Nivara Academy · IB Maths Exam Technique
IB Maths How to Show Working Correctly
You can reach the right answer and still leave marks on the table if the page doesn't show how you got there. This guide explains what clear IB Maths working looks like, how much to write, and how to fix the habits that quietly cost students marks.
Picture a student who finishes a paper feeling confident. Every final answer matches the answer key. Yet the marked paper comes back with marks missing. Where an answer needed a method, there was only a number. Where a result needed justification, there was a calculator value with nothing around it. The mathematics may have been sound, but the page didn't prove it.
This happens to capable students every year. IB Maths how to show working correctly is really a question about communication: can an examiner follow your reasoning from the question to the conclusion? This page explains how to write IB Maths working steps that are clear, logical and easy to assess, written from the tutoring side, where we see the same patterns repeatedly. Parents will find it useful for understanding what to look for in their child's written solutions.
Why Showing Working Matters in IB Maths
Mathematics is a language of reasoning. An answer on its own tells an examiner very little: it could come from a correct method, a lucky guess, or a calculator misuse that happened to land close. Written solutions let the examiner see which.
In many questions, particularly multi-mark ones, the mark scheme rewards a valid approach as well as the final result. These are often called method marks. Where a question is marked that way, a correct method with a small slip can still earn credit, while a bare wrong answer usually can't. Showing working also:
- Makes calculations traceable. The examiner can see where a result came from, and so can you when checking.
- Demonstrates mathematical reasoning. Especially for "show that", "justify" and "hence" questions, where the route is the point.
- Avoids unsupported answers. A number with no setup is hard to credit.
- Helps you catch errors. Clear lines make it easier to spot a sign slip than a crowded mess.
Some questions, especially short one-step ones, may need very little written. Reading the command term and the marks available tells you how much the question expects.
IB Maths How to Show Working Correctly: 10 Practical Habits
1. State the formula or relationship
When a formula is used, write it before substituting, e.g. A = ½ab sin C. Where a formula is provided in the booklet, writing it still shows your intent.
2. Substitute clearly
Write the numbers into the formula, in brackets where needed, so each value is visible.
3. Show key intermediate steps
If a result feeds into the next part of the solution, write it down with enough accuracy to use.
4. Keep equals signs honest
An "=" means both sides have the same value. Don't chain unrelated lines together with equals signs.
5. Use proper notation
Write dy/dx, f′(x), P(A ∩ B) and x ∈ ℝ correctly, and avoid calculator syntax like "^" or "E" in written answers.
6. Give exact values when asked
If the question wants an exact answer, leave surds and π intact rather than converting to decimals.
7. Round only at the end
Keep full values (or store them on the calculator) through the solution, and round at the final step to the requested accuracy.
8. Include units
Where a question gives units, give units in the answer: cm², m s⁻¹, $, degrees.
9. Make the final answer obvious
Write a clear concluding line, or underline or box the result, so the examiner doesn't have to hunt for it.
10. Make reasoning visible
In multi-step problems, a short phrase such as "since the triangle is right-angled" or "setting f′(x) = 0" helps the logic read cleanly.
How Much Working Should You Show in IB Maths?
There are three common patterns, and two of them cost marks.
Too little
Only a final answer, or large jumps between lines. The examiner can't tell what you did.
Appropriate
The method, key substitutions and important results are present, in a logical order that a classmate could follow.
Too messy
Crossed-out fragments, side calculations scattered around the page, or competing methods with no clear final choice.
A good test
Cover your answer and ask: could someone else reproduce it from my working alone?
If you make an error, cross out neatly with a single line and continue. If you start a new method, make clear which attempt is your final one.
Common IB Maths Working Mistakes (and Fixes)
- Writing only the final calculator answer. Add the setup: the equation, formula or command you used.
- Skipping substitutions. Write the formula, then the substituted version, then the result.
- Jumping between unexplained steps. Add the missing line, or a few words of explanation.
- Missing brackets. Write (x + 3)² rather than x + 3², and −(2x − 1) rather than −2x − 1.
