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MOEMS - How to Prepare for Math Olympiads and Common Topics

Updated: 2 days ago

MOEMS (Mathematical Olympiads for Elementary and Middle Schools) or APSMO (Australasian Problem Solving Mathematical Olympiads) is a good math contest for Elementary/ Primary students who love math. It exposes the students to various problem-solving techniques and builds a strong foundation for Middle school math competitions. While MOEMS Level M exists for grades 6-8, the other middle school math competitions, like AMC 8 and Math Counts, are more popular for those grades.

Table of Contents

Popular topics



Facts about MOEMS contests

  1. It consists of 5 math contests held from November to March of every academic year.

  2. Each test is for 30 min and consists of 5 questions

  3. The students have to fill in the answers in the blanks provided.

  4. Divisions:

    1. Division E - Elementary level for grades 4-6

    2. Division M - Middle school level for grades 6-8

  5. Enrolment: Through schools, homeschools or registered institutions only http://www.moems.org/enroll.htm. Post pandemic, they have opened it for individual registration as well.

    Update: They've now closed the individual registration. Registration is open to only schools, homeschools or registered institutions

  6. Open for individual enrolment: No

  7. Important dates:

    • Contest 1 - November,

    • Contest 2 - December,

    • Contest 3 - January,

    • Contest 4 - February

    • Contest 5 - March



APSMO (Australasian Problem Solving Mathematical Olympiads)

This is the Australasian version of the MOEMS competition. It is held mainly in Australia and New Zealand. Any registered school within Australia and New Zealand can register for this competition. While the topics and the questions remain almost the same, the dates of the contests differ. It also has only 4 contests.

Important dates for 2026 APSMO contest

  • Competition One - Wednesday, 6th May 2026

  • Competition Two - Wednesday, 10th June 2026

  • Competition Three - Wednesday, 29th July 2026

  • Competition Four - Wednesday, 9th September 2026

There are 2 divisions available for the Maths Olympiad here as well

  • Junior: Division J - for students in school Years 5 and 6

  • Senior: Division S - for students in school Years 7 and 8

Open for individual enrolment: No


The contest problems in APSMO are also mainly based on the metric unit system, unlike MOEMS, which uses both Metric and US standards. Books to help prepare for APSMO can be purchased on their website. I would highly recommend Volume 4, the latest set of competition papers and "Creative Problem Solving in School Mathematics" by Dr. George Lenchner to help with preparation.


How to Prepare for MOEMS/ APSMO

MOEMS and APSMO papers consist of just 5 questions to be solved in 30 minutes. This means students have ample time to think carefully and work through each problem step by step—making it an excellent starting point for beginners.

Typically, the difficulty level progresses gradually:

  • The first two questions are relatively straightforward

  • The next two are of moderate difficulty

  • The final question is more challenging and requires deeper thinking

This structure helps students build confidence while also pushing them to develop stronger problem-solving skills.


Resources/ Books to prepare for MOEMS/ APSMO

  1. Beast Academy (BA) curriculum is great for preparing for all Elementary math competitions. It is a solid math curriculum as well. (I'm not an affiliate of BA, I just love their curriculum.)

    If you'd like to know about how to use the Beast Academy math curriculum, you can look up my blog on it.

  2. Past papers are a great way to know what to expect in any competition. MOEMS past papers have been published in 5 books, which give plenty of practice questions. Hints and detailed solutions are also available in these books.

    Links to the books from Amazon

    1. Math Olympiad Contest Problems for Elementary and Middle Schools, Vol. 1

    2. Math Olympiad Contest Problems, Volume 2

    3. MOEMS Contest Problems, Volume 3

    4. Moems Contest Problems Vol. 4, The International Edition

      You can also find sample contest papers on their own website. Here's a link to all MOEMS preparation books from their own website.

  3. One other definitely useful book (if you are close and need to do it fast) is Creative Problem Solving in School Mathematics by George Lenchner



Popular Topics with MOEMS/ APSMO

Now that we’ve covered the registration process, exam format, and recommended preparation books, let’s move on to exploring the common topics and working through a few sample questions.

  1. Algebra, fractions and ratios through bar modelling

    1. Amy reads a lot, and she has 20 more books than Betty. Both of them together have 44 books. How many books does Betty have?

    2. Bala had some marbles. His sister gave him 12 more marbles than what he already had for his birthday. Now he has 82 marbles. How many marbles did his sister give him?

    3. Mark and Jack together had 91 marbles. If Marlene had twice as many marbles as Jacob, how many marbles did Marlene have?

    4. Michelle gave 3/8th of the cookies he had to his friend. If he gave his friend 33 cookies, how many cookies did Michelle have to start with?

  2. Number Theory - GCF, LCM and its applications; divisibility rules; prime numbers

    1. What is the least number greater than 1000 that is divisible by 15?

    2. What is the least number greater than 1000 that is a multiple of 12 and 5?

    3. Find the Mystery Number.

      1. I am a 3-digit even number between 500 and 600.

      2. I am divisible by 45.

      3. What number am I?

    4. Raj loves his collection of marbles. He has lots and lots of marbles. If he counts them 3 at a time, he has 1 left over. If he counts them out 4 at a time, he has 1 left over. If he counts them out 5 or 6 at a time, he still has 1 left over. What is the minimum number of marbles he has?

