6 Challenging PSLE Maths Questions You'll Likely See (With Examples)

The Primary School Leaving Examination (PSLE) Math paper can be daunting, especially with the increasing number of challenging PSLE maths questions that go beyond routine problem-solving.

These questions are designed to assess a student’s ability to apply concepts, not just memorise formulas.

In this article, we’ll explore why some PSLE math questions are particularly tricky and how you and your child can better prepare for them.

We’ll walk through examples, explain why they're challenging, and offer step-by-step guidance to solve them.

What Makes a PSLE Maths Question Challenging?

Some PSLE maths problem sums are non-routine, unfamiliar to students, and require more than just direct computation.

These types of questions often demand multi-step solutions and a deep understanding of mathematics concepts.

Memorising formulas isn't enough; students must apply what they’ve learned at the right moment, often under pressure.

That’s why questions may involve drawing models, using assumption methods, or working through a complex sequence of logic.

These challenges are intentionally designed to be a test of higher-order thinking and reasoning, not just calculation.

Types of Challenging PSLE Maths Questions

Here are six common types of challenging PSLE Maths questions that often trip students up.

Each type tests different thinking skills — from strategic guessing to handling multi-step word problems.

Understanding these categories helps students tackle tricky questions with greater confidence.

Heuristics-Based Questions

Heuristics are problem-solving strategies that students use when a straightforward method isn’t available.

These include approaches such as guess and check, working backwards, and the before-and-after concept.

They are particularly common in PSLE math papers when problems don’t fit familiar formats.

For example, a question may involve finding how many people are in a group given shifting conditions over time.

Instead of plugging numbers into a formula, students must consider how there are often multiple steps to uncover the answer.

The key to mastering heuristic questions is building the habit of strategic thinking and being comfortable with trial and error when needed.

Fraction and Ratio Word Problems

These are among the most common PSLE math questions.

What makes them tricky?

• Multiple quantities to compare

• Use of both fraction of and the ratio of values

• Sometimes include concepts like "at first" or "an equal number of"

• 
  

Example Question:

A class has the ratio of boys to girls as 3:5.

The total number of pupils is 40. How many boys are there?

Solution:

• Total parts = 3 + 5 = 8

• 1 part = 40 ÷ 8 = 5

• Boys = 3 parts = 15

Answer: 15 boys

Assumption-Based Questions

Assumption questions involve making educated guesses about values to determine differences or totals.

These often appear in problems involving weights, costs, or ages, where the challenge is figuring out how much of a value is unknown or needs to be assumed.

Example Question:

Two bags contain apples and oranges. Each bag weighs the same.

The mass of an apple is 200g, and the mass of an orange is 300g.

If Bag A has 2 apples and 3 oranges, how many apples are in Bag B if it contains 4 oranges?

Solution:

• Bag A = 2(200) + 3(300) = 400 + 900 = 1300g

• Bag B = 4(300) = 1200g

• Need 100g more to match 1300g

• 1 apple = 200g → not possible

Assume 1 apple, 4 oranges: 200 + 1200 = 1400g → too much

Assume 0.5 apple (100g) → correct mass but not possible with whole fruit

Answer: No solution with whole apples.

Try rephrasing: Bag B has 4 oranges and 1 apple? Check again.

This illustrates why assumption questions can trip students up, especially if students don’t know how to solve this type of logic puzzle step by step.

Rate and Speed Questions

Questions involving time, distance, and speed are often hidden in everyday story contexts, which makes them harder to recognise and decode.

A typical example might describe two people walking towards each other from different points at different speeds, asking when or where they’ll meet.

Example Question:

Amy walked from her house to the mall at 4 km/h. She took 1.5 hours. What is the distance?

Solution:

• Distance = Speed × Time = 4 × 1.5 = 6 km

Answer: 6 km

These may seem simple but become complex when speed changes, rests are added, or if two people travel at different rates.

Percentage and Discount Puzzles

Often appear as multi-step word problems involving discounts, increases, or profit/loss. These require:

• Calculating original or final values

• Keeping track of "the amount left" or "the difference in prices"

Example Question:

A $200 jacket is discounted by 25%. Then a 7% GST is added. What is the final price?

