How To Calculate Faster In Singapore: A Practical Tutorial For Secondary & O Level Students

If you’re in Secondary school or preparing for O Levels in Singapore, you already know this:

Very often, it’s not the concept that kills your marks – it’s speed.

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You sort of know what to do… but by the time you finish your working, the invigilator says, “Last 10 minutes.” And suddenly, your brain just blanks.

This guide is for you if:

• You’re doing Sec 1–4 / O Levels $NA/Express/IP$.
• You can follow lessons, but you’re too slow in tests.
• You want practical calculation tricks that actually match the MOE syllabus and O Level style questions.

I’ll walk you through:

• Fast calculation methods (with examples you’ll actually see in school).
• How to apply them in O Level Paper 1 & 2.
• Practice questions (including harder variants).
• How to use Tutorly.sg to train speed in a smart, low-stress way.

Tutorly.sg is a 24/7 AI tutor website built specifically for Singapore students, aligned to the MOE syllabus from Primary 1 to JC 2. It has already been used by thousands of students in Singapore and was even mentioned on Channel NewsAsia (CNA) – so you’re not experimenting on something random.

Main links you’ll need:

• About the AI tutor: https://tutorly.sg/ai-tutor-singapore
• Start practising now: https://tutorly.sg/app

Let’s fix your speed, step by step.

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Step-by-step tutorial

We’ll go through 5 core areas where faster calculation really matters for Secondary/O Level maths:

1. Mental shortcuts with numbers
2. Fast fraction and percentage work
3. Algebra speed tricks
4. Indices, standard form, and surds
5. Calculator discipline (yes, this also affects speed)

1. Mental shortcuts with numbers

These are especially useful in:

• Sec 1–2: Number & Algebra
• Sec 3–4 / O Level E-Maths: Paper 1 $non-calculator for some schools$, and simplifying steps in Paper 2

(a) Multiplying numbers ending in 0 s

Instead of punching everything directly:

Example: $40 \times 0.25$

Instead of:
$40 \times 0.25 = 40 \times \dfrac{25}{100} = 40 \times 0.25$ (then key into calculator)

Do this mentally:

1. $0.25 = \dfrac{1}{4}$
2. So $40 \times 0.25 = 40 \times \dfrac{1}{4} = 10$

Another example: $600 \times 0.05$

1. $0.05 = \dfrac{5}{100} = \dfrac{1}{20}$
2. $600 \div 20 = 30$

You should aim to recognise these quickly:

• $0.5 = \dfrac{1}{2}$
• $0.25 = \dfrac{1}{4}$
• $0.2 = \dfrac{1}{5}$
• $0.1 = \dfrac{1}{10}$
• $0.05 = \dfrac{1}{20}$

These pop up often in percentage and rate questions (e.g. interest, speed).

(b) Multiplying near 100 (good for approximations)

Example: $98 \times 102$

You don’t always need the exact value in the middle of a long question. Sometimes, a quick approximate check is enough.

Observe:

• $98 = 100 - 2$
• $102 = 100 + 2$

So $98 \times 102 \approx 100^2 - 2^2 = 10000 - 4 = 9996$

Even if you don’t fully remember the formula, you can think:

• “Both are about 100, so answer is around $100 \times 100 = 10\,000$.”

This helps you quickly check if your calculator answer is nonsense.

If your calculator shows $980$ or $98\,000$, you know something went wrong.

(c) Dividing by 5 quickly

Instead of keying $\div 5$ directly, think:

$\dfrac{1}{5} = \dfrac{2}{10} = 0.2$

So $x \div 5 = x \times 0.2$

Example: $360 \div 5$

• $360 \times 0.2 = 36 \times 2 = 72$

Or use this trick:

1. Double the number.
2. Then divide by 10.

$360 \div 5$
$\Rightarrow 360 \times \dfrac{2}{10}$
$\Rightarrow 720 \div 10 = 72$

This is handy when you’re in the middle of algebra and don’t want to keep pressing calculator buttons.

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2. Fast fraction and percentage work

You see this everywhere:

• Sec 1–2: Fractions, ratios, percentages
• Sec 3–4: Financial maths, probability, statistics, algebra fractions

(a) Cancel before multiplying

Example: $\dfrac{3}{4} \times \dfrac{8}{9}$

Slow method:

• Multiply numerator: $3 \times 8 = 24$
• Multiply denominator: $4 \times 9 = 36$
• Simplify: $\dfrac{24}{36} = \dfrac{2}{3}$

Faster method (cancel first):

1. $8 \div 4 = 2$, so
   $\dfrac{3}{\cancel{4}} \times \dfrac{\cancel{8}}{9} = \dfrac{3}{1} \times \dfrac{2}{9}$
2. $3$ and $9$ simplify:
   $\dfrac{\cancel{3}}{1} \times \dfrac{2}{\cancel{9}} = \dfrac{1}{1} \times \dfrac{2}{3} = \dfrac{2}{3}$

Same answer, but less writing and smaller numbers = less chance of careless mistakes.

