If you’re a Secondary student in Singapore, you’ve probably heard this a thousand times:
“Show your working!”
“Stuck on a question? See simple explanations that help you understand fast.”
👉 Give it a try and turn confusion into clarity in minutes.
But how exactly are you supposed to show it?
How many steps is enough? What if you do it in your head? What if your answer is correct but your working is messy?
In Singapore exams , clear math working is not just “good to have”. It’s literally marks on the table.
This guide will walk you through:
- How to show working clearly for typical O-Level style questions
- What examiners actually want to see
- Step-by-step examples for algebra, graphs, and geometry
- Practice questions (including harder variants)
- Common mistakes that cost marks even when your answer is right
- How to use Tutorly.sg as your 24/7 “working coach” for Singapore math
Tutorly.sg is a 24/7 AI tutor website built specifically for Singapore students, aligned to the MOE syllabus. It’s been mentioned on Channel NewsAsia (CNA) and used by thousands of students here, so everything you see will feel familiar to your school worksheets and O-Level papers.
Step-by-step tutorial
Let’s start with what “good working” actually looks like in the Singapore context.
What examiners are looking for
For O-Level E-Math / A-Math and school exams, markers are usually checking:
- Method – Did you use an appropriate method? (e.g. correct formula, correct algebraic manipulation)
- Logical flow – Can they follow your steps from question to answer?
- Accuracy – Are your calculations correct?
- Communication – Are you using proper notation, labels, and statements?
Even if your final answer is wrong, clear working can still earn method marks. That’s why you should never skip steps just because you “can do it in your head”.
Let’s break this down by topic.
1. Algebra: solving equations
Example 1: Linear equation
Solve .
Good working (Sec 2 / 3 level):
-
Expand brackets
So the equation becomes:
-
Bring all terms to one side
-
Simplify
-
Solve for
-
Final answer clearly stated
Key things examiners like:
- Every algebraic change is on a new line.
- Equal signs are aligned and not misused as arrows.
- Final answer is clearly separated (with “” or “Hence”).
Example 2: Quadratic equation (factorisation)
Solve .
Good working:
-
Factorise
-
Use zero-product property
-
Solve each
-
Final answer
Important:
Don’t just jump from to with no factorisation shown. In O-Level style marking, you can lose method marks if the step is not obvious.
2. Algebra: simultaneous equations
Example 3: Simultaneous equations by substitution
Solve the simultaneous equations:
Good working:
-
Label equations
-
Make the subject from
-
Substitute into
-
Expand and simplify
-
Substitute back to find
-
Final answer
Why this is good:
- Equations are labelled , , – very clear.
- Substitution step is shown explicitly.
- Fractions are simplified properly.
When you practise with Tutorly.sg, you can type your answer, and it will show you a full worked solution like this, step by step, aligned to how teachers in Singapore present it.
3. Geometry: angles and proofs
For geometry questions , reasons are crucial.
Example 4: Angles in parallel lines
In the figure, . .
Find .
Good working style:
-
State angle relationship
-
Substitute value
-
Final answer
Even if the diagram “looks obvious”, you must still write the reason (alternate angles, corresponding angles, vertically opposite angles, etc.) in Singapore exams.
4. Coordinate geometry: gradient and equation of line
Example 5: Equation of a line through two points
Points and lie on a straight line.
(a) Find the gradient of .
(b) Find the equation of the line.
