Mental Math Tricks Singapore Students Can Use To Boost Speed And Accuracy

If you’re doing N(A), N(T), or Express stream in secondary school, you already know this:

In Math exams, speed matters.

“Stuck on a question? See simple explanations that help you understand fast.”
👉 Give it a try and turn confusion into clarity in minutes.

Not just speed in punching the calculator, but speed in thinking — estimating, spotting patterns, and checking if an answer is obviously wrong. That’s where mental math becomes your secret weapon.

This guide is written for Secondary / O Level students in Singapore. I’ll walk you through:

• A step-by-step mental math tutorial (with examples you’ll actually see in school)
• How to use these tricks in O Level–style questions
• Practice questions (including harder variants)
• Common mistakes Singapore students make
• How to use Tutorly.sg to drill these skills anytime, even at 1am before your paper

Tutorly.sg is a 24/7 AI tutor website (not an app) built specifically for the MOE syllabus, from Lower Sec all the way to O Levels and A Levels. It’s been used by thousands of students in Singapore and even mentioned on Channel NewsAsia (CNA), so you’re not experimenting with something random.

You can try it here:

• Main AI tutor page: https://tutorly.sg/ai-tutor-singapore
• Direct access to the web app: https://tutorly.sg/app

Let’s start with the actual tricks.

---

Step-by-step tutorial

We’ll focus on mental math that actually helps in Secondary / O Level topics:

• Algebra (simplifying, expanding, factorising)
• Percentages and ratio
• Speed & time, rate questions
• Basic statistics
• Geometry and area/perimeter/volume

1. Fast multiplication tricks you’ll actually use

(a) Multiplying by 5, 25 and 50

You see things like $5\%$, $25\%$, $50\%$ everywhere (discounts, GST, profit & loss, etc.). If you can multiply by 5, 25, 50 quickly, you save a lot of time.

Multiply by 5

• Trick: Multiply by 10, then divide by 2.

Examples:

• $38 \times 5$
  $38 \times 10 = 380$
  $380 \div 2 = 190$

• $126 \times 5$
  $126 \times 10 = 1260$
  $1260 \div 2 = 630$

You can do this in your head much faster than punching every digit.

Multiply by 50

• Trick: Multiply by 100, then divide by 2.

Example:

• $46 \times 50$
  $46 \times 100 = 4600$
  $4600 \div 2 = 2300$

Multiply by 25

• Trick: Multiply by 100, then divide by 4.

Example:

• $72 \times 25$
  $72 \times 100 = 7200$
  $7200 \div 4 = 1800$

You’ll see this a lot in percentage of an amount questions. If you can do $25\%$ of something quickly, you can also find $75\%$ (just 3 × $25\%$) etc.

---

(b) Squaring numbers ending in 5

Useful for checking algebra answers like $(x+5)^2$ or $(15)^2$, $(25)^2$, $(35)^2$, etc.

Pattern:
For any number ending in 5, say $n 5$ (where $n$ is the digit/number before 5):

1. Multiply $n$ by $(n+1)$
2. Put “25” behind

Examples:

• $15^2$
  $n = 1$
  $1 \times 2 = 2$
  Answer: $225$

• $25^2$
  $n = 2$
  $2 \times 3 = 6$
  Answer: $625$

• $35^2$
  $n = 3$
  $3 \times 4 = 12$
  Answer: $1225$

This is very handy when checking if you expanded something like $(x+15)^2$ correctly.

---

(c) Multiplying numbers close to 100

You sometimes get estimation questions like:

Is $98 \times 103$ closer to 9000 or 10000?

There’s a neat trick for numbers around 100:

If you have $(100 - a)(100 + b)$, then:

$(100 - a)(100 + b) = 10000 + 100(b - a) - ab$

But you don’t even need the full formula if $a$ and $b$ are small.

Example: $98 \times 103$

• $98 = 100 - 2$
• $103 = 100 + 3$

Approximate first:

• $100 \times 103 = 10300$
• But we removed $2 \times 103 = 206$

So:

• $10300 - 206 = 10094$

In an exam, for MCQ, you only need to know it’s slightly above $10000$, so you can already choose the right option quickly.

---

2. Percentages and fraction tricks

O Level Paper 1 loves to throw quick percentage questions at you. Here are some mental shortcuts.

(a) Turning common fractions into percentages (and back)

Memorise these:

• $\frac{1}{2} = 50\%$
• $\frac{1}{3} \approx 33.3\%$
• $\frac{2}{3} \approx 66.7\%$
• $\frac{1}{4} = 25\%$
• $\frac{3}{4} = 75\%$
• $\frac{1}{5} = 20\%$
• $\frac{2}{5} = 40\%$
• $\frac{3}{5} = 60\%$
• $\frac{4}{5} = 80\%$
• $\frac{1}{8} = 12.5\%$
• $\frac{3}{8} = 37.5\%$
• $\frac{5}{8} = 62.5\%$
• $\frac{7}{8} = 87.5\%$

These appear a lot in discount, profit/loss, GST questions and in probability.

