Common PSLE Math Question Types In Singapore (With Strategies & Practice)

PSLE Math in Singapore can feel very “standard”, but also very tricky at the same time.

You’ve probably heard this from teachers, seniors, or even your parents:

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“The questions are all common types… but the wording can really trap you.”

This article is for you if:

• You’re in Primary 5–6 and aiming to be ready for PSLE Math
• You keep getting stuck on certain problem sums
• You want clear strategies, not just more practice papers

I’ll walk you through common PSLE Math question types, how to think about them, and how to practise them properly — including some harder variants that often appear in Paper 2.

Whenever you want instant practice or step-by-step solutions, you can also jump straight into Tutorly’s PSLE Math tutor here:
👉 https://tutorly.sg/ai-tutor-singapore
👉 https://tutorly.sg/app

Tutorly.sg is a 24/7 AI tutor website built for Singapore students, aligned to the MOE syllabus. It’s been mentioned on Channel NewsAsia (CNA) and used by thousands of students in Singapore, especially around PSLE season.

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Step-by-step tutorial

Let’s go through the big, common PSLE Math question types you must be comfortable with:

1. Whole number & fraction word problems (including units and ratios)
2. Model drawing questions (part–whole, comparison, before–after)
3. Ratio and percentage problems
4. Rate, time, and speed questions
5. Age and “years later/ago” problems
6. Geometry & area/perimeter word problems
7. Heuristic-type questions (guess & check, work backwards, etc.)

We’ll keep each section:

• Focused on how to think
• With at least one worked example
• With specific exam tips

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1. Whole Number & Fraction Word Problems

These are everywhere in PSLE Paper 2. Often they look simple, but they hide multiple steps.

Key ideas

• Identify what 1 unit represents $or what 1 fraction means$.
• Decide if you need to find the whole, find a part, or compare two parts.
• Translate words like “more than”, “less than”, “remainder”, “shared equally”.

Example 1: Fraction of a whole

A tank was $\frac{3}{5}$ full of water. After 48 litres of water were added, it became $\frac{4}{5}$ full.
(a) What is the capacity of the tank?
(b) How much water was in the tank at first?

Step-by-step thinking:

1. The difference between $\frac{4}{5}$ and $\frac{3}{5}$ is $\frac{1}{5}$.
2. This $\frac{1}{5}$ of the tank corresponds to 48 litres.
3. So 1 unit (or $\frac{1}{5}$) = 48 L.
   The whole $5 units$ = $5 \times 48 = 240$ L.
4. At first, it was $\frac{3}{5}$ full:
   $3 \times 48 = 144$ L.

Answer:

• (a) 240 L
• (b) 144 L

Exam tip:
When you see a “before” and “after” fraction of the same whole, always check if you can find 1 unit from the difference.

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2. Model Drawing Questions

Model drawing is still very important in upper primary. It helps you visualise part–whole and comparison relationships.

Common model types

• Part–whole: One whole broken into parts (e.g. $A + B =$ total)
• Comparison: One amount is more/less than another
• Before–after: Something changes (e.g. “gave away”, “added”, “shared”)

Example 2: Comparison model

Ali has 48 marbles. He has 3 times as many marbles as Ben.
(a) How many marbles does Ben have?
(b) How many more marbles must Ben receive so that he has the same number of marbles as Ali?

Step-by-step thinking:

1. “Ali has 3 times as many as Ben”

   • Let Ben = 1 unit
   • Ali = 3 units
   • Total units = 4 units

2. Ali = 3 units = 48 marbles
   So 1 unit = $48 \div 3 = 16$ marbles.

3. (a) Ben = 1 unit = 16 marbles.

4. (b) To have the same as Ali $48$, Ben must receive
   $48 - 16 = 32$ marbles.

Answer:

• (a) 16
• (b) 32

Exam tip:
Whenever you see “times as many” or “more than/less than”, draw the model first before trying to compute.

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3. Ratio and Percentage Problems

These are extremely common in PSLE, often combined with “before–after” stories.

Core ideas

• Ratio is just units.
• You can change ratios by:
  • Adding or removing from one side
  • Adding the same amount to both sides
• Percentages can often be converted to fractions or ratios.

Example 3: Changing ratio (before–after)

The ratio of the number of boys to girls in a class is 3 : 5.
When 4 more boys join the class, the ratio becomes 1 : 1.
How many pupils are there in the class in the end?