- Incorrect equality signs. Start a new line instead of writing "= 12 = 12 × 3 = 36".
- Poor notation. Learn the standard symbols for the topic and use them consistently.
- No required diagram or setup. A quick sketch, labelled triangle or tree diagram often organises the whole solution.
- Rounding too early. Carry extra digits, then round at the end.
- Missing units. Check the question, then attach the unit to the final answer.
- No conclusion. Finish with a sentence answering the question that was asked.
- Copying calculator output without interpreting it. Say what the number means in context.
- Using an unexplained method. If you rely on a calculator function or a shortcut, add a short statement of what you did.
Calculator Answers vs Showing Mathematical Working
Calculators are a normal, permitted and sometimes essential part of IB Maths. The goal isn't to avoid them, and you don't need to write down every key press. The point is that the calculator should support your solution, not replace it.
A strong written solution usually has three layers: the mathematical setup before the calculator, a brief note of what the calculator was used for, and the interpreted result after.
x = 3.27 (3 s.f.) or x = −0.765
Only x = 3.27 is valid since x > 0
Here the equation is stated, the technology is named, and the final choice of solution is justified. Where a question says "show that" or asks for an algebraic method, a calculator solution alone may not be enough, so read the command term carefully.
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How to Show Working in Different IB Maths Questions
These examples are general illustrations, not predictions of what any paper will contain.
Algebra
Show each rearrangement as its own line, doing the same operation to both sides. Expand brackets visibly before collecting terms, and check your solution by substituting back where practical.
Functions
For f(x) = 2x² − 3, write f(4) = 2(4)² − 3 before evaluating. For transformations, name them: "translation by (3, 0), then vertical stretch by factor 2". For inverse or composite functions, write the swap or substitution explicitly.
Calculus
Write the function, the derivative or integral in correct notation, then the substitution. For optimisation, show "set f′(x) = 0" and say why the result is a maximum or minimum if the question requires it. For definite integrals, write the limits and the setup, even if technology evaluates it.
Statistics and Probability
State the distribution (e.g. X ~ B(10, 0.3)), write the probability being found (P(X ≥ 4)), then compute. For hypothesis tests, write hypotheses, the test statistic or p-value and a conclusion in context. Interpretation often carries as much weight as calculation.
Trigonometry
Write the equation, such as sin θ = 0.6, then the principal solution and the other solutions in the given domain. For triangles, name the rule (sine or cosine rule), substitute and then solve. Check whether the angle mode is correct.
Geometry and Mensuration
Label a diagram, write the volume or area formula, substitute with units, and then state the final measure with units. If a multi-stage solid is involved, show each part separately before combining.
Financial Mathematics
Identify the model and its variables, such as N, I%, PV, PMT, FV and P/Y, or write the compound interest formula with substituted values. Then state the result in context. A bare calculator value rarely shows that you understood the model.
Showing Working for IB Maths AA vs AI
Both Analysis and Approaches (AA) and Applications and Interpretation (AI) expect clear mathematical communication. The emphasis differs in broad terms, though the exact assessment requirements can change, so check the current subject guide.
- Algebraic manipulation and reasoning: tends to feature more strongly in AA, where clear step-by-step algebra and proof-style justification matter.
- Modelling and interpretation: is central to AI, where you often define a model, use technology and then explain what the result means in context.
- Technology use: appears in both. In AI, naming the function or model used can be especially important.
- Written communication: applies equally. In both courses, a conclusion that answers the actual question is part of a complete solution.
How IB Maths Tutors Help Students Improve Their Working
Many students don't realise their working is unclear until someone else reads it. One-to-one tutoring at Nivara Academy is built around that kind of feedback. In a session, a tutor can help a student to:
- identify incomplete solutions and unsupported jumps
- improve mathematical notation and equation layout
- understand where marks may be lost in a given type of question
- learn to structure answers for multi-step problems
- review past-paper style questions and analyse mistakes
- practise exam technique under timed conditions
- build confidence in written mathematical communication
We can't promise specific grades, because results depend on many factors, but a student who learns to present reasoning clearly is better placed to show what they know. Nivara Academy provides personalised online IB Maths tutoring, and the demo class is a low-pressure way to see whether it's the right fit.