Example:

A shop gives a $\frac{3}{8}$ discount on an item. What percentage discount is this?

If you already know $\frac{3}{8} = 37.5\%$, you answer almost instantly.

---

(b) Fast percentage of an amount

Instead of doing:

$17\%$ of $240$

You can break it:

• $10\%$ of $240 = 24$
• $5\%$ of $240 = 12$
• $2\%$ of $240 = 4.8$

So:

• $17\%$ of $240 = 10\% + 5\% + 2\% = 24 + 12 + 4.8 = 40.8$

Train yourself to get $10\%$, $5\%$, $1\%$ quickly:

• $10\%$ = move decimal 1 place left
• $1\%$ = move decimal 2 places left
• $5\%$ = half of $10\%$

From there, you can build up any weird percentage like $17\%$, $23\%$, $37\%$ etc.

---

3. Mental shortcuts for algebra

You can’t “mental math” full algebra questions, but you can speed up:

• Simplifying
• Checking if your answer is reasonable
• Basic substitution

(a) Spotting perfect squares and cubes

When you see things like:

• $\sqrt{196}$
• $\sqrt{225}$
• $\sqrt{400}$
• $\sqrt[3]{125}$

It helps if you can recognise them instantly:

• $196 = 14^2$
• $225 = 15^2$
• $400 = 20^2$
• $125 = 5^3$

Memorise at least:

• Squares from $1^2$ to $25^2$
• Cubes from $1^3$ to $10^3$

This helps in:

• Surds
• Pythagoras’ theorem
• Area/volume questions
• Simplifying indices and roots

You don’t need to sit there and calculate $17 \times 17$ if you already know $289$.

---

(b) Fast substitution checks

For questions like:

Given $y = 3 x - 4$, find $y$ when $x = 7$.

You should be able to do:

• $3 \times 7 = 21$
• $21 - 4 = 17$

…in your head.

To get faster:

• Practise your 3, 4, 6, 7, 8, 9 times tables until they are instant.
• When multiplying 2-digit by 1-digit (e.g. $14 \times 7$), break it:
  • $14 \times 7 = (10 \times 7) + (4 \times 7) = 70 + 28 = 98$

This is especially useful in linear functions, gradient-intercept form, and sequences.

---

4. Ratio and rate questions

Many Secondary and O Level questions are basically ratio + basic arithmetic disguised in a long story.

(a) Ratio scaling

Example:

The ratio of boys to girls is $3 : 5$. If there are 45 girls, how many boys?

Think:

• $5$ units → $45$
• $1$ unit → $45 \div 5 = 9$
• $3$ units → $3 \times 9 = 27$

Try to do the division and multiplication mentally:

• $45 \div 5 = 9$ (because $9 \times 5 = 45$)
• $9 \times 3 = 27$

This comes up in:

• Mixture questions
• Sharing cost/profit
• Map scales

---

(b) Speed, time, distance

Basic formula:

$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$

You don’t always need a calculator if numbers are nice.

Example:

A car travels 150 km in 3 hours. Find its average speed.

• $150 \div 3 = 50$
  So speed = $50 \text{ km/h}$.

If you practise dividing numbers like $120, 150, 180, 240$ by $2,3,4,5,6$, you’ll be much faster in Paper 1.

---

Exam strategy guide

Mental math is not about showing off. It’s about saving time and avoiding careless mistakes in your O Level and school exams.

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

Here’s how to use these tricks strategically.

1. Know when NOT to use the calculator

In O Level Math (both E Math and A Math):

• Paper 1: No calculator. Mental math and written working are everything.
• Paper 2: Calculator allowed, but mental checks still help.

For Paper 1:

• Use mental math for:
  • Simple fractions and percentages
  • $1$–$2$ digit multiplications
  • Estimations
• Reserve written working for:
  • Long division
  • Multi-step algebraic manipulation
  • Complicated fractions

For Paper 2 (calculator allowed):

• Use mental math to:
  • Estimate the answer before you key into the calculator
  • Check if the calculator answer is obviously wrong (e.g. negative area, absurdly large percentage)
  • Decide between MCQ options quickly

---

2. Use estimation as a “sanity check”

Before you commit to an answer, ask yourself:

Roughly, should this be small? Big? Around what number?

Example $Paper 2 style$:

A shirt costs $48 before GST. GST is $8\%$. Find the price after GST.

