How maths mark schemes work

The big idea

A mark scheme splits a question into small mark points. Each one is a separate decision: did the student show this step or not? Your total is simply the number of points you earned. That is why a wrong final answer can still score most of the marks — and why a right answer with no working can score very few.

• Which board uses which codes
• M and A marks
• B marks
• R marks (IB)
• Marks in brackets
• AG — answer given
• dM — dependent marks
• ft — follow-through
• cao, oe, awrt
• isw
• SC — special case
• CBSE step marking
• Mark your own work: a routine

M1 A method mark: for choosing a correct method and applying it to the right numbers — even if you then make a slip.

A1 An accuracy mark: for a correct value. It usually depends on the M mark before it, so a lucky right answer from a wrong method gets nothing.

Example: solve 3x − 7 = 11 (M1 for isolating 3x, A1 for x = 6).

B1 A mark for a correct result or statement on its own. It does not need a method mark first.

Example: "Write down the gradient of y = 5 − 2x." (B1 for −2)

R1 For a clear reason or justification — the "because" part of an answer.

Example: show that x = 2 gives a maximum of f, where f″(2) = −6.

(M1) A bracketed mark can be implied: if a later correct line could only have come from that step, you get the mark even if the step is not written down.

AG (or A1* at A Level) The answer is printed in the question, so writing it down earns nothing — the marks are for the working that gets there, and every step must be shown.

Example: "Show that the rectangle's area is 48 cm²" for sides 6 cm and 8 cm.

dM1 A method mark that is only available if an earlier method mark was earned. It stops a later "method" being credited when it is built on a wrong start.

Example: find the stationary point of y = x² − 6x + 1. M1 for differentiating, dM1 for setting the derivative to zero, A1 for x = 3.

ft A later mark can still be earned using your own earlier wrong answer, as long as you use it correctly. You lose the mark once, not over and over.

Example: (a) find the gradient between (1, 2) and (3, 8). (b) Use it to find y when x = 5 on the line through (1, 2).

IB applies follow-through between parts when working is shown; within the same part, later accuracy marks that use the wrong value are usually lost. Edexcel only allows it where the scheme writes ft.

cao Correct answer only: no follow-through — only the exact right answer earns it.

oe Or equivalent: any equivalent correct form is accepted, e.g. 0.75, 3/4 or 75/100.

awrt Answers which round to: any answer that rounds to the stated value earns the mark, e.g. awrt 2.36 accepts 2.357 and 2.36.

isw Once the correct answer has been seen, extra working after it is ignored — you are not penalised for going on to do something unnecessary.

SC A mark the scheme allows for one particular partly-right route, for example a correct answer found by trial and improvement when the question asked for algebra. It is usually worth less than the full method.

CBSE schemes give each step its own share of the marks — typically for writing the formula, substituting correctly, and the final answer. An arithmetic slip at the end still keeps the earlier step marks, and any correct alternative method earns full credit.

1. Change pen colour. Mark in green or red so your corrections stand out from your original attempt.
2. Go point by point. For every mark point, tick it and write the code (M1, A1, B1…) next to the line that earned it — or cross it and write what was missing.
3. Find the first lost mark. Write the correct next line underneath, in your marking colour.
4. What Went Well (WWW): one sentence on what you did right, e.g. "set up the equation correctly".
5. Even Better If (EBI): one sentence on the single change that would have gained the most marks.
6. Log silly mistakes. Keep a running list: date, question, the slip, and the check that would have caught it. Patterns (sign errors, units, rounding) show up within a week.