Solution:

• Discounted price = $200 - 25% = $150

• GST = 7% of $150 = $10.50

• Final price = $150 + $10.50 = $160.50

Answer: $160.50

Area and Perimeter Problems with a Twist

These questions look simple but often involve irregular shapes, missing sides, or real-world scenarios in the question context.

To solve these correctly, you need to apply multiple formulas and read the question carefully.

Example Question:

A rectangular garden measures 15 m by 10 m. A square flowerbed (4 m by 4 m) is cut out from one corner.

What is the remaining area?

What is the total length of fencing needed (excluding the flowerbed)?

• Area of garden: 15 × 10 = 150 m²

• Area of flowerbed: 4 × 4 = 16 m²

• Remaining area: 150 – 16 = 134 m²

• Fencing needed (perimeter of original garden): 2 × (15 + 10) = 50 m

Watch out for:

• Mistaking area for perimeter

• Adding the flowerbed’s sides into the fencing (not needed if it’s cut out)

Quick tip:

Sketch the figure and label all sides clearly — you can avoid common errors with just this one step.

Real PSLE-Style Challenging Questions (With Step-by-Step Solutions)

Here are some real PSLE-style maths problems that test different skills — from logical reasoning to algebraic thinking.

Follow the step-by-step solutions to understand how to solve this type of question effectively.

Question 1:

The total mass of 3 bags is 12kg. Bag A is twice as heavy as Bag B, and Bag C is 2kg lighter than Bag B.

Find the mass of each bag.

Concepts Tested: Algebraic thinking, logical assumptions

Solution:

• Let Bag B = x

• Bag A = 2x, Bag C = x - 2

Now use these expressions to find the total mass of the bags.

• Total = 2x + x + x - 2 = 4x - 2 = 12

• 4x = 14 → x = 3.5

• Bag A = 7kg, B = 3.5kg, C = 1.5kg

Tip: Always define variables clearly, especially when dealing with the total amount of mass, cost, or quantity in a problem.

Question 2:

The value of 5 identical pens and 2 erasers is $9. 3 pens and 4 erasers cost $7. Find the price of one pen.

Solution:

Let pen = p, eraser = e

• 5p + 2e = 9

• 3p + 4e = 7

Use elimination: Multiply first by 2: 10p + 4e = 18 Subtract second: 10p + 4e - (3p + 4e) = 18 - 7 → 7p = 11 → p = $1.57 (approx.)

Tip: Watch out for rounding if question expects whole number answers.

Question 3:

Peter and John had the same number of marbles. Peter gave John 10 marbles.

Now John has twice as many marbles as Peter. How many marbles did each boy have at first?

Solution:

Let original number = x After exchange:

• Peter: x - 10

• John: x + 10

x + 10 = 2(x - 10) x + 10 = 2x - 20 30 = x

Answer: Each had 30 marbles at first

Common Mistake: Forgetting to reflect changes correctly in equations.

How to Prepare for These Challenging Questions

Preparing for the PSLE math paper involves more than just doing practice problems.

Students need to deeply understand concepts to tackle a wide variety of unfamiliar problem types confidently.

Reviewing mistakes thoroughly—also known as error analysis—helps students learn from incorrect assumptions or misapplied formulas.

It's also important to build stamina. PSLE math questions, especially Section C, can be long and mentally draining.

Students should practise completing full papers under timed conditions to get comfortable with the pace and complexity.

Encouraging your child to explain how they solved a question, even when they get it right, helps solidify their understanding and builds their confidence.

Crack Challenging Maths Questions with Confidence!

At Elixir Academy, we know how intimidating the PSLE math paper can be.

Our experienced tutors guide students through challenging PSLE maths questions with patience and proven strategies.

We cover everything—from fraction of a quantity, to ratio of, to area and perimeter questions commonly found on the PSLE paper.

Our goal is to make the entire PSLE maths experience less stressful and more manageable for your child.

With personalised coaching and a step-by-step approach, we can help your child feel ready, confident, and capable.

Contact us today to help your child master tough maths problems and succeed in PSLE Maths!