Estimation:

• $10\%$ of $48$ is $4.80$
• So $8\%$ should be slightly less than $4.80$, maybe around $3.80$
• So final answer should be around $48 + 4 = 52$

If your calculator gives you something like $84, you know you typed something wrong.

---

3. Time management using mental math

In an O Level E Math paper:

• You have 1 h 30min for Paper 1 $80 marks$
• Roughly 1 minute per mark

To manage time:

1. Scan the paper quickly
   Identify questions where mental math can speed you up (simple arithmetic, easy substitution, basic geometry).

2. Do the “mental-friendly” questions first
   These are usually the earlier parts (a), (b) of each question.

3. Leave calculator-heavy / algebra-heavy parts for later
   For Paper 2, you can use mental estimation to check calculator answers quickly, instead of re-doing the whole thing.

---

4. Use mental math to reduce careless errors

Common careless errors:

• Misplacing decimal points
• Copying numbers wrongly
• Forgetting to square or cube something

Before you move on from a question, do a 5-second mental check:

• Is the answer sign correct? $positive/negative$
• Is the size reasonable? (e.g. $300\%$ discount doesn’t make sense)
• Does it match the units? (cm, m, $, etc.)

This short check can save you marks, especially in Paper 1, where you can’t rely on the calculator to “look” correct.

---

5. Training like it’s exam day (with Tutorly.sg)

Mental math is a skill — you only get fast if you practise under some time pressure.

This is where Tutorly.sg is genuinely helpful:

• It’s a 24/7 AI tutor website built for Singapore’s MOE syllabus.
• You choose your level (e.g. Sec 3 Express) and subject (E Math / A Math).
• Then you can ask it things like:
  • “Give me 10 mental math questions on percentage for O Level E Math, without calculator.”
  • “Give me speed-distance-time questions that I should be able to do in my head.”

Tutorly will:

• Generate questions instantly
• Let you try them yourself
• Check your final answer
• Then show you step-by-step working, so you can see faster methods

Because it’s online at https://tutorly.sg/app, you can practise a quick 10-minute set:

• On the bus
• During breaks between tuition and CCA
• The night before tests

Over time, your brain gets used to doing these calculations faster, so by the time it’s O Levels, it feels natural.

---

Worksheet practice

Let’s go through some practice questions you can try mentally (or with minimal rough work), including some harder variants similar to what you might see in school exams or O Levels.

I’ll group them by skill. Try them first, then check the solution.

---

A. Percentages and fractions

Q 1 (Basic)

Find mentally:

1. $15\%$ of $80$
2. $35\%$ of $200$

Suggested answers (with mental steps):

1. $10\%$ of $80 = 8$
   $5\%$ of $80 = 4$
   So $15\%$ of $80 = 8 + 4 = 12$

2. $10\%$ of $200 = 20$
   $30\%$ of $200 = 3 \times 20 = 60$
   $5\%$ of $200 = 10$
   So $35\%$ of $200 = 60 + 10 = 70$

---

Q 2 (Intermediate)

A shop offers a $12.5\%$ discount on a shirt that costs $64. Find the discount amount.

Hint: $12.5\% = \frac{1}{8}$.

Solution (mental-friendly):

• $12.5\%$ of an amount = $\frac{1}{8}$ of it
• So discount = $\frac{1}{8} \times 64$
• $64 \div 8 = 8$

Discount = $8

---

Q 3 (Hard variant – O Level style)

A phone is sold at a $20\%$ discount and then a further $5\%$ discount on the reduced price. The final selling price is $456. Find the original price.

Try to do as much as possible mentally.

Solution outline:

Let original price = $x.

After $20\%$ discount:

• Price becomes $80\%$ of $x$
• So price = $0.8 x$

After another $5\%$ discount:

• New price = $95\%$ of $0.8 x$
• So final price = $0.95 \times 0.8 x = 0.76 x$

Given:

• $0.76 x = 456$

So:

• $x = \frac{456}{0.76}$

To avoid calculator, think:

• Multiply top and bottom by 100:
  $x = \frac{45600}{76}$

Now do $45600 \div 76$:

• $76 \times 600 = 45600$

So $x = 600$

Original price = $600

Notice how understanding percentages and simple mental division helps a lot here.

---

B. Ratio and rate

Q 4 (Basic)

The ratio of cats to dogs is $2 : 5$. If there are 40 dogs, how many cats are there?