Good working:
(a) Gradient
= \frac{12 - 4}{5 - 1} = \frac{8}{4} = 2$$ **$\therefore m = 2$** (b) Equation of line Use $y = mx + c$ with $m = 2$ and point $A(1,4)$: $$4 = 2(1) + c$$ $$4 = 2 + c$$ $$c = 2$$ So: **$\therefore y = 2 x + 2$** Again, every algebraic move is shown. You don’t just write the final equation. --- ### 5. Word problems: setting up equations In MOE exams, a lot of marks are for **setting up correct equations** from words. **Example 6: Number problem** > The sum of two numbers is 35. The larger number is 7 more than twice the smaller number. > Find the two numbers. **Good working:** 1. Let the smaller number be $x$. 2. Larger number $= 2 x + 7$. 3. Use the “sum” information: $$x + (2 x + 7) = 35$$ 4. Simplify $$3 x + 7 = 35$$ $$3 x = 28$$ $$x = \frac{28}{3}$$ 5. Larger number $$2 x + 7 = 2\left(\frac{28}{3}\right) + 7 = \frac{56}{3} + 7 = \frac{77}{3}$$ 6. Final answer **Smaller number $= \dfrac{28}{3}$, Larger number $= \dfrac{77}{3}$.** Even if the fractions are ugly, you must **still show all steps**. That’s where method marks are. --- ## Exam strategy guide Knowing how to show working is one thing. Doing it under exam pressure is another. > “Access more than 1000+ past year papers to practice” > [👉 Start a paper today and test yourself like it’s the real exam.](https://tutorly.sg/app)  Here are practical strategies specific to Singapore Secondary / O-Level exams. --- ### 1. Aim for “3–6 lines” per long question part This is not a fixed rule, but a good mental guide: - 1-mark question: Usually 1–2 short lines is enough. - 2–3 mark question: Expect 3–6 lines of working. - 4–5 mark question: You’ll likely need multiple parts (a), (b), (c) with clear sub-steps. If you find yourself writing **only one line** for a 3-mark question, you’re probably skipping too much. Examiners cannot read your mind. --- ### 2. Always write the formula first For topics like: - Trigonometry (Sec 3–4) - Area / volume (Sec 2–3) - Kinematics (if you’re doing A-Math) You should **start with the general formula**, then substitute. **Example (trigonometry):** > Find $x$. $$\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}$$ $$\sin 35^\circ = \frac{x}{10}$$ $$x = 10 \sin 35^\circ$$ $$x = 5.74 \text{ (3 s.f.)}$$ This style makes markers happy because they can see: 1. You know which formula to use. 2. You didn’t randomly punch numbers into your calculator. --- ### 3. Use proper mathematical symbols Singapore markers are used to certain standards: - Use “$=$” only when two expressions are equal. - Use “$\Rightarrow$” or “$\therefore$” to show conclusion. - Use “$\angle ABC$” for angles, not “angle B” if it’s ambiguous. - Use “$\approx$” when you round (e.g. $x \approx 4.32$). Messy symbols can cause confusion and may cost communication marks. --- ### 4. Leave space between steps When you rush, it’s tempting to cram everything into one line. That makes it hard for you **and** the marker. Try this layout: - One line per algebraic step. - Skip a line between different parts (a), (b), (c). - Keep your equal signs lined up vertically when possible. This is something you can practise on your own worksheets, and also when you use [Tutorly.sg](https://tutorly.sg/ai-tutor-singapore). After you see the model solution, compare: - Did you skip any important step? - Is your layout as readable as the solution? --- ### 5. Don’t erase wrong working completely In O-Level marking, you can still get method marks even if your final answer is wrong, **as long as your working is visible**. If you realise a mistake: - Put a neat cross over the wrong line. - Start the correct method below. Don’t scribble everything into a black hole. If the examiner can’t read it, they can’t award marks. --- ### 6. Time management: when to skip full working You