A Simple IB Maths Working Checklist
Before moving on from a question, ask:
- ☐ Did I identify the correct method?
- ☐ Did I show the important mathematical steps?
- ☐ Did I substitute values clearly?
- ☐ Are my equations logically written?
- ☐ Did I avoid unnecessary early rounding?
- ☐ Did I include units where needed?
- ☐ Did I interpret the answer where required?
- ☐ Is my final answer easy to identify?
- ☐ Does my working clearly communicate my method?
IB Maths How to Show Working Correctly — Worked Examples
All three examples below are original and written for illustration.
Example 1: Solving an equation
Question: Solve 3(2x − 5) = 4x + 7.
6x − 15 = 4x + 7
2x = 22
x = 11
Why it's clearer: Each line follows from the last, the expansion is visible, and a small slip (say, −15 written as +15) would still leave a traceable method.
Example 2: Gradient using calculus
Question: Find the gradient of y = 2x³ − 5x at x = 2.
dy/dx = 6x² − 5
At x = 2: dy/dx = 6(2)² − 5
= 19
The gradient is 19.
Why it's clearer: The derivative is shown, the substitution is visible, and the conclusion answers the question asked.
Example 3: Compound interest
Question: $5000 is invested at 4% per year, compounded quarterly. Find its value after 6 years.
= 5000(1.01)^24
= $6348.67 (2 d.p.)
The investment is worth $6348.67.
Why it's clearer: The model, the values and the rounding are all visible. If a value were mistyped, the setup would still show the right idea.
Not sure where your marks are slipping?
Bring a recent set of solutions to a demo class and we'll look at your IB Maths working together, one-to-one.
Frequently Asked Questions
How much working should I show in IB Maths?
Show enough relevant mathematics for someone else to follow your method: the formula or setup, key substitutions, important intermediate results and a clear final answer. Match the amount to the marks available.
Do I need to show calculator working in IB Maths?
You don't need to write every key press, but you should show the mathematical setup and state what the calculator was used for, such as solving an equation or finding a regression line. Check the command term in the question.
Can I lose marks if I only write the final answer?
Yes, it's possible. If a question awards marks for method or reasoning, a bare answer may not earn them, particularly if it's incorrect. Some short questions may award full marks for a correct answer, so it depends on the mark scheme.
What counts as good working in IB Maths?
Good working is logical, readable and relevant. It uses correct notation, connects each step to the next and lets the examiner see the method, not just the result.
How can I improve my IB Maths exam technique?
Practise past-paper style questions, read command terms carefully, review your own mistakes, and compare your working with mark scheme style solutions. Timed practice helps you balance clarity and speed.
Should I show formulas in IB Maths?
Usually yes, when a formula is used. Writing the formula and then substituting makes your method visible, even if the formula is in the booklet.
How can I make my IB Maths solutions easier to follow?
Write one step per line, align equals signs, use brackets carefully, label diagrams and finish with a clear concluding statement. IB Maths how to show working correctly is mostly about making each step easy to follow.
Is showing working important in both IB Maths AA and AI?
Yes. Both courses expect clear mathematical communication. The style differs, with more algebraic reasoning in AA and more modelling and interpretation in AI, but clear written solutions matter in both.
Can an IB Maths tutor help me improve my written solutions?
Yes. A tutor can read your working, point out unclear steps and notation, and help you practise structuring solutions. Nivara Academy offers one-to-one online IB Maths tutoring with this kind of feedback.
How can I practise showing working correctly?
Redo a few old solutions and rewrite them as if for an examiner. Swap work with a classmate, or ask a tutor to review it. Practising IB Maths how to show working correctly regularly makes it a habit.
Final Thoughts
Learning IB Maths how to show working correctly won't change what you know, but it changes how well your knowledge is seen. Start with the checklist, rewrite a few of your own solutions, and notice which habits keep appearing. If you'd like a tutor to look at your work with you, a demo class is an easy first step.
Ready to improve your IB Maths working?
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