You should always look out for:

• Numerators and denominators with common factors
• Especially with 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72 – these are common in O Level questions.

(b) Percentage to fraction (and back) in your head

Useful conversion pairs:

• $10\% = \dfrac{1}{10}$
• $20\% = \dfrac{1}{5}$
• $25\% = \dfrac{1}{4}$
• $33\frac{1}{3}\% \approx \dfrac{1}{3}$
• $50\% = \dfrac{1}{2}$
• $75\% = \dfrac{3}{4}$

Example (O Level style):

A shirt is sold at a 25% discount and the sale price is $36. Find the original price.

Method 1 (percentage form):

• $75\%$ of original price = $36
• So original = $\dfrac{36}{0.75} = 48$

Method 2 (fraction form, faster mentally):

• $25\% = \dfrac{1}{4}$, so discount is $\dfrac{1}{4}$
• Sale price = $\dfrac{3}{4}$ of original
• So $\dfrac{3}{4}$ of original = 36
• Original $= 36 \times \dfrac{4}{3} = 12 \times 4 = 48$

You can do the second method very quickly once you’re used to it.

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3. Algebra speed tricks

Algebra is where many Sec 2–4 students lose time. Let’s fix that.

(a) Factorising quickly

You don’t want to expand everything then re-factorise again. That wastes time and increases error chances.

Common patterns to memorise:

1. $(a + b)^2 = a^2 + 2ab + b^2$
2. $(a - b)^2 = a^2 - 2ab + b^2$
3. $(a + b)(a - b) = a^2 - b^2$

Example:

Factorise $x^2 - 9$

You should immediately see:

• $x^2 - 9 = x^2 - 3^2 = (x - 3)(x + 3)$

Example:

Expand $(2 x - 5)^2$

• $a = 2 x$, $b = 5$
• $(2 x - 5)^2 = (2 x)^2 - 2(2 x)(5) + 5^2$
• $= 4 x^2 - 20 x + 25$

If you know the pattern, you don’t have to multiply everything out slowly.

(b) Avoiding unnecessary expansion

Example (typical O Level algebra fraction):

$\dfrac{(x + 3)(x - 2)}{x - 2}$

You don’t need to expand the numerator at all.

• Just cancel $(x - 2)$:
  $\dfrac{\cancel{(x - 2)}(x + 3)}{\cancel{(x - 2)}} = x + 3$

This is faster and cleaner. Only expand when you really need to.

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4. Indices, standard form, and surds

These topics are common in Sec 3–4 E-Maths and some A-Maths.

(a) Indices rules at your fingertips

You should be able to apply these without thinking:

1. $a^m \times a^n = a^{m+n}$
2. $\dfrac{a^m}{a^n} = a^{m-n}$
3. $(a^m)^n = a^{mn}$
4. $a^{-n} = \dfrac{1}{a^n}$
5. $a^{\frac{1}{2}} = \sqrt{a}$

Example:

Simplify $2^3 \times 2^{-5}$

• $2^{3 + (-5)} = 2^{-2} = \dfrac{1}{2^2} = \dfrac{1}{4}$

If you hesitate on the negative index, you lose time.

(b) Standard form quick habits

Example:

$0.00045$ in standard form:

1. Move decimal to get a number between 1 and 10: $4.5$
2. Count how many places: 4 places to the right
3. So $0.00045 = 4.5 \times 10^{-4}$

You will see standard form especially in physics and maths Paper 1. It’s often only 1–2 marks, so you must do it fast.

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5. Calculator discipline

Even though O Level E-Maths is calculator-allowed, your speed depends on how you use it.

Some quick rules:

1. Type expressions exactly as written using brackets.
   Example: For $\dfrac{3 + 5}{2}$, type (3+5)/2, not 3+5/2.

2. Reuse previous answers with the ANS button instead of retyping long decimals.

3. Do NOT round too early.
   Keep full calculator values until the last step, then round to 3 s.f. (or as required).

4. For repetitive structures (like geometric sequences, interest), use:

   • $A = P(1 + r)^n$ directly in one line
   • Or your calculator’s power function ^ properly.

