7 Question Types Mathematics Competitions Expose Students To Beyond School Revision

Standard school revision often focuses on repeating the same steps until a child can do them without thinking. While this helps with school exams, it does not prepare them for the challenges found in mathematics competitions.

We see this often: students who ace school tests can stumble when faced with their first competition paper. This happens because these events require a different way of thinking from the standard education curriculum.

At Terry Chew Academy, we focus on helping your child handle these non-routine challenges.

Key Takeaways

• Mathematics competitions require logical intuition and non-routine problem-solving skills that go beyond the standard school curriculum.
• Mastering question types, such as Combinatorics and Geometric Intuition, helps students navigate complex puzzles without relying on rote memorisation.
• Developing a strong grasp of number properties through Diophantine Equations and Modular Arithmetic simplifies large-scale mathematical challenges.
• Competitive maths formats, ranging from proof-based questions to team relays, build essential skills in accuracy, communication, and mental agility.
• Specialised training through frameworks such as RA*CE can significantly improve both school grades and medal prospects at prestigious Olympiads.

How are Mathematics Competitions and School Revision Different?

School revision is mostly about following a set of instructions. Your child learns a formula, sees an example, and then completes twenty similar questions. This method ensures they remember the steps for their exams. However, it does not always teach them how to handle a problem they have never seen before.

Mathematics competitions are different. They do not prompt your child on which formula to use. 

Instead, they provide a puzzle that requires logical reasoning. Your child must look at the information and decide on a strategy from scratch.

School revision is like following a map, while competition maths is like navigating a forest with only a compass. One relies on memory while the other relies on logic.

Popular Mathematics Competitions in Singapore

Singapore is home to several prestigious events. These competitions test a range of skills and logic. We recommend that your child participate in these to build confidence and enjoy a more engaging learning journey.

• SMKC (Singapore Maths Kangaroo Contest): Held in April, this competition focuses on logical puzzles rather than just difficult sums.
• SEAMO (Southeast Asian Mathematical Olympiad): Round 1 typically begins in August, with Round 2 (the invitational round) held in January each year. The exact date varies across countries and regions. This competition emphasises mathematical intuition and the ability to apply logic to unfamiliar scenarios. 
• SASMO (Singapore & Asian Schools Maths Olympiad): This is one of the largest competitions in Asia. It is held in April and serves as a great starting point for primary and secondary students.
• RMO (Raffles Mathematical Olympiad), previously known as RIPMWC: This event takes place in April (Round 1) and May (Round 2), for Primary 4 to Primary 6 students across Junior and Open Categories.
• SMO (Singapore Mathematical Olympiad): The biggest competition for secondary school students. It has categories such as Junior, Senior, and Open. Round 1 is typically held in late May or early June, with Round 2 in late June.

7 Question Types Students Will See in Mathematics Competitions

When entering maths competitions, your child will encounter a different question style than what they see in class.

These question types are rarely found in standard textbooks. Specialist Maths Olympiad programmes train students to recognise these question types and develop reliable solving strategies.

Combinatorics

Combinatorics is the branch of mathematics focused on counting. Problems involve counting vast numbers of possibilities without actually listing them out.

Take, for example, how many different ways can you arrange the letters in the word "BANANA"?

Combinatorics deals with solving this without listing every arrangement by hand. Here’s how you can do it. 

1. First, count the total number of letters. There are 6 letters.
2. If all letters were different, there would be 6x5x4x3x2x1 = 720 ways. The formula is this way because when you go to fill the first position, you have 6 different letters to choose from. You pick one and place it down. Now, you move to the second position. Since you have already used one letter, you have only 5 left in your hand. And so on.
3. However, some letters repeat. There are three 'A's and two 'N's. When letters repeat, swapping two identical letters (like one 'A' with another 'A') does not create a new, distinct arrangement. To fix the over-counting from Step 1, we must divide the total by the number of ways those repeating letters can be shuffled amongst themselves.
4. Divide 720 by the arrangements of 'A's (3! = 6) and 'N's (2! = 2).
5. The calculation is 720 / (6 x 2) = 60.
6. There are 60 ways.

Through combinatorics, your child develops systematic thinking. They learn to break down large, messy groups into organised parts.

Geometric Intuition

School geometry is often about using a protractor or applying a formula. Your child knows that to find the area of a rectangle, you multiply length by width, and to find the perimeter, you add the lengths of all the sides.

Competition geometry asks for something more. Your child has to see shapes within shapes, and often draw auxiliary lines to make a problem solvable. It is about spatial awareness and visual logic.