Show Your Work: Why the Right Answer Still Loses Marks

A mark is not a fraction of a question. It is a specific thing the examiner is looking for, described in a document written before anyone sat the paper, and it either appears on your script or it does not. Pearson Edexcel's general marking guidance for A-level mathematics defines three kinds:

• M marksare method marks, awarded for "knowing a method and attempting to apply it". Note what is absent from that sentence: getting the right number.
• A marks are accuracy marks, and they can only be awarded if the relevant M marks have been earned. An accuracy mark hanging off a method mark you did not earn is unreachable.
• B marks are unconditional accuracy marks, independent of any M mark. They tend to attach to a stated fact, a correctly quoted formula, a value read off a graph, or a set of units.

The structural consequence is the whole article in one sentence: on a five-mark question, three or four of those marks are typically M marks that reward the approach, and every one of them is available to you even if your final number is wrong. They are only available if the approach is visible.

The same architecture appears under different names elsewhere. College Board's AP Calculus scoring guidelines allocate points to a correct setup, a correct Riemann sum, a correct separation of variables, a justification — and then state, repeatedly, when an unsupported answer earns nothing. The 2023 AB guidelines include lines such as "a response of 12 with no supporting work does not earn either point" and "an unsupported response of $-\frac{8}{9}$earns no points".

Here is the part most students have never been told, quoted from a live Pearson Edexcel International GCSE mathematics mark scheme:

If no working is shown then correct answers normally score full marks. If no working is shown then incorrect (even though nearly correct) answers score no marks.

Read carefully, that is not an instruction to always show working. It is a description of a gamble: write nothing but the answer, and you keep every mark if you are right and lose every mark if you are wrong — including when you were wrong by one sign in the last line, having done four correct steps nobody can see.

So the real argument for showing working is expected value, not obedience. On a five-mark question, working costs you nothing when you are right and returns three or four marks when you are not. Across a paper with eight multi-mark questions, that difference is routinely a grade boundary.

The corollary is that on a one-mark "write down the value of" question, working genuinely is a waste of time. Read the mark allocation in the margin; it is telling you how many things the examiner wants to see.

They can credit a correct method that leads nowhere, a correct method applied to your own earlier wrong number where the scheme allows follow through, a correct formula quoted before it is used, an answer in the body of the script when the answer line is blank, and a correct answer transcribed wrongly onto the answer line — Edexcel instructs examiners to mark the correct one in that last case.

They cannot creditanything you did in your head, a method they can only infer from a wrong answer, an answer in a form the question did not ask for, or a correct value that the visible working shows was reached by an invalid route. On that last point Edexcel is blunt: if it is clear from the working that the correct answer has been obtained from incorrect working, award zero. College Board's notes cut the same way from the other side — an unsupported approximation earns nothing, and a response that does present the approximation loses the point if it has been simplified incorrectly.

There is also a provision most students never hear about, and it only helps people who write things down. If you misread a number from the question — using 252 where the paper said 255 — the Edexcel guidance permits method marks to be awarded anyway, provided the misreading has not simplified the question. At A-level the instruction is to deduct two from the accuracy marks in the affected part rather than to zero it. A candidate who copied the number onto their script and then worked correctly with it can be given most of the question. A candidate who did everything in their head and wrote a single wrong number has no way of demonstrating that a misread is what happened.

One more mechanism worth knowing by name. Ignore subsequent working, abbreviated $\text{isw}$, lets an examiner disregard what you wrote after arriving at a correct answer — but only when the extra work does not make the answer wrong. Edexcel draws the line explicitly at algebra: incorrectly cancelling a fraction that was already right may be ignored, whereas manipulating a correct algebraic answer into an incorrect one is not. If you have the answer, stop writing.

The points $A(-1,4)$ and $B(5,-2)$ are given, and you are asked for the perpendicular bisector of $AB$ in the form $ax+by+c=0$. Five marks. A representative scheme allocates them as M1 for the midpoint method, A1 for the midpoint, M1 for the gradient method, M1 for taking the negative reciprocal, and A1 for the final equation in the requested form.

The standard is not maximum verbosity, but one visible line per decision the examiner is being asked to credit.

This is the honest counterweight to "always show your working". Working is evidence, and evidence can be used both ways. The instruction that actually follows from the mark schemes is narrower: show your working, and make sure the working you show is correct.