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Exam strategy guide

Now that you’ve seen the techniques, how do you use them under exam pressure, especially for O Levels?

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1. Know where speed matters most in E-Maths

For O Level E-Maths:

• Paper 1 (80 marks, 2 hours): Shorter questions, lots of topics mixed. Speed is crucial.
• Paper 2 (100 marks, 2.5 hours): Longer questions, but you still need to move efficiently.

Speed is most important in:

• Algebra manipulation (simplifying, factorising, solving)
• Fractions & indices
• Coordinate geometry (substitution & simplification)
• Trigonometry (substituting values, simplifying)
• Statistics $mean, median, probability with fractions/decimals$

For NA / Express streams, timing is similar, so your strategy is the same: don’t get stuck early.

2. 3-pass method for the paper

Pass 1: Secure & fast (about 40% of time)

• Do all the questions you find “okay” or “easy”.
• Apply your speed tricks: cancel fractions early, factorise by pattern, use calculator cleanly.
• Skip anything that makes you hesitate more than ~30 seconds.

Pass 2: Medium questions (about 40% of time)

• Go back to questions you skipped.
• Work through them more calmly.
• Use estimation to check if your answers are reasonable (e.g. areas should not be negative).

Pass 3: Hard / stubborn questions (last 20% of time)

• Now you can afford to think more deeply.
• If you’re really stuck, write down some working (method marks!), then move on.

This method prevents you from spending 15 minutes on one tough algebra question while leaving 10 easy marks blank at the back.

3. When to use mental vs calculator

Use mental / quick working for:

• Simple fractions ($\dfrac{1}{2}, \dfrac{1}{4}, \dfrac{1}{5}$ etc.)
• Checking reasonableness $is your answer too big / too small?$
• Simple factorisation patterns

Use calculator for:

• Long decimals, surds approximations
• Trigonometry values (sine, cosine, tangent)
• Large powers and standard form

The goal is not to be a human calculator. It’s to save time on easy parts, so you can think more on the harder reasoning parts.

4. How to train speed (not just “do more papers”)

Just doing more papers doesn’t automatically make you faster. You need targeted practice.

A simple routine:

1. Pick a topic (e.g. algebra fractions).
2. Do 5 questions in 10 minutes – time yourself.
3. After that, review your mistakes AND slow steps.
4. Ask: “Where did I hesitate?” – was it:
   • Factorising?
   • Converting fractions?
   • Using indices?

Then, drill that sub-skill separately.

This is where Tutorly.sg helps a lot:

• Go to: https://tutorly.sg/app
• Choose your level and maths topic.
• Throw in exam-style questions $e.g. “Give me 5 hard algebra fraction questions with answers”$.
• After you try, you can check the final answers and see step-by-step solutions to understand the fastest route.

Because it’s 24/7 and built for the MOE syllabus, you can do short, focused speed drills even on busy days (CCA, tuition, etc.).

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Worksheet practice

Here are some practice questions you can try now to apply the speed tricks.

Try them under a time limit. That’s the only way to actually improve your speed.

Part A: Basic to intermediate (aim: 10–12 minutes)

Q 1: Fractions & percentages

(a) Simplify $\dfrac{6}{15} \times \dfrac{25}{8}$

(b) $35\%$ of a number is 42. Find the number.

(c) A price increases by 20% and then decreases by 20%. Is the final price the same as the original? Explain briefly.

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Q 2: Algebra & indices

(a) Simplify: $(2 x - 3)^2$

(b) Simplify: $\dfrac{5 x^3 y}{10 x^2}$

(c) Express $0.00032$ in standard form.

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Q 3: Rates & ratios

A car travels 180 km in 2.5 hours.

(a) Find its average speed in km/h.

(b) If the car uses 15 litres of petrol for this journey, find the petrol consumption in km per litre.

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Suggested answers for Part A (check your speed and accuracy)

Try to do all questions first before checking.

Q 1

(a) $\dfrac{6}{15} \times \dfrac{25}{8}$

• Cancel: $\dfrac{\cancel{6}}{15} \times \dfrac{25}{\cancel{8}} = \dfrac{3}{15} \times \dfrac{25}{4}$ is one way, but faster:
  • $6$ and $8$ both divisible by 2: $\dfrac{3}{4}$
  • $15$ and $25$ both divisible by 5: $\dfrac{3}{4} \times \dfrac{5}{3} = \dfrac{\cancel{3}}{4} \times \dfrac{5}{\cancel{3}} = \dfrac{5}{4}$

Final: $\dfrac{5}{4}$ or $1\dfrac{1}{4}$

(b) $35\%$ of number $= 42$

• $0.35 \times \text{number} = 42$
• Number $= \dfrac{42}{0.35} = 120$

(c) Let original price = 100 (for easy comparison)

• After +20%: $100 \times 1.2 = 120$
• After -20%: $120 \times 0.8 = 96$

Final price is 96, not 100. So it is not the same as the original.