    5. The sum of 2 prime numbers a and b is 99. What is a*b?

    6. 7M4,393 is divisible by 11. What is M?

    7. A18AA is divisible by 18. Find A

    8. How many different perimeters are possible for a rectangle with integer side lengths and an area of 160?

  3. Geometry – Areas and Perimeters of rectangles and rectilinear figures

    1. A square has an area of 81 sq. cm. What is its perimeter?

    2. ABCD is a square. Points E and F trisect the side AD. G is the midpoint of side AB. If the area of the triangle EFG is 25 sq units, what is the area of the square ABCD?

b. The following figure is made up of 7 congruent squares. If the area of the given figure is 63, then what is the perimeter of

the shape?


c. ABCD is a rectangle with AB=30 and AD=10. If the total area of the shaded region is 120,

  1. What is the sum of the areas of triangles ADE and BEF?

  2. What is the area of triangle DFC?

  1. Counting and Probability - Basics of the Counting Principle

    1. 5 teams are playing in a round-robin tournament, where each team plays exactly 3 games with every other team. How many games are played in total in the tournament?

    2. A circle has 6 equally spaced points drawn on its circumference. How many lines can be drawn joining any 2 of the points?

    3. How many 4-digit numbers can be formed using the digits 1, 2, 3, 4, 5 (no repetition) such that the 4-digit number is divisible by 3?

    4. How many integers from 1 to 100 are divisible by either 4 or 6?

    5. A fair die is rolled twice. How many outcomes have a sum greater than 8?

    6. How many rectangles (including squares) are there in a 3×3 grid?


  1. Logic, Patterns and Cryptogram Puzzles

    Cryptogram Puzzles are my favourite, and my students' favourite too. Here are some for practice

    1. ER + ER + ER = GR8 where E, R and G are non-zero digits. Find G, R and E.

    2. AB + A = BOO. Find A and B. (This is a fun Halloween Puzzle that I wrote)

    3. DAD * AA = DEED. DEED is a multiple of 9. Find DAD. This is a Cryptogram along with divisibility rules from Number Theory.

    4. ABCD + ABC + AB + A = 2026. Find A, B, C and D.

    5. BRIBE + BRIB + BRI + BR + B = 79415. Find B, R, I and E.

    Patterns

    1. 10/7 = 1.428571428571428571..... What is the 50th digit after the decimal

    2. Kenny starts writing a list that goes 19, 27, 35, 43 and so on. What is the 30th number in her list?

    3. What day is 100 days after Tuesday?

    4. The first number of a sequence is 1. The next number is 3 more than twice the previous number. The sequence goes on this way. What is the units digit of the 2026th number in this sequence?

    5. A pattern of dots is formed as follows:

      • Figure 1 has 1 dot

      • Figure 2 has 5 dots

      • Figure 3 has 13 dots

        Each new figure is formed by adding a layer of dots around the previous figure.

        How many dots are in Figure 6?

    6. A robot starts at 0 on a number line. It moves +3, then −2, and repeats this pattern. Where is the robot after 91 moves?

    Logic

    1. On an island, all inhabitants are either truth-tellers or liars.

      A says: “B is a liar.”

      B says: “C is a liar.”

      C says: “A and B are both liars.”

      Who is telling the truth?

    2. Four children—Anna, Ben, Cara, and Dan—each have a different favourite colour: green, blue, red, and yellow.

      Anna does not like red

      Ben likes blue

      Cara does not like green

      Dan likes neither yellow nor red

      Who likes Yellow?

    3. Five houses are in a row, numbered 1 through 5 from left to right. Each house is painted a different colour: red, blue, green, yellow, or white.

      The following clues are true:

      1. The red house is somewhere to the left of the blue house.

      2. The green house is not next to the yellow house.

      3. The yellow house is not on either end.

      4. The white house is immediately to the right of the green house.

      5. The blue house is not in the middle.

      Which colour is in the third house from the left?


  2. Basic Arithmetic Problems

    1. Evaluate 1/5÷1/5÷5÷1/5÷1/5. (These are very popular in MOEMS. Order of operations is important, and so is writing the steps here.)

    2. What is 25×48+25×35+25x17

    3. What is 5/6 of 6/7 of 7/8 of 8/9 of 9/10 of 180?

    4. What is 15*36÷45?


What do students gain through APSMO?

• Strong foundations in arithmetic, algebra, and number theory

• Confidence in tackling non-routine problems

• Exposure to logical reasoning, patterns, and mathematical thinking


🏆 Results that speak

My students have consistently performed at a high level, including achieving top 2% rankings in their region/country and earning prestigious awards.

If you’re looking for your child not just to participate—but truly excel, focused guidance and the right training approach make all the difference.

📩 If you’d like your child to be coached for APSMO, feel free to reach out.



For more problems, check out my blogs on Cryptograms and Find the Mystery Numbers



You can also visit Interesting Math Problems. I've posted several pages of problems or my FB page, where I post fairly often


About Me:

Hi, I'm Vasudha, an Online Math Tutor. I help prepare students for all Elementary and Middle school Math Competitions. If you'd like to talk to me about preparing your child for math competitions, please do contact me here.


 
 
 

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