don’t need full working for: - Very simple mental arithmetic (e.g. $10 \times 3 = 30$). - Obvious simplifications (e.g. $\frac{4}{8} = \frac{1}{2}$). But **borderline cases** (like $17 \times 23$) should still be written out or done in a clear calculator step. A good rule: If you think you might forget how you got the number 5 minutes later, **write it down**. --- ## Worksheet practice Let’s try some questions together. I’ll show you **model working style** that fits Singapore Sec / O-Level expectations. You can then try similar questions on [Tutorly.sg](https://tutorly.sg/ai-tutor-singapore) and compare your working with the full solutions it generates. --- ### Practice Set A: Core algebra (moderate) #### Question A 1 (Linear equation) Solve: $5(3 x - 2) - 4 = 3(2 x + 1)$. **Suggested working:** $$5(3 x - 2) - 4 = 3(2 x + 1)$$ $$15 x - 10 - 4 = 6 x + 3$$ $$15 x - 14 = 6 x + 3$$ $$15 x - 6 x = 3 + 14$$ $$9 x = 17$$ $$x = \frac{17}{9}$$ **$\therefore x = \dfrac{17}{9}$.** --- #### Question A 2 (Simultaneous equations) Solve the simultaneous equations: $$3 x + 2 y = 14 \quad (1)$$ $$2 x - y = 1 \quad (2)$$ **Suggested working (elimination):** From (2): $$2 x - y = 1 \Rightarrow -y = 1 - 2 x \Rightarrow y = 2 x - 1 \quad (3)$$ Substitute (3) into (1): $$3 x + 2(2 x - 1) = 14$$ $$3 x + 4 x - 2 = 14$$ $$7 x - 2 = 14$$ $$7 x = 16$$ $$x = \frac{16}{7}$$ Substitute back to find $y$: $$y = 2 x - 1 = 2\left(\frac{16}{7}\right) - 1 = \frac{32}{7} - 1 = \frac{25}{7}$$ **$\therefore x = \dfrac{16}{7},\ y = \dfrac{25}{7}$.** --- ### Practice Set B: Geometry & trigonometry (moderate) #### Question B 1 (Angles in a triangle) In $\triangle ABC$, $\angle A = 45^\circ$, $\angle B = 63^\circ$. Find $\angle C$. **Suggested working:** Sum of angles in a triangle: $$\angle A + \angle B + \angle C = 180^\circ$$ $$45^\circ + 63^\circ + \angle C = 180^\circ$$ $$108^\circ + \angle C = 180^\circ$$ $$\angle C = 180^\circ - 108^\circ = 72^\circ$$ **$\therefore \angle C = 72^\circ$.** --- #### Question B 2 (Right-angled triangle, trigonometry) In a right-angled triangle, $\angle A = 30^\circ$ and the side opposite $\angle A$ is 5 cm. Find the length of the hypotenuse, correct to 3 significant figures. **Suggested working:** Using $\sin \theta = \dfrac{\text{opposite}}{\text{hypotenuse}}$: $$\sin 30^\circ = \frac{5}{h}$$ $$h = \frac{5}{\sin 30^\circ}$$ $$h = \frac{5}{0.5} = 10$$ **$\therefore$ Hypotenuse $= 10.0 \text{ cm}$.** (You can still write 10 cm, but in exams they may want 3 s.f. depending on instructions.) --- ### Practice Set C: Harder variants (O-Level style) Now let’s look at questions closer to real O-Level difficulty. Focus on the **clarity of working**. --- #### Question C 1 (Algebraic fractions, hard variant) Simplify: $$\frac{3 x}{x^2 - 9} - \frac{2}{x + 3}$$ **Suggested working:** First factorise the denominator: $$x^2 - 9 = (x - 3)(x + 3)$$ Rewrite both fractions with common denominator $(x - 3)(x + 3)$: > “Doing Secondary Science? Pick a topic and practise like it’s a real exam — with clear answers right after.” > [👉 Try Tutorly now and start a Science topic in seconds.](https://tutorly.sg/app)  $$\frac{3 x}{(x - 3)(x + 3)} - \frac{2(x - 3)}{(x + 3)(x - 3)}$$ Combine: $$= \frac{3 x - 2(x - 3)}{(x - 3)(x + 3)}$$ $$= \frac{3 x - 2 x + 6}{(x - 3)(x + 3)}$$ $$= \frac{x + 6}{(x - 3)(x + 3)}$$ **$\therefore \dfrac{3 x}{x^2 - 9} - \dfrac{2}{x + 3} = \dfrac{x + 6}{(x - 3)(x + 3)},\ x \neq \pm 3$.