Key Takeaways:
- What Are the Smartest Ways to Tackle the Hardest PSLE Maths Questions?
- To tackle the hardest PSLE Maths questions, students need to rely on smart strategies. Supported by consistent practice and guided learning, they should work backwards for math questions, use estimation, and sharpen visual-spatial reasoning.
- They should also master the MOE heuristics such as “Draw a Diagram,” “Make a Supposition,” “Look for Patterns,” and “Work Backwards,” which appear frequently in Paper 2.
By doing so, students can reduce careless mistakes and feel less overwhelmed when working on multi-step and complex questions.
Introduction
Every year, the hardest PSLE Maths questions strike fear into the hearts of even the most confident students. These logic-based curveballs test how well you think, visualise, and stay calm under pressure. If you’ve ever stared at a tricky diagram or a confusing word problem and felt stuck, you’re not alone.
The truth is, mastering these math “boss levels” isn’t about being a genius. It’s about strategy, practice, and learning how to break the question down smartly. PSLE exam setters often hide simple concepts inside complex contexts. If you can strip away the ‘story’ to reveal the underlying operation, you’re halfway there!
In this article, we walk you through some of the toughest question types and how to tackle them like a pro.
What Makes These PSLE Questions So Difficult?
The PSLE Math paper is infamous for featuring a few twist-your-brain logic-based questions each year. These questions test much more than basic arithmetic; they challenge:
- Critical thinking
- Visual-spatial reasoning
- Problem-solving stamina
To beat these, you need more than just formulas. You need the right PSLE Math problem-solving mindset. It is important to know which heuristic fits the situation and how to apply it without panicking under time pressure. Many students lose marks not because the concept is hard, but because they miss a hidden condition or misinterpret a remainder.
Next, we explore the five common “boss-level” question types from recent papers that left many students scratching their heads. We also share techniques that can help you solve them smarter.
What are Some of the Hardest PSLE Maths Questions (2023-2024)?
1. Ticket Combinations
This question involves figuring out combinations of ticket prices based on total cost. The key is to use trial and error systematically but not randomly. Keep your workings neat and logical so you can spot patterns and avoid repeating steps.
Start by assuming all tickets are of one type, calculate the total, then adjust your assumption. This prevents you from missing a possible combination or wasting time on repeated attempts.
Here is an example of a similar question:
Tickets cost $2 and $3. If you buy 5 tickets in total and spend $12, how many of each ticket did you buy?
Here’s how to solve it:
Assume all tickets cost $2:
5 × $2 = $10 (less than $12, so need more $3 tickets)
Replace one $2 ticket with a $3 ticket:
4 × $2 + 1 × $3 = $8 + $3 = $11 (still less than $12)
Replace two $2 tickets with two $3 tickets:
3 × $2 + 2 × $3 = $6 + $6 = $12 (matches total!)
Answer: 3 tickets cost $2 and 2 tickets cost $3.
Strategy: Assume all tickets are $2 first (5 × $2 = $10), which is less than $12. Increase the number of $3 tickets by 1 and reduce $2 tickets accordingly, then check totals. This method avoids guessing blindly and finds the right combination efficiently.
2. Coin Assumption Strategy
These questions often involve two types of coins with a final amount that’s either too much or too little. Assume one coin type first, calculate the result, then adjust based on the excess or shortage. This method works because it reduces a two-variable problem into a single calculation step.
Here is an example of a similar question:
You have some 10-cent and 20-cent coins adding up to $1.20. If you assume all coins are 10 cents, you get 12 coins. The actual number is 9 coins. How many of each coin do you have?
Here’s how to solve it:
Suppose all coins are 10 cents → total 12 coins → $1.20 (given)
Actual total number of coins = 9 (less than 12), meaning some 10-cent coins were replaced by fewer 20-cent coins.
Difference in number of coins = 12 − 9 = 3 fewer coins
Each 20-cent coin replaces two 10-cent coins (because 20c = 2 × 10c)
So number of 20-cent coins = 3 (the difference)
Number of 10-cent coins = 9 − 3 = 6
Here’s how to check the total value:
6 × 10c = 60c
3 × 20c = 60c
Total = 120c = $1.20
Answer: 6 ten-cent coins and 3 twenty-cent coins.
