Edexcel Maths: "You Must Show All Stages of Your Working"

Some Edexcel questions start with "In this question you must show all stages of your working." Underneath it there's a second sentence, and Edexcel uses two versions of that sentence. They look almost the same, but they don't mean the same thing, and in my experience most students don't notice which one they've got.

It matters because this is one of the few ways you can get a question completely right and still score nothing for it.

There are two versions, and one word separates them

Edexcel publishes a short guide explaining the difference. The two sentences are:

Solutions relying entirely on calculator technology are not acceptable.

and

Solutions relying on calculator technology are not acceptable.

The only difference is the word entirely, and it changes what you're allowed to do.

• With "entirely". You can use the calculator to help you along, but it mustn't solve the problem for you.
• Without "entirely". This is the stronger version. You need to show all your workings and calculations, and the calculator isn't there to help you answer it.

What you can still use the calculator for

For the "entirely" version, Edexcel gives examples of what is fine:

• Working out a numerical expression
• Finding a square root
• Inverse trigonometry
• Evaluating logarithms

And what isn't:

• Using graphing to solve a problem, such as finding where two lines cross
• Using the calculator to integrate or differentiate
• Using it to solve a cubic

So the line is between processing and solving. Arithmetic is processing, and finding the roots of an equation is solving.

Edexcel says the stronger version is used on questions like solving quadratic equations and inequalities, finding exact solutions to trigonometric equations, factorising and solving cubics, and equations involving surds and indices.

Why one missing line costs four marks

This is worth understanding, because it explains why the penalty is so heavy.

Edexcel uses three types of mark. M marks are for method, A marks are for accuracy and B marks stand on their own.

The rule that causes the problem is this one, in Edexcel's own words:

Accuracy marks can only be awarded if the relevant method (M) marks have been earned.

So if you skip the method and just write the answer, you lose the method mark, and because the accuracy marks depend on it you lose those as well. A four-mark question can end up scoring zero even though every number you wrote was right.

Edexcel's guidance works through exactly this. A question solved properly scores M1 A1 dM1 A1. The same two correct answers found on a calculator with no working score M0 A0 dM0 A0.

A worked example

Suppose you're asked to solve

\[ 4^{x} - 5\left(2^{x}\right) + 4 = 0 \]

A calculator with an equation solver may well give you \( x = 0 \) and \( x = 2 \). Both are right, but with no working, on a question with this instruction, they don't score anything.

What the question wants is the substitution that turns it into something you can factorise. Writing \( y = 2^{x} \), and noting that \( 4^{x} = \left(2^{x}\right)^{2} = y^{2} \):

\[ y^{2} - 5y + 4 = 0 \]

\[ (y - 1)(y - 4) = 0 \]

\[ y = 1 \quad \text{or} \quad y = 4 \]

Then back to \( x \):

\[ 2^{x} = 1 \Rightarrow x = 0 \qquad 2^{x} = 4 \Rightarrow x = 2 \]

Most of those lines carry a mark or part of one. The substitution is the step the question is testing, and it's the step a calculator skips.

You don't need to write an explanation

I mention this because students who have been taught on another board sometimes overcorrect.

Edexcel doesn't give marks for explaining. Unlike some boards, there's no mark type for an explanation or for reasoning in Edexcel A Level Maths, so a paragraph about why you chose a substitution won't earn anything.

What earns the marks is the algebra, written down in order. Show the line where you substituted, the factorised form and the equation you solved. That's the working the instruction is asking for.

A checklist for the exam

• Read the sentence under the instruction and check whether it says "entirely".
• Write down the step the question is testing. If it's a disguised quadratic, show the substitution. If it's a cubic, show the factorisation.
• Use the calculator to check your answer, not to find it. Checking is always sensible.
• Don't write explanations. Write the maths.
• If an exact answer is asked for, leave it exact. Edexcel says marks are normally lost when a candidate resorts to rounded decimals where surds were wanted.