** Note how each algebraic manipulation is shown. Don’t jump directly to the simplified fraction. --- #### Question C 2 (Simultaneous equations with a quadratic, hard variant) Solve the simultaneous equations: $$y = x^2 - 3 x + 2 \quad (1)$$ $$y = 2 x - 1 \quad (2)$$ **Suggested working:** Equate (1) and (2): $$x^2 - 3 x + 2 = 2 x - 1$$ Bring all terms to one side: $$x^2 - 3 x + 2 - 2 x + 1 = 0$$ $$x^2 - 5 x + 3 = 0$$ Solve the quadratic (by formula or factorisation if possible). Using quadratic formula: $$x = \frac{5 \pm \sqrt{(-5)^2 - 4(1)(3)}}{2(1)}$$ $$= \frac{5 \pm \sqrt{25 - 12}}{2}$$ $$= \frac{5 \pm \sqrt{13}}{2}$$ So: $$x = \frac{5 + \sqrt{13}}{2} \quad \text{or} \quad x = \frac{5 - \sqrt{13}}{2}$$ Find corresponding $y$ using $y = 2 x - 1$: For $x = \dfrac{5 + \sqrt{13}}{2}$: $$y = 2\left(\frac{5 + \sqrt{13}}{2}\right) - 1 = 5 + \sqrt{13} - 1 = 4 + \sqrt{13}$$ For $x = \dfrac{5 - \sqrt{13}}{2}$: $$y = 2\left(\frac{5 - \sqrt{13}}{2}\right) - 1 = 5 - \sqrt{13} - 1 = 4 - \sqrt{13}$$ **$\therefore$ The solutions are }$$(x, y) = \left(\frac{5 + \sqrt{13}}{2},\ 4 + \sqrt{13}\right) \text{ and } \left(\frac{5 - \sqrt{13}}{2},\ 4 - \sqrt{13}\right).$$ This is the kind of question where clear working matters a lot, because there are many places to slip. --- #### Question C 3 (Trigonometry in non-right triangle, hard variant) In $\triangle ABC$, $AB = 7$ cm, $AC = 10$ cm and $\angle BAC = 42^\circ$. Find the length of $BC$, correct to 3 significant figures. (Use Cosine Rule – typical Sec 3 / 4 E-Math.) **Suggested working:** Using Cosine Rule: $$BC^2 = AB^2 + AC^2 - 2(AB)(AC)\cos \angle BAC$$ Substitute values: $$BC^2 = 7^2 + 10^2 - 2(7)(10)\cos 42^\circ$$ $$= 49 + 100 - 140\cos 42^\circ$$ $$= 149 - 140\cos 42^\circ$$ Use calculator: $$\cos 42^\circ \approx 0.7431$$ So: $$BC^2 \approx 149 - 140(0.7431)$$ $$BC^2 \approx 149 - 104.034$$ $$BC^2 \approx 44.966$$ $$BC \approx \sqrt{44.966} \approx 6.71 \text{ cm (3 s.f.)}$$ **$\therefore BC \approx 6.71 \text{ cm (3 s.f.)}$.** Notice: - Formula is written clearly first. - Substitution is on a new line. - Rounding is indicated with “$\approx$”. --- ### How to use [Tutorly.sg](https://tutorly.sg/app) for worksheet practice When you’re practising these types of questions, you don’t always have a teacher beside you at 11pm. That’s where [Tutorly.sg](https://tutorly.sg/ai-tutor-singapore) is genuinely useful: - You pick your level (e.g. Sec 3 Express) and subject (E-Math or A-Math). - You type the question (from your school worksheet, TYS, or assessment book). - Tutorly checks your final answer, and then shows you a **full step-by-step worked solution**, written in a style that matches MOE expectations. - If you’re stuck, you can ask it to explain a specific step in simpler terms. Because [Tutorly.sg](https://tutorly.sg/app) is a website, you can open it on your laptop or tablet during study sessions, just like how you’d open Google Docs or YouTube. No need to download anything. Thousands of students in Singapore already use it as their “on-demand tutor” when they’re revising for weighted assessments, Sec 3 EOYs, or the O Levels. --- ## Common mistakes Let’s fix the habits that quietly lose marks, even if you “know” the topic. --- ### 1. Doing too much in one step **Example (bad):** $$3 x + 5 = 2 x - 7 \Rightarrow x = -12$$ The marker has no idea how you got $x = -12$. If you made a small sign error, they can’t see it, so they may not give you method marks. **Better:** $$3 x + 5 = 2 x - 7$$ $$3 x - 2 x = -7 - 5$$ $$x = -12 --- > “Practice PSLE Science questions and get clear, step-by-step answers instantly.” > [👉 Try a question now and see how fast you can improve.](https://tutorly.sg/app)  ## 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/ai-tutor-singapore) - [https://tutorly.sg/app](https://tutorly.sg/app) --- ## Related Articles - ['Live Math Tutor: Smarter, Cheaper Alternative Singapore' (2026)](/blog/live-math-tutor) - ['Advanced Math Tutor: How To Actually Understand Hard...' (2026)](/blog/advanced-math-tutor) - ['Best Online Math Tutor: Expert Guide' (2026) That Actually Help](/blog/best-online-math-tutor)