Step-by-step thinking:

1. Let original boys : girls = 3 u : 5 u.

2. After 4 boys join, boys become $(3 u + 4)$, girls still $5 u$.
   New ratio: $3 u + 4 : 5 u = 1 : 1$.

3. So $3 u + 4 = 5 u$
   $5 u - 3 u = 4$
   $2 u = 4$
   $u = 2$.

4. Original boys = $3 u = 6$
   Original girls = $5 u = 10$

5. After 4 more boys join:
   Boys = $6 + 4 = 10$
   Girls = 10

6. Total pupils in the end = $10 + 10 = 20$.

Answer: 20 pupils

Exam tip:
When ratios change after adding or removing people, convert the final ratio into an equation using units.

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4. Rate, Time, and Speed Questions

These often appear as distance-speed-time or work-rate problems.

Key formulas

• $\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
• $\text{Distance} = \text{Speed} \times \text{Time}$
• $\text{Time} = \dfrac{\text{Distance}}{\text{Speed}}$

Example 4: Simple speed question

A cyclist travels 18 km in 45 minutes at a constant speed.
(a) What is his speed in km/h?
(b) How far will he travel in 2 hours at this speed?

Step-by-step thinking:

1. Convert 45 minutes to hours:
   $45 \text{ min} = \frac{45}{60} = 0.75$ hours.

2. Speed $= \dfrac{18}{0.75} = 24$ km/h.

3. In 2 hours at 24 km/h:
   Distance $= 24 \times 2 = 48$ km.

Answer:

• (a) 24 km/h
• (b) 48 km

Exam tip:
Always standardise units first, especially minutes to hours and metres to kilometres.

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5. Age and “Years Later/Ago” Problems

These look confusing because of the wording, but they are usually about constant difference or constant ratio.

Example 5: Age with ratio

The ratio of Ali’s age to his sister’s age is 3 : 5.
In 6 years’ time, the sum of their ages will be 40.
How old is Ali now?

Step-by-step thinking:

1. Let Ali = 3 u, Sister = 5 u now.
   Total now = $3 u + 5 u = 8 u$.

2. In 6 years’ time, each gets 6 years older:
   Ali: $3 u + 6$
   Sister: $5 u + 6$
   Total = $3 u + 6 + 5 u + 6 = 8 u + 12$.

3. We’re told this total is 40:
   $8 u + 12 = 40$
   $8 u = 28$
   $u = 3.5$.

4. Ali now = $3 u = 3 \times 3.5 = 10.5$ years.

This looks odd because age is usually a whole number. A more PSLE-style question would be set up so $u$ is a whole number. But the method is what matters.

Exam tip:

• Draw a simple timeline: “Now” and “In X years” / “X years ago”.
• Keep track of how many times you add or subtract that number.

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6. Geometry & Area/Perimeter Word Problems

These are not just about formulas; they often mix with fractions, ratios, or units.

Common topics

• Rectangles and squares (area, perimeter)
• Composite figures $L-shapes, combined shapes$
• Fractions of area shaded

Example 6: Composite figure

A rectangular garden is 12 m long and 8 m wide.
A square flower bed of side 4 m is placed inside the garden.
Find the area of the garden not occupied by the flower bed.

Step-by-step thinking:

1. Area of garden = $12 \times 8 = 96 \text{ m}^2$
2. Area of square bed = $4 \times 4 = 16 \text{ m}^2$
3. Unoccupied area = $96 - 16 = 80 \text{ m}^2$

Answer: $80 \text{ m}^2$

Exam tip:
For composite shapes, break them into basic shapes (rectangles, squares, triangles), find each area, then add or subtract.

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7. Heuristic-type Questions

These are the ones students often call “tricky problem sums”. They test how you think, not just your formulas.

Common heuristics:

• Draw a diagram or model
• Guess and check (systematically)
• Work backwards
• Use before–after tables

Example 7: Work backwards

Peter had some money. He spent $\frac{1}{3}$ of it on a book and $12$ dollars on a pen. He had $28$ dollars left. How much money did he have at first?

Step-by-step thinking:

1. Let the original amount be $x$.

2. He spent $\frac{1}{3}x$ on a book and $12$ on a pen.
   Left with $28$:
   $x - \frac{1}{3}x - 12 = 28$

3. Simplify:
   $x - \frac{1}{3}x = \frac{2}{3}x$
   So $\frac{2}{3}x - 12 = 28$

4. Move 12 over:
   $\frac{2}{3}x = 40$
   $x = 40 \times \frac{3}{2} = 60$

Answer: He had $60 at first.

