14 Common PSLE Math Questions

PSLE Math often feels unpredictable to parents and students alike. However, the examination actually follows a rigid structure. From the infamous “Helen and Ivan” coins question to standard remainder concepts, the same question types appear annually, just with different numbers and contexts.

This guide breaks down the essential problem types your child must master to secure an AL1. By understanding these 14 specific categories, you can shift your focus from worrying about random “killer” questions to mastering proven patterns.

The “Big Three”: Fractions, Ratios, and Percentages

These three topics form the backbone of the PSLE Math syllabus. They are often interchanged in word problems, but the underlying methods to solve them remain consistent.

1. The Remainder Concept

This is arguably the most common type of fraction question in Paper 2. Students often confuse a “fraction of the total” with a “fraction of the remainder.”

How to spot it:
Look for keywords like “remaining” or “remainder.”

• Example: “John spent 1/3 of his money on a bag. He then spent 1/4 of the remainder on a shirt.”

The Strategy:
There are two ways to handle this: the Branching Method or the Model Method.

• Branching: Draw a “tree” diagram. The first branch splits the total into “Spent” and “Remainder.” The second branch splits the Remainder into further sections. This prevents the student from accidentally calculating 1/4 of the total instead of the remainder.
• Model Drawing: Draw a long bar for the total. Cut 1/3. Focus only on the remaining 2/3. Cut that remaining portion into 4 parts (based on the denominator of the second fraction).

2. The Equal Fractions Concept

This question type tests a student’s ability to compare two different quantities based on a commonality.

How to spot it:
The question equates parts of two different totals.

• Example: “2/5 of Ali’s money is equal to 3/4 of Ben’s money.”

The Strategy:
The goal is to make the numerators the same.

1. Find the Lowest Common Multiple (LCM) of the numerators (2 and 3). The LCM is 6.
2. Convert the fractions:
   • Ali: 2/5 becomes 6/15.
   • Ben: 3/4 becomes 6/8.
3. Once the numerators (the parts they have in common) are equal, the denominators represent the total units each person has.
4. Ratio of Ali to Ben = 15 : 8.

3. The Repeated Identity

In this scenario, a single variable (a person or an item) appears in two different ratios or comparisons, linking them together.

How to spot it:

• Example: “The ratio of A:B is 2:3. The ratio of B:C is 4:5.”
• Here, ‘B’ is the repeated identity.

The Strategy:
You cannot simply combine the numbers because ‘B’ has a value of 3 in the first ratio and 4 in the second.

1. Find the LCM of B’s units (LCM of 3 and 4 is 12).
2. Scale up both ratios so B is 12 in both.
   • A:B becomes 8:12 (multiplied by 4).
   • B:C becomes 12:15 (multiplied by 3).
3. Combine: A : B : C = 8 : 12 : 15.

Heuristics-Based “Logic” Questions

These questions often panic students because they don’t seem to have a standard formula. However, they rely on specific logical heuristics. These are among the most difficult PSLE questions.

4. The Assumption Method (Supposition)

This is a classic PSLE staple. It usually involves two items with different “values” (like number of legs, cost, or value) and a fixed total.

How to spot it:

• Example: “There are 20 animals on a farm, consisting of chickens and cows. There are 56 legs in total.”
• Example: “Helen and Ivan have a mix of 50-cent and 20-cent coins…”

The Strategy:
Do not use “Guess and Check”, it takes too long. Use Assumption.

1. Assume all 20 animals are the one with fewer legs (chickens).
2. Calculate the total legs: 20 x 2 = 40 legs.
3. Find the Gap: Real total (56) – Assumed total (40) = 16 legs.
4. Divide the Gap by the Difference per item (Cow has 4 legs, Chicken has 2 legs, difference is 2).
5. 16 / 2 = 8. This is the number of Cows.

5. Working Backwards

This heuristic is used when the starting number is unknown, but the final result and the sequence of events are provided.

How to spot it:

• Example: “A bus left the interchange. At Stop A, 1/2 the passengers got off and 5 got on. At Stop B… In the end, there were 20 people.”