Be careful with crossing out. Edexcel's guidance is that crossed-out work is still marked unless you have replaced it with an alternative response, and that where several attempts are left uncrossed, the examiner marks the final and most complete one. A scored-through complete attempt next to a half-finished replacement is therefore the worst arrangement available to you: the replacement is what gets marked.

One sign slip, four marks

Same question, and this time a genuine error: the candidate reaches $y=x-1$ correctly and then rearranges it to $x-y+1=0$, flipping the sign of the constant. With the midpoint, the gradient, the negative reciprocal and the point-gradient line all on the page, the examiner awards M1 A1 M1 M1, withholds the final A1, and moves on: four out of five. With nothing but the answer, the no-working rule applies without discretion: zero out of five.

Four marks, lost to one sign, purely because the four correct lines before it were never written down.

Both candidates made the same mathematical error and understood the same amount. That four-mark gap measures their layout, not their mathematics, and layout is entirely within your control.

Follow through — written $\text{ft}$ in the schemes — is the mechanism that stops one early slip from destroying a long question. If the scheme marks a step as ft, the examiner accepts a value that is wrong because of an earlier error, provided you have used it correctly.

Suppose the candidate miscomputes the midpoint as $(2,3)$, having taken $(4+2)/2$ instead of $(4+(-2))/2$. The midpoint method mark is still earned, the accuracy mark is not. The gradient of $AB$ does not depend on the midpoint, so that method mark is unaffected, and so is the negative reciprocal. The candidate then produces $y-3=1(x-2)$, giving $x-y+1=0$. Three of the five marks survive an error made in the very first line.

Two things limit this. Follow through is not a general principle; it appears where the scheme writers put it, and a final accuracy mark is often marked $\text{cao}$ — correct answer only — which admits none. And it requires an intermediate value on the page to follow through from. A candidate who computes the midpoint mentally, gets it wrong, and writes only the final equation gives the examiner nothing to trace, and the question collapses to zero.

1. One idea per line. Two operations on one line means the examiner cannot tell which of them you knew and which you guessed, and a method mark that cannot be located cannot be awarded.
2. Write the formula before the numbers go into it. Quoting a correct formula is frequently a B mark in its own right, and it costs one line.
3. Substitute before you simplify. The unsimplified substitution is usually the M mark. Simplify in your head and a slip takes both the method mark and the accuracy mark instead of one.
4. Keep equals signs honest. One relation per line. A chain like $3+4=7\times 2=14$ asserts that 7 equals 14, and an examiner is entitled to read it that way.
5. Do not erase — cross out once, and only when the replacement is complete. Erased work cannot earn anything, and sometimes the version you erased was carrying the method mark.
6. Carry units and keep them attached to the number. Units are a common B mark and the fastest sanity check you have on an answer.
7. Answer in the form requested. $y=x-1$ and $x-y-1=0$ are the same line and only one of them answers a question that specified $ax+by+c=0$.
8. Stop when you have the answer. Subsequent working can be ignored, but not when it turns a correct answer into an incorrect one.

Show that and prove print the answer in the question, which means the answer is worth nothing and every mark is in the derivation. A gap in the middle usually costs the whole question, because the absence of gaps is the thing being assessed.

Hence requires you to use the previous part; a fresh, correct, independent method can score zero. Hence or otherwise removes that constraint and invites the shortcut.

Exact value forbids decimals: leave the surd, leave the $\pi$, leave the logarithm unevaluated. To 3 significant figures means round once, at the end — rounding an intermediate value and carrying it forward is a classic way to miss the accepted range.

Explain and justifywant a sentence. A correct number with no reason attached scores nothing on those marks, and AP scoring notes allocate points to a justification that is consistent with the candidate's own declared value. Write down means the opposite: no working expected, take the mark and move on.

Write out a solution in full, then compare it against a complete set of steps, checking not whether your answer matches but whether every stage you would need to be credited for is present as its own line. Do that on five questions and the layout stops being a conscious decision.

Most of the slips that make partial credit necessary come from a short list — the twelve on our page about algebra mistakes that cost marks account for most of what we see in marked work. For coordinate geometry specifically, the systems of equations guide covers the same substituted-before-simplified discipline. And when you check a completed solution against full worked steps, compare line by line and stop at the first divergence rather than only looking at the final answer.