Exam tip:
If the story ends with “left with ___”, consider working backwards:
Final amount → Undo each step → Original amount.

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Exam strategy guide

Now that you’ve seen the common types, let’s talk about how to handle them under exam conditions, especially for PSLE Paper 2.

“Access more than 1000+ past year papers to practice”
👉 Start a paper today and test yourself like it’s the real exam.

1. Prioritise question types you’re strong in

During revision:

• List out topics (fractions, ratio, percentage, speed, geometry, etc.).
• Mark:
  • ✅ Confident
  • ⚠️ Sometimes careless
  • ❌ Often stuck

Focus first on turning ⚠️ into ✅. These are usually the fastest marks to gain.

During the exam:

• Start with questions you recognise and know how to start.
• Don’t waste 10 minutes staring at one strange question while leaving easier ones behind.

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2. Use a fixed “problem sum routine”

For each word problem, follow a consistent routine:

1. Underline key information

   • Numbers, units, phrases like “twice”, “remainder”, “ratio becomes”.

2. Decide the topic

   • Is this fractions? Ratio? Speed? Area?
   • This tells you which strategies to use.

3. Choose a representation

   • Model, table, or equation.

4. Plan the steps

   • Ask: “What must I find first?”
   • Many questions need an intermediate step $e.g. find 1 unit first$.

5. Check units and reasonableness

   • Is the answer too big or too small?
   • Are the units correct (kg vs g, km vs m, hours vs minutes)?

Using the same routine reduces panic and careless mistakes.

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3. Time management for PSLE Math

Rough guideline $for Paper 2, 1 h 20min$:

• Q 1–5 (short questions): ~1–2 min each
• Mid-level questions: ~3–4 min each
• Last few harder questions: up to 6–8 min each

If you are:

• Stuck for more than 2–3 minutes with no progress, put a small mark, move on, and come back later.
• Almost done but stuck on final step, write down what you know clearly. Sometimes you can get method marks even if the final answer is wrong.

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4. Learn from your own mistakes (properly)

Don’t just mark right/wrong and move on.

For every mistake, ask:

1. What type of question was this?
   (e.g. ratio before–after, speed, fraction of remainder)

2. What went wrong?

   • Misread the question?
   • Wrong model?
   • Algebra error?
   • Careless calculation?

3. What will I do differently next time?

   • Draw a model first
   • Write units at every step
   • Highlight key phrases

You can even keep a “Mistake Book”:
Write down the question, your wrong working, and the corrected solution. Review it weekly.

If you’re practising online, you can copy tricky questions into Tutorly and ask it to re-teach the method step-by-step:
👉 https://tutorly.sg/ai-tutor-singapore

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5. Use Tutorly.sg smartly for PSLE Math

Since Tutorly.sg is built for the MOE syllabus and used widely by Singapore students, here’s how you can make it work for you:

• After school or tuition, when you’re doing homework or practice papers and get stuck on a question, paste it into Tutorly.
• It will:
  • Check your final answer
  • Show you a step-by-step solution
  • Explain the concept in Primary-level language
• You can then ask follow-up questions like:
  • “Can you show this using a model method instead?”
  • “What if the ratio is changed differently?”

Because it’s available 24/7 and it’s a website (not a mobile app), you can use it on a laptop or tablet at home without needing to download anything:
👉 https://tutorly.sg/app

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Worksheet practice

Here are some practice questions arranged by type, with a mix of standard and harder variants $PSLE-style$. Try them on your own first, then check the solutions.

You can also paste any of these into Tutorly.sg to see a detailed solution and alternative methods.

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A. Fractions & Remainders

Q 1 (Standard)

A box contains 120 sweets. $\frac{2}{5}$ of them are strawberry-flavoured and the rest are orange-flavoured.
(a) How many sweets are strawberry-flavoured?
(b) How many are orange-flavoured?

Solution outline:

• $\frac{2}{5} \times 120 = 48$ strawberry
• Orange = $120 - 48 = 72$

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Q 2 (Harder – remainder type)

A baker had some cupcakes. He sold $\frac{3}{8}$ of them in the morning and $\frac{1}{4}$ of the remainder in the afternoon. He had 90 cupcakes left.
How many cupcakes did he have at first?