The Strategy:
Start from the final number (20) and reverse every operation step-by-step up to the start.

• If the question says “Plus 5”, you “Minus 5”.
• If the question says “Multiplied by 2”, you “Divide by 2”.
• If the question says “1/2 got off”, it means 1/2 remained. You multiply by 2 to get the previous total.

6. The Grouping Concept

This concept involves grouping items into sets to find a total value or quantity.

How to spot it:

• Example: “Packets of 3 pens cost $5. Packets of 2 pens cost $4. John paid $44. How many pens did he buy?”

The Strategy:

1. Create one “Group” containing one set of each item.
   • One Group = (3 pens + 2 pens) = 5 pens.
   • Cost of One Group = ($5 + $4) = $9.
2. Take the Total Cost ($44) and divide it by the Cost of One Group ($9) to find how many groups there are.
   • Note: If it doesn’t divide evenly, there is a remainder to handle.
3. Multiply the number of groups by the number of pens in one group.

Advanced Word Problems (The “Killer” Types)

These questions usually appear in the 4 or 5-mark sections of Paper 2. They require identifying what stays the same (the constant).

7. Constant Total (Internal Transfer)

This occurs when items are moved between two parties, but nothing is added or removed from the system entirely.

How to spot it:

• Example: “Ali gave 20 marbles to Ben. In the end, they had an equal number of marbles.”

The Strategy:
The Total number of marbles before the transfer and after the transfer is the same.

1. Draw a model or write a ratio for “Before” and “After”.
2. Make the Total Units in the ratio equivalent.
3. Compare the change in units for Ali (or Ben) to the actual number transferred (20 marbles) to find the value of 1 unit.

8. Constant Difference (Age Difference)

This is most commonly seen in age problems, but can apply to other scenarios where equal amounts are added to or subtracted from both sides.

How to spot it:

• Example: “Mr Tan is 40 years old and his son is 10. In how many years will Mr Tan be 3 times as old as his son?”

The Strategy:
The Difference in age between two people never changes.

1. Calculate the age difference (40 – 10 = 30 years).
2. In the future ratio (3:1), the difference between the units (3u – 1u = 2u) must represent that 30-year gap.
3. 2 units = 30 years. 1 unit = 15 years.
4. Solve for the required age.

9. One Item Unchanged (Constant Part)

Here, an action affects one variable while the other remains untouched.

How to spot it:

• Example: “A box had an equal number of red and blue balls. 20 red balls were added. The ratio of red to blue became 3:1.”

The Strategy:
Identify the variable that did not change (Blue balls).

1. Look at the “Before” ratio (1:1) and “After” ratio (3:1).
2. The units for Blue must be the same in both. In this case, they are already 1.
3. Compare the change in Red units. Red went from 1 unit to 3 units.
4. The increase (2 units) represents the 20 balls added.

Geometry and Measurement Challenges

Geometry questions often rely on visualising shapes in ways that aren’t immediately obvious.

10. Folded Angles and Shapes

Paper folding questions test the understanding of properties before and after folding.

How to spot it:
A diagram shows a rectangular or triangular piece of paper with a corner folded over.

The Strategy:
The key principle is Congruency.

• The folded part is identical to the original part it came from.
• This means the angles and side lengths are exactly the same.
• Students should mark out equal angles immediately (e.g., x=x, y=y) 
• and look for “Z-angles” (alternate angles) if the paper is rectangular (parallel sides).

11. Composite Figures (Circles and Squares)

These questions ask for the area or perimeter of strange, irregular shapes formed by overlapping quadrants, semi-circles, and squares.

How to spot it:
The shape looks like a “rugby ball” or a “leaf” pattern inside a square.

The Strategy:
Use the “Cut and Paste” method.

• Often, the weird shape is just a standard shape rearranged.
• Visualise cutting a semi-circle from one side and pasting it into a gap on the other side to form a complete square or rectangle.
• Never try to calculate the area of the irregular shape directly unless you can decompose it into squares and quadrants.

12. Volume with Rate of Flow

These combine volume calculations with rate/speed concepts.

