How difficulty is calculated

Cambridge sets grade boundaries after the papers are marked, not before. That ordering is what makes boundaries useful. If a paper turns out to be brutal, examiners lower the mark needed for each grade so that students are not punished for sitting a hard version of the exam.

Ofqual states the relationship directly:

So the mark needed for an A is a record of how the cohort actually performed. A low A boundary is evidence that the paper was hard. That is the entire premise.

The obvious approach — call anything under 70% “hard” — is the one thing you must not do, and it is what ShinyPapers used to do.

Boundary position encodes more than difficulty. It also reflects how a paper is built: how many grades it has to span, how much it needs to stretch the strongest candidates, and how marks are distributed across questions. Cambridge Assessment has documented boundaries sitting as low as 13% of the maximum purely as a structural consequence of paper design, with no implication that the paper was mispitched.

The practical effect is severe. A Level Physics 9702 Paper 1 sits far below Maths 9709 Paper 1 in essentially every session. An absolute cutoff therefore marks almost all of Physics “hard” and almost all of Maths “easy” — which tells you which subject you are looking at, not which sitting was difficult. It also hides the thing you actually want to find: the unusually nasty Maths paper.

Each paper is compared with every other recorded sitting of the same subject and component. Three measurements are combined:

• Where the A boundary sits (55%). How far below the usual A boundary for this exact paper this sitting fell, measured in standard deviations. This is the core signal.
• Whether the whole curve dropped (30%). The same comparison applied to the average of all five boundaries, A through E. This catches the paper where the A boundary looks ordinary but B, C, D and E all collapsed beneath it — meaning candidates struggled across the entire mark range, not just at the top.
• A pull toward the raw number (15%). A small absolute term, so a component whose entire history is punishing does not read as merely “typical” just because it is typical for itself.

The first two are relative measures, so the result answers “unusual for this paper?” rather than “low in absolute terms?”. They are combined and mapped onto a 0–100 scale where 50 is an ordinary sitting of that component. Higher is harder.

Scores of 67 and above are labelled Hard, 34 to 66 Medium, and below 34 Easy.

ShinyPapers records how compressed a paper’s boundaries are — the gap between the A and E thresholds — and shows it on each paper page, but it is not part of the score.

It is tempting to treat bunched boundaries as evidence of a hard paper. The direction does not hold up. On a genuinely difficult paper examiners often drop the E boundary further than the A, which widensthe spread rather than compressing it. Cambridge’s own writing on the subject frames compression as a grading-fairness problem — small mark differences swinging grades sharply — not as evidence about difficulty. Scoring it would add noise dressed up as signal, so it is reported and left out of the maths.

A relative measure needs history to be relative to. Every score is tagged with the reference class it was computed against:

• Component — four or more recorded sittings of this exact paper. The strongest comparison, and the normal case.
• Subject — too few sittings of this component, so the comparison widens to the whole subject. Directionally useful, less precise.
• Absolute — not enough history for any meaningful comparison, so the raw threshold is all there is. Treat these as a rough hint.

Because scores are relative, they shift as more sittings are ingested. A paper that looks exceptional against six sittings may look ordinary against twenty. That is the method working, not a bug — but it does mean a rating can change over time.

• Cohort effects are not separated. Boundaries respond to how candidates performed, which blends paper difficulty with the strength of that year’s cohort. ShinyPapers cannot untangle the two. Over many sittings this mostly averages out; for a single session it may not.
• Hard for others is not hard for you. A score describes how a global cohort fared, not how you will fare. A paper heavy on your weakest topic will hurt regardless of its rating.
• Question-level data is not used. Only published boundaries are available, so nothing here reflects which individual questions were hard.
• There is no A* at component level. Cambridge awards A* on the overall subject grade, not per paper — every grade threshold document states this explicitly. The top boundary on any individual component is A, and that is what ShinyPapers uses.

Grade boundaries are parsed from the official grade threshold documents Cambridge publishes after each exam series. Question papers and mark schemes are linked from PapaCambridge. ShinyPapers is not affiliated with Cambridge Assessment International Education — see About for more.