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Q 2

(a) $(2 x - 3)^2$

• $a = 2 x, b = 3$
• $(2 x)^2 - 2(2 x)(3) + 3^2 = 4 x^2 - 12 x + 9$

(b) $\dfrac{5 x^3 y}{10 x^2}$

• Coefficients: $\dfrac{5}{10} = \dfrac{1}{2}$
• Indices: $x^{3-2} = x^1 = x$

So: $\dfrac{1}{2}xy$

(c) $0.00032$ in standard form:

• $3.2 \times 10^{-4}$

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Q 3

(a) Speed:

• $180 \div 2.5 = 72$ km/h

(b) Petrol consumption:

• $180 \div 15 = 12$ km/litre

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Part B: Harder exam-style variants (aim: 15–18 minutes)

These are closer to O Level difficulty. Time yourself seriously.

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Q 4: Algebra fractions (harder)

Simplify each expression fully:

(a) $\dfrac{2 x}{x^2 - 9} + \dfrac{3}{x + 3}$

(b) $\dfrac{5}{2 x} - \dfrac{3}{4 x}$

(c) $\dfrac{6}{x^2 - 4} \div \dfrac{3}{x - 2}$

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Q 5: Percentage & growth (O Level style)

A sum of money, $P$, is invested at a compound interest rate of 5% per year.

(a) Write an expression for the amount of money, $A$, after 3 years.

(b) If $P = 800$, find $A$ correct to 2 decimal places.

(c) Without using logarithms, explain why the amount does not increase by exactly $15\%$ over 3 years.

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Q 6: Standard form & indices (harder)

(a) Express $480\,000$ in standard form.

(b) A bacteria population is $3.2 \times 10^5$ at the start of an experiment and grows to $8 \times 10^6$ after 5 hours.
Find the growth factor $i.e. final ÷ initial$ in standard form.

(c) Hence, or otherwise, find the approximate growth factor per hour, assuming it is constant each hour.
$Give your answer correct to 3 s.f.$

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Suggested answers for Part B (with speed-focused comments)

Again, try everything first.

Q 4

(a) $\dfrac{2 x}{x^2 - 9} + \dfrac{3}{x + 3}$

First factorise:

• $x^2 - 9 = (x - 3)(x + 3)$

Rewrite with common denominator:

• $\dfrac{2 x}{(x - 3)(x + 3)} + \dfrac{3(x - 3)}{(x + 3)(x - 3)}$

Combine:

• $\dfrac{2 x + 3(x - 3)}{(x - 3)(x + 3)}$
• $= \dfrac{2 x + 3 x - 9}{(x - 3)(x + 3)}$
• $= \dfrac{5 x - 9}{(x - 3)(x + 3)}$

No further factorisation, so this is final.

Speed tip: Immediately factorise $x^2 - 9$; don’t expand anything unnecessarily.

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(b) $\dfrac{5}{2 x} - \dfrac{3}{4 x}$

Common denominator: $4 x$

• $\dfrac{5}{2 x} = \dfrac{10}{4 x}$
• So expression $= \dfrac{10}{4 x} - \dfrac{3}{4 x} = \dfrac{7}{4 x}$

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(c) $\dfrac{6}{x^2 - 4} \div \dfrac{3}{x - 2}$

First, rewrite division as multiplication by reciprocal:

• $= \dfrac{6}{x^2 - 4} \times \dfrac{x - 2}{3}$

Factorise:

• $x^2 - 4 = (x - 2)(x + 2)$

So:

• $= \dfrac{6}{(x - 2)(x + 2)} \times \dfrac{x - 2}{3}$
• Cancel $(x - 2)$ and simplify $\dfrac{6}{3} = 2$
• $= \dfrac{2}{x + 2}$

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Q 5

(a) Compound interest formula:

• $A = P(1 + r)^n$
• Here, $r = 0.05$, $n = 3$

So: $A = P(1.05)^3$

(b) If $P = 800$:

• $A = 800(1.05)^3$
• $1.05^3 \approx 1

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