How to spot it:

• Example: “Tap A fills the tank in 10 mins. Tap B empties it in 5 mins. Both taps are turned on…”

The Strategy:
Do not subtract the minutes. You must work with the Rate per Minute.

1. Tap A fills 1/10 of the tank per minute.
2. Tap B empties 1/5 of the tank per minute.
3. Find the net flow per minute (1/10 – 1/5).
4. Use the net flow to calculate how long it takes to reach the desired water level.

High-Level Thinking Questions

These distinguish the AL1 students from the AL3 students.

13. Number Patterns

Students are given a sequence of numbers or a growing pattern of shapes and asked to find the value for Figure 100 or Figure n.

The Strategy:

1. Look for a Constant Difference. If the pattern increases by 3 each time (4, 7, 10…), the formula involves 3n.
2. Look for Square Numbers. If the pattern is 1, 4, 9, 16, the formula involves n×n.
3. Look for Triangular Numbers (Sum of consecutive numbers).
4. Create a table with three columns: Pattern Number, Total Value, and “How we got there.”

14. Speed (Catching Up and Meeting)

Speed questions in PSLE often involve two objects moving relative to each other.

How to spot it:

• Example: “Train A leaves at 8am. Train B leaves at 9am at a faster speed. When will B catch up with A?”

The Strategy:
Draw a Distance-Time Line Diagram. This is non-negotiable for clarity.

1. Calculate the “Head Start” distance (how far Train A travelled between 8am and 9am).
2. Calculate the “Catch Up Speed” (Difference in speed between B and A).
3. Time taken to catch up = Head Start Distance / Catch Up Speed.

Conclusion On Common PSLE Math Questions

Success in PSLE Math is not about luck; it is about pattern recognition. By identifying these 14 common question types, students can apply the correct heuristic immediately, saving time and reducing stress. Consistent practice on these specific categories is the most efficient way to revise, rather than blindly drilling random test papers.

Is your child struggling to identify these patterns? Let our specialists at Tutify help them decode the paper. Contact us today for a consultation.

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Frequently Asked Questions About Common PSLE Math Questions

What are the hardest topics in PSLE Math?

Generally, students find “Speed,” “Volume with Rate of Flow,” and “Advanced Geometry” (involving circles and composite figures) the most challenging. However, word problems involving “Ratio” and “Percentage” with multiple step changes (like the “Constant Total” or “Everything Changed” concepts) are often where high-achieving students lose marks due to carelessness or conceptual errors.

How do I identify which heuristic method to use?

You identify the method by looking for keywords. If the question gives a “Total” and two items with different values, use Assumption. If the question involves moving items between two people with no external addition, use Constant Total. If the question gives the final answer and asks for the start, use Working Backwards. We recommend creating a “cheat sheet” of these keywords during revision.

Is the “Helen and Ivan” question likely to appear again?

The exact “Helen and Ivan” question (based on mass of coins) will likely not appear exactly as it was, but the concept behind it, which is Assumption or Supposition, appears almost every year. The PSLE recycles concepts, not specific numbers. Preparing for the Assumption method ensures your child can answer any variation of that question.

What is the weightage of Paper 1 vs Paper 2 in PSLE Math?

Paper 1 (Booklet A and B) accounts for 45% of the total score and prohibits calculators. It focuses on speed, accuracy, and foundational concepts. Paper 2 accounts for 55% of the score, allows calculators, and contains the longer, more complex problem sums and heuristic questions. Scoring well in Paper 1 is crucial for building a safety net for the harder Paper 2.

How can I help my child if I am bad at Math?

You do not need to be a Math expert to help. Focus on helping your child identify the type of question rather than solving it for them. Ask questions like, “Is this a remainder concept?” or “Is the total constant here?” Using the Model Method is also a visual way to learn alongside your child, as it relies less on algebra and more on drawing blocks to represent numbers.

Where can I find past year PSLE Math papers for practice?

Past year PSLE Math papers are available at major bookstores in Singapore, usually published by approved publishers. Additionally, many parents use “Top School Papers” (preliminary exams from schools like Nanyang, Raffles, etc.), which are widely available online or at neighbourhood printing shops. These are excellent for exposing students to a variety of question types.