units to the right. Therefore there are some numbers that the marker cannot land on, such as 1, 2, 4 and 5. What is the greatest whole number on the number line that cannot be landed on?

Download AMO Sample Paper

Download American Mathematics Olympiad Sample Paper Here :

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