Maths exams: show the working, or lose the marks you earned

A maths mark scheme does not only check the final answer. It breaks a solution into steps and gives marks along the way. Cambridge mark schemes for Additional Mathematics (4037) give method marks for correct working even when the final answer is wrong. Pearson Edexcel mark schemes for Further Pure Mathematics (4PM1) give method marks and accuracy marks.

So two students with the same wrong answer can score very differently. One wrote only the answer and gets nothing for it. The other set out a correct method, slipped once in the arithmetic, and can keep some of the marks.

It works the other way too. A bare correct answer can lose marks, especially when the question says show your working or show that. When a question asks you to show something, the working is the answer.

Details vary between boards, but the idea is the same:

• Method marks are for a correct approach: the right formula, a correct substitution, a sensible first step.
• Accuracy marks are for a correct result. They usually depend on the method mark before them, so a right answer reached by a wrong method may not get them.
• Some schemes also have marks that stand on their own, for a correct value or statement.

If you slip early and then carry the wrong value forward with a correct method, later method marks can still be available. But only if the examiner can see your method.

In Edexcel Further Pure Mathematics (4PM1), writing clear and accurate solutions carries 35 to 50% of the marks, so setting out is part of what is assessed. When you mark your own practice, read the notes in the mark scheme, not just the answers.

Working scores when someone else can follow it. These habits help:

1. Say what you are finding. "Area of triangle =" or "Let x be the width" tells the reader where you are.
2. Write the formula before the numbers. Then substitute, then simplify. A correct substitution is often where the first method mark sits.
3. One step per line, with the equals signs roughly under each other. Do not write a chain like 3 + 4 = 7 × 2 = 14, which is false as written.
4. Keep it in the answer space for that question. Working written somewhere else risks being missed.
5. Leave one final answer. If you change your mind, cross out the old work with a single line and write the new version clearly. Two answers left standing make it unclear which one you mean.

A diagram counts as working too. A sketch of a triangle with the sides and angles marked often shows your method better than a sentence.

Rounding in the middle of a calculation is one of the easiest ways to lose an accuracy mark with a correct method. Keep full figures all the way through, and round once, at the end, to the accuracy the question asks for.

An invented example. A right-angled triangle has shorter sides of 5.3 cm and 7.8 cm. Part (a) asks for the hypotenuse to 3 significant figures. Part (b) asks for the area of a square drawn on the hypotenuse, also to 3 significant figures.

The method is the same in every row. Only the last one gets the wrong answer, and it got there by rounding too early. Here, 3 significant figures happened to be enough. That is not always true, so carry the full value.

With a calculator, use its memory or answer key to carry the full value. On paper, write down more figures than you need and round at the end. If a question does not say how accurately to answer, check the instructions on the front of the paper.

Since 2025, Paper 1 of Cambridge O Level Additional Mathematics (4037) has been taken without a calculator. Papers set before 2025 allowed one, so an older Paper 1 is not a guide to what the new Paper 1 asks or how long it takes. Single older questions can still be useful practice, done by hand, where the numbers are workable.

Without a calculator, every step is on the page anyway. Set it out so it is easy to check:

• Keep answers exact when the question asks for an exact value: fractions, surds and π stay as they are.
• Simplify as you go. Cancel fractions before multiplying, not after.
• Learn the standard results by heart: the ones your syllabus expects you to use by hand. Practise them until they are automatic.
• Estimate first. A rough answer in your head tells you when the worked answer is far off.

If you sit another maths syllabus, such as Cambridge Mathematics D (4024) or Edexcel Mathematics A (4MA1), check your syllabus for which papers allow a calculator.

Save a few minutes at the end for the questions most likely to hide a slip, not for rereading the easy ones.

• Substitute back. If you solved an equation, put your answer into the original and see whether it works.
• Check the size. A person 17 m tall or a probability of 1.3 means something went wrong.
• Reread the last line of the question. Did it ask for the nearest degree, centimetres, a fraction, or the simplest form?
• Check signs and units. A negative length or a missing unit is an easy mark to lose.

Practise the way you will sit the exam: working written in full, no calculator for non-calculator practice, then marked against the real scheme, mark by mark. For every lost mark, ask one question: was it the method or the accuracy?

On Eudika Learn, written maths questions can be practised by topic for Edexcel Mathematics B and Further Pure Mathematics. You type your working or photograph it, then the real mark scheme is revealed and you tick each mark you earned. The on-screen calculator is offered on every paper, so leave it closed when you practise for a non-calculator paper.