How method marks work: M1, A1 and B1 explained

In O-Level, SEC and A-Level mathematics, most marks are awarded for the steps, not the final answer. Mark schemes label each mark with a letter: M for a method mark, A for an accuracy mark that depends on the method, and B for a mark given on its own. A student who writes only the answer can lose most of the marks for a question they got right.

The three kinds of mark

M · method: For applying a correct method to the problem. An arithmetic slip inside a correct method usually keeps the M mark.
A · accuracy: For a correct answer or intermediate result. It depends on the related M mark: a right answer from a wrong or missing method earns no A mark.
B · independent: For a correct result or statement that stands on its own, such as a derivative written down correctly.

The number after the letter is how many marks of that kind are available at that step, so M1 is one method mark and B2 is two independent marks.

A worked example

Here is a six-mark stationary-points question, marked in the style schools use. The scheme is illustrative, not an official one.

y = x³ − 3x² + 4. Find the stationary points and determine their nature. [6]

dy/dx = 3x² − 6xB1

3x² − 6x = 0 ⇒ 3x(x − 2) = 0M1

x = 0 or x = 2A1

(0, 4) and (2, 0)A1

d²y/dx² = 6x − 6M1

x = 0: −6 < 0, max · x = 2: 6 > 0, minA1

A student who writes only “(0, 4) maximum, (2, 0) minimum” has every answer right. Under a scheme like this they can still lose most of the six marks, because the A marks depend on M marks that were never shown.

The abbreviations

Cambridge-style mark schemes, which Singapore school schemes generally follow, use a short set of abbreviations next to the marks.

ft: Follow through. Credit for correct working that uses an earlier wrong answer.
dep: Dependent. The mark is only available if the previous mark was earned.
cao: Correct answer only. No follow-through allowed.
awrt: Answer which rounds to. Any answer that rounds to the given value is accepted.
oe: Or equivalent. An equivalent form of the answer is accepted.
soi: Seen or implied. The step can be credited if later working shows it was done.
isw: Ignore subsequent working. Once the correct answer is seen, later working is not marked against it.

Five ways students lose method marks

Writing only the answer. On “show that” questions the answer is printed in the question, so the working is the only thing being marked.
Skipping the line a mark lives on. Finding the stationary points without ever writing dy/dx = 0 leaves the marker nothing to award the M1 for.
Rounding too early. O-Level papers ask for non-exact answers to 3 significant figures, and angles in degrees to 1 decimal place. Rounding halfway through a calculation can push the final answer outside what the scheme accepts. Keep more figures until the last line.
Ignoring “hence”. “Hence” means use the result you have just found. A different method, even a correct one, may score nothing. “Hence or otherwise” allows another method.
Giving a decimal when the question says “exact”. Exact means surds, fractions, logarithms or π left in the answer. A calculator decimal does not earn the final mark.

Why official schemes are hard to find

SEAB does not publish the mark schemes for the national papers. Students mostly see schemes through school prelims and their teachers’ marking, which is why the conventions above are worth learning directly.

How we use this

Every piece of homework at Method & Mark comes back marked this way, in classes of five, so students see exactly which line earned or lost each mark. See Additional Mathematics, Mathematics (E Math) and IP Mathematics, or book a trial class.