If you sit AQA A Level Maths, you will meet the words "fully justify your answer" again and again. It is not padding. It is AQA telling you that some of the marks are for explaining, not for calculating, and you can lose them with a completely correct answer.

It is AQA's own phrase. The other boards have their own versions, so if a friend on a different board has never heard of it, that is why.

In this guide

What the phrase is telling you

AQA publishes a list explaining its command words. On this one it says:

Any reasoning to reach the required conclusion should be explicitly stated in the solution.

Two words there are doing the work.

Explicitly means written down. Not implied by your working, not obvious from the numbers, not something the examiner could reasonably assume you knew. Written down.

Reasoning means the why, not the what. You have probably already done the calculation. This is asking you to say what the calculation proves.

One thing it does not mean. AQA is clear that "fully justify" does not stop you using your calculator for routine work. You are being asked to explain your reasoning, not to do the arithmetic the long way.

What it looks like in a real question

Here is the shape of it. A question gives you a model for the velocity of a runner:

\[ v = 11.71 - 11.68\mathrm{e}^{-0.9t} - 0.03\mathrm{e}^{0.3t} \]

and asks you to find the maximum velocity, fully justifying your answer. It is worth 8 marks.

You would differentiate, set the derivative to zero, solve for \( t \), and substitute back to get the maximum velocity. That is the maths, and it is most of the question.

But two of those eight marks are not for any of that. They are for saying two things out loud:

  • That a maximum happens where \( \dfrac{\mathrm{d}v}{\mathrm{d}t} = 0 \). You have to state the principle, not just use it.
  • That the value you found really is a maximum, rather than a minimum or a point of inflection.

A student who differentiates perfectly, solves correctly, and writes down the right velocity to one decimal place, but says neither of those things, loses a quarter of the marks on the question.

Maximum and minimum questions

This is where the phrase turns up most often, so it is worth knowing exactly what AQA will accept.

To show that your stationary point is a maximum, you have four options and any one of them is enough:

  • Use the second derivative. Work out \( \dfrac{\mathrm{d}^2v}{\mathrm{d}t^2} \) at your value and show it is negative. This is the one most students are taught.
  • Check the gradient either side. Show the derivative is positive just before your point and negative just after.
  • Sketch the curve with the maximum clearly marked.
  • Argue it is the only one. If there is only one stationary point and the context makes a maximum obvious, say so.

Pick whichever is quickest for the function in front of you. If the second derivative is horrible to differentiate, testing either side is usually faster, and it scores the same.

Do not skip the conclusion. Working out that \( f''(x) = -0.063 \) is not the mark. The mark is for writing "this is negative, so the point is a maximum". The examiner is looking for the sentence, not the number.

Three other AQA words worth knowing

Hence

AQA says plainly that hence means use the result from the previous part, and that using another method "will typically lead to fewer or no marks being given".

So if part (a) asks you to show that \( 3x^2 - 12x + 9 = 3(x-1)(x-3) \) and part (b) starts with "hence", part (b) wants you to use those factors. Starting again with the quadratic formula may get you the same answer and very few marks.

Show that

You are given the answer, so the answer is not what you are being paid for. AQA asks for "every step of a process that will lead to the required outcome", plus a closing statement saying what you have shown.

The practical trap is working backwards from the printed answer. Start from what you were given and move towards it.

Exact

Leave it as a fraction, a surd, or in terms of \( \ln \) or \( \mathrm{e} \). A rounded decimal will not get full marks however many figures you write. If a question asks for the exact solution of \( \ln x = 2 \), the answer is \( \mathrm{e}^2 \), not \( 7.389 \).

A checklist for the exam

When you see "fully justify your answer", before you move on to the next question:

  • Have I said why my method finds what the question asked for? For a maximum, that means stating that it happens where the derivative is zero.
  • Have I shown my answer is the right kind of point? Second derivative, gradient either side, or a sketch. Any one.
  • Have I written a sentence, not just a number? The mark is for the conclusion in words.
  • Have I answered in context? If the question is about a runner, the maximum velocity is a speed, not just a value of \( v \).

None of this needs extra revision. It needs about thirty seconds at the end of a question you have already done the hard part of.

Go to the source. AQA publishes a command words document explaining what every instruction in the paper is asking for, and it is free to download from their website. It is written for students rather than teachers, and it is worth twenty minutes of your time before your next mock.