OCR and MEI Maths: What "You Must Show Detailed Reasoning" Means

Some OCR questions begin "In this question you must show detailed reasoning." It's easy to read that as "show your working" and carry on as normal. It means something more specific than that, and in my experience it's where a lot of students lose marks on questions they can actually do.

It appears on several questions in every paper, so it's worth knowing what the examiners want.

What the instruction means

OCR explains it to students like this:

It's always good practice to show workings, but the statement "In this question you must show detailed reasoning" emphasises there are marks allocated for workings. You can still use your calculator to check the answer though.

There are two things worth taking from that.

You can still use your calculator. You can check your answer with it, or evaluate a function with it. It just can't replace the working that earns the marks.

The marks are already there. This is the part students tend to miss. Detailed reasoning doesn't add an extra mark for explaining. It means the marks in that question won't be given unless the marker can see how you got there.

The words to look for: "must be seen"

If you read a few OCR mark schemes for these questions, one phrase comes up a lot, which is "must be seen". The mark schemes are free on OCR's website, and I'd suggest this is the first thing to look out for in them.

Some examples from OCR mark schemes:

• "DR so method must be seen"
• "Explicit use of limits must be seen in a correct integral"
• "Some evidence of finding critical values must be seen"
• "Sufficient working must be seen. Discriminant must have been set \( > 0 \) before dividing by 8"

In the last one, reaching the right inequality isn't enough. The examiner needs to see the discriminant set greater than zero before the tidying up, because that's the step being tested.

Say why you threw a solution away

This one is particular to OCR and it often catches students out. Marks regularly depend on giving a reason for rejecting a solution, and OCR says so in its examiner guidance.

If you solve an equation and get two answers, and one of them doesn't make sense in the question, don't just write down the one you want. Say why the other one goes.

• "\( t = -3 \) is rejected because time cannot be negative."
• "\( x = -2 \) is outside the given domain \( 0 \leqslant x \leqslant 5 \)."
• "This root is rejected because \( \ln x \) is undefined for \( x \leqslant 0 \)."

A short clause is usually enough. OCR's examiner guidance asks candidates to justify "giving a reason when discarding solutions to an equation that are not valid".

A worked example

Suppose a detailed reasoning question asks you to solve

\[ 3^{2x+1} = 4^{100} \]

giving your answer to three significant figures.

A calculator will give you \( x = 62.6 \) in one step. On a detailed reasoning question that scores nothing, because none of the method is on the page. What the examiner wants to see is each step:

\[ \log 3^{2x+1} = \log 4^{100} \]

\[ (2x+1)\log 3 = 100 \log 4 \]

\[ 2x + 1 = 126.18\ldots \]

\[ x = 62.6 \text{ (3 s.f.)} \]

OCR's guidance says using a solve function to skip any one of those lines "would not result in a complete analytical method". So the intermediate value matters as much as the logarithm step.

The other OCR words that change the answer

OCR publishes what each of its command words means, which not every board does. Three of them are worth knowing because they change how much you need to write.

Determine, not find

These look like they mean the same thing, but they don't.

• Find, solve, calculate. You get full marks for the correct answer with no justification at all. OCR says this directly, and says the answer may come from a calculator or a graph.
• Determine. You need to justify the result. As OCR puts it, "you can't just state the answer, even if you can generate it from the calculator".

OCR uses determine in about a third of its questions, far more than any other board, so you'll see it often.

Verify, not show that

• Verify. Substitute the given value in and show it works. You're confirming something you've been told, so it's usually quick.
• Show that. You've been given the answer, so you need to write out every step that gets there.

Doing the show that amount of work on a verify question uses up time you'll need later in the paper.

Exact

Leave surds, fractions, \( \pi \), \( \mathrm{e} \) and logarithms as they are. 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 a question says you must show detailed reasoning:

• Write one step per line. Don't combine steps or skip any.
• Show the step the question is testing, not just the line after it. If it's about a discriminant, the discriminant needs to appear.
• Give a reason for any solution you reject. A short clause is enough.
• Use the calculator to check, not to answer. OCR is happy for you to check.
• Read the first word of every other question too. "Determine" wants justification and "find" doesn't.