Solution:

• $5$ units → $40$
• $1$ unit → $40 \div 5 = 8$
• $2$ units → $2 \times 8 = 16$

Answer: 16 cats

---

Q 5 (Intermediate)

A cyclist travels 72 km in 3 hours. Find his average speed in:

1. km/h
2. m/s $give your answer to 1 decimal place$

Solution:

1. Speed in km/h:
   $72 \div 3 = 24$
   So speed = $24 \text{ km/h}$

2. Convert to m/s:

   • $24 \text{ km/h} = 24 \times \frac{1000}{3600} \text{ m/s}$
   • Simplify $\frac{1000}{3600} = \frac{10}{36} = \frac{5}{18}$

“Doing Secondary Science? Pick a topic and practise like it’s a real exam — with clear answers right after.”
👉 Try Tutorly now and start a Science topic in seconds.

![Secondary Science topics you can practise on Tutorly.sg]$/app/blog-images/middle 2.png$

So:

• $24 \times \frac{5}{18} = \frac{24}{18} \times 5 = \frac{4}{3} \times 5 = \frac{20}{3} \approx 6.7 \text{ m/s}$

Answer: 24 km/h, 6.7 m/s (1 d.p.)

---

Q 6 (Hard variant – speed & time)

Two towns A and B are 210 km apart. A car travels from A to B at 70 km/h. Another car travels from B to A at 60 km/h at the same time. How long will it take before they meet?

Try to reason mentally.

Solution:

Combined speed (towards each other):

• $70 + 60 = 130 \text{ km/h}$

Time = $\dfrac{\text{Distance}}{\text{Speed}} = \dfrac{210}{130}$ hours

Simplify:

• $\dfrac{210}{130} = \dfrac{21}{13}$ hours

Convert to hours and minutes:

• $21 \div 13 \approx 1$ remainder $8$
• So $1$ hour and $\dfrac{8}{13}$ of an hour

Now, $\dfrac{8}{13} \text{ hour}$ in minutes:

• $1 \text{ hour} = 60$ minutes
• So $\dfrac{8}{13} \times 60 \approx \dfrac{480}{13} \approx 36.9$ minutes

So they meet after about 1 hour 37 minutes (to nearest minute).

If you had a calculator, you’d key in $210 \div 130$, but the mental structure is the same.

---

C. Squares, roots, and algebra checks

Q 7 (Basic)

Find the following without a calculator:

1. $15^2$
2. $35^2$

Solution (using “ending in 5” trick):

1. $15^2$

   • $n = 1$
   • $1 \times 2 = 2$
   • Answer: 225

2. $35^2$

   • $n = 3$
   • $3 \times 4 = 12$
   • Answer: 1225

---

Q 8 (Intermediate)

Evaluate mentally:

1. $\sqrt{196}$
2. $\sqrt[3]{125}$

Solution:

1. $\sqrt{196}$

   • Recall $14^2 = 196$
   • So answer = 14

2. $\sqrt[3]{125}$

   • Recall $5^3 = 125$
   • So answer = 5

---

Q 9 (Hard variant – algebra & estimation)

Given $y = 3 x^2 - 5 x + 2$, estimate $y$ when $x = 5$ using mental math.

Solution:

Substitute $x = 5$:

• $3 x^2 = 3 \times 25 = 75$
• $-5 x = -5 \times 5 = -25$
• Constant term = $+2$

So:

• $y = 75 - 25 + 2 = 50 + 2 = 52$

Answer: $y = 52$

In an exam, you might still write working, but being able to do the arithmetic mentally is much faster.

---

D. Mixed practice (exam-style)

Q 10 (O Level style composite question – harder)

A shop increases the price of a bag by $20\%$ and then offers a $10\%$ discount on the new price. The final selling price is $237.60.

(a) Find the original price of the bag.
(b) What is the overall percentage change from the original price?

Try to think in terms of multipliers.

Solution:

Let original price = $x.

After $20\%$ increase:

• New price = $120\%$ of $x = 1.2 x$

After $10\%$ discount:

• Final price = $90\%$ of $1.2 x = 0.9 \times 1.2 x = 1.08 x$

Given:

• $1.08 x = 237.60$

So:

• $x = \dfrac{237.60}{1.08}$

To avoid messy decimals, multiply top and bottom by 100:

• $x = \dfrac{23760}{108}$

Now simplify:

• Divide both by 12:
  $23760 \div

---

“Practice PSLE Science questions and get clear, step-by-step answers instantly.”
👉 Try a question now and see how fast you can improve.

Ready to practise?

If you want a Singapore-focused AI tutor you can use immediately $website, no sign-up$, try Tutorly here:

• https://tutorly.sg/ai-tutor-singapore
• https://tutorly.sg/app

---

Related Articles

• 'Preply Math Tutor Vs [Tutorly.sg](https: //tutorly.sg/app): Which
• How To Get Better With Practice For Singapore Exams (Especially O Levels)
• 'Live Math Tutor: Smarter, Cheaper Alternative Singapore' (2026)