Strategy: Use the supposition by assuming all coins are one type, then adjust based on the difference. This reduces a two-variable problem into one calculation.
3. Folded Shapes
This is where visual-spatial reasoning matters. Can you picture a cube unfolding or refolding in your head? Keep track of which sides are visible or hidden. It helps to sketch it out if you’re stuck. Mark each face with a letter or colour code before ‘unfolding’ it on paper. This keeps track of relative positions and prevents flipping errors.
Here is an example of a similar question:
A cube is folded from a cross-shaped net with faces labelled A to F. If face A is opposite face F, which faces touch face B?
Strategy: Sketch the net and label each face. Visualise folding it in your mind or on paper to see how faces relate, preventing errors from flipping or misreading positions.
4. Ribbon Roll Division
This can be a deceptively simple question until you forget to round up. If the leftover ribbon can still be used, it counts. Be aware of the trap: PSLE often tests whether you know to round up for whole items, like buses or rolls, instead of rounding down. Always re-read the question to decide if the remainder is usable.
Here is an example of a similar question:
You have 125 cm of ribbon and each roll requires 30 cm. How many full rolls can you make?
Here’s how to solve it:
Divide 125 by 30:
125 ÷ 30 = 4 remainder 5
You can make 4 full rolls (4 × 30 = 120 cm)
Answer: 4 full rolls.
Strategy: Calculate 125 ÷ 30 = 4 remainder 5 cm. Because the leftover 5 cm is not enough for a full roll, you can only make 4 rolls. The key PSLE trap is to understand if remainder counts or not.
5. Coin Weight Estimation
Instead of detailed calculations, go for estimation strategies. Estimate totals using round numbers first, then fine-tune. This speeds up the elimination of impossible options and gives you a quick ‘sense check’ before committing to a final answer.
Here’s an example of a similar question:
A fruit seller packs apples and oranges into baskets. Each apple weighs about 180 g, and each orange about 220 g. He packs a total of 50 fruits, and the combined weight is about 10 kg.
Here’s how to solve it:
Step 1: Check extremes
If all apples: 50×180=9000 g (9 kg).
If all oranges: 50×220=11,000 g (11 kg).
So the actual mix must give us 10,000 g, which lies between 9 kg and 11 kg.
Step 2: Try an equal split (25 apples + 25 oranges)
25 × 180 = 4500
25×180=4500 g
25 × 220 = 5500
25×220=5500 g
Total = 10,000 g
Step 3: Conclusion
The fruit seller packed 25 apples and 25 oranges.
Strategy: Estimate totals using rounded numbers, consider the extremes for each type, start with a balanced split, and adjust until the total is close to the target.
What are the Winning Strategies to Master the PSLE Math Boss Level?
Even the best students can get tripped up. Here are some tried-and-tested techniques to help you conquer the most “brutal” questions:
- Read Slowly
Underline all the important conditions so you don’t miss hidden clues. Misreading just one word can change the entire operation needed.
- Work Backwards
If you know the result, reverse each step to trace back to the starting value. This is especially helpful when questions ask about outcomes or end results.
- Estimate First
Before diving into full calculations, do a sense check. Is your answer reasonable? If your estimate is way off, you know you’ve misunderstood something before wasting time.
- Draw a Model or Diagram
Bar models, number lines, and table layouts are lifesavers for multi-step word problems. In PSLE, many complex ratio and fraction questions are much easier once modelled visually.
- Practise with Guidance
Whether you join a PSLE maths tuition programme or ask your school teacher, don’t be afraid to seek help.
Why Math Tutoring Can Make a Big Difference
You don’t have to fight the hardest PSLE Maths questions alone. A good math tutoring programme teaches you not just what to learn, but how to think. Tutors can show you smarter methods, guide your practice, and help you build the confidence to tackle complex problems independently.
Look for a PSLE math tuition centre in Singapore that goes beyond drill-and-practice. You want a place that nurtures analytical thinking, not just speed. At Sirius Mathematics, we are committed to delivering quality education that prepares students for meaningful and accurate assessments. With our techniques, practice, and support, you can level up your skills.
Contact us to start training for your own PSE ‘boss level’ victory!