Step-by-step solution:

1. Let original number = $x$.

2. Morning: sold $\frac{3}{8}x$, left with $x - \frac{3}{8}x = \frac{5}{8}x$.

3. Afternoon: sold $\frac{1}{4}$ of remainder:
   Sold $\frac{1}{4} \times \frac{5}{8}x = \frac{5}{32}x$.
   Left with:
   $\frac{5}{8}x - \frac{5}{32}x = \frac{20}{32}x - \frac{5}{32}x = \frac{15}{32}x$

4. This equals 90:
   $\frac{15}{32}x = 90$
   $x = 90 \times \frac{32}{15} = 192$

Answer: 192 cupcakes

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B. Ratio & Before–After

Q 3 (Standard)

The ratio of red beads to blue beads is 5 : 3. There are 24 more red beads than blue beads.
How many beads are there altogether?

Solution outline:

1. Difference in ratio units = $5 - 3 = 2$ units.
2. 2 units = 24 → 1 unit = 12.
3. Red = $5 \times 12 = 60$
   Blue = $3 \times 12 = 36$
4. Total = $60 + 36 = 96$ beads.

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Q 4 (Harder – both sides change)

At first, the ratio of the number of boys to girls in a hall was 4 : 7. After 6 boys left and 8 girls entered the hall, the ratio became 2 : 5.
How many pupils were there in the hall at first?

Step-by-step solution:

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1. Let original boys : girls = $4 u : 7 u$.

2. After changes:
   Boys = $4 u - 6$
   Girls = $7 u + 8$
   New ratio = $2 : 5$

3. Form equation:
   $\frac{4 u - 6}{7 u + 8} = \frac{2}{5}$

4. Cross-multiply:
   $5(4 u - 6) = 2(7 u + 8)$
   $20 u - 30 = 14 u + 16$
   $20 u - 14 u = 16 + 30$
   $6 u = 46$
   $u = \frac{46}{6} = \frac{23}{3}$

This gives a fraction, which is unusual for a pure-ratio question. A more exam-typical version would be set so $u$ is whole. But the algebraic method is correct: cross-multiply and solve.

To practise a nicer-number version, you can change the numbers $e.g. “After 8 boys left and 6 girls entered, the ratio became 3 : 5”$ and try again, or ask Tutorly to generate similar questions with whole-number answers.

Exam learning point:
The method — setting up and solving the ratio equation — is what PSLE tests, not just the final number.

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C. Speed & Time

Q 5 (Standard)

A car travels at a constant speed of 72 km/h.
(a) How far will it travel in 20 minutes?
(b) How long will it take to travel 30 km?

Solution outline:

(a) 20 minutes = $\frac{1}{3}$ hour
Distance $= 72 \times \frac{1}{3} = 24$ km

(b) Time $= \dfrac{30}{72}$ hours
Simplify: $\dfrac{5}{12}$ hour = $25$ minutes.

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Q 6 (Harder – two moving objects)

John and Mary started walking towards each other from two towns 24 km apart. John walked at 4 km/h and Mary walked at 2 km/h.
How long did they take to meet?

Step-by-step solution:

1. Combined speed = $4 + 2 = 6$ km/h.
2. Distance between them = 24 km.
3. Time $= \dfrac{\text{Distance}}{\text{Combined speed}} = \dfrac{24}{6} = 4$ hours.

Answer: 4 hours

Exam tip:
When two people move towards each other, add their speeds.

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D. Geometry & Area

Q 7 (Standard)

A rectangle has a length of 15 cm and a width of 7 cm.
(a) Find its perimeter.
(b) Find its area.

Solution outline:

(a) Perimeter $= 2(15 + 7) = 44$ cm
(b) Area $= 15 \times 7 = 105 \text{ cm}^2$

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Q 8 (Harder – fraction of area)

A rectangular piece of cardboard is 30 cm long and 18 cm wide. One-third of the length is cut off.
(a) What is the area of the remaining piece of cardboard?
(b) What fraction of the original area is this?

Step-by-step solution:

1. Original area = $30 \times 18 = 540 \text{ cm}^2$.

2. One-third of the length is cut off:
   Length cut off = $\frac{1}{3} \times 30 = 10$ cm.
   Remaining length = $30 - 10 = 20$ cm.
   Width remains 18 cm.

3. Area of remaining piece = $20 \times 18 = 360 \text{ cm}^2$.

4. Fraction of original area:
   $\frac{360}{540} = \frac{2}{3}$

Answer:

• (a) $360 \text{ cm}^2$
• (b) $\frac{2}{3}$ of the original area

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E. Mixed Heuristics

Q 9 (

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