The syllabus, followed exactly.

Additional Mathematics is where most students first meet reasoning that has to be justified rather than applied: the factor and remainder theorems, the discriminant, logarithmic and exponential manipulation, and the calculus that follows.

Elementary Mathematics rewards precision and speed more than depth, and it is where careless marks quietly accumulate over two years.

IP students cover much of the same ground earlier and with more abstraction, often alongside investigation work. The teaching follows the school's own sequence rather than a generic O-Level one.

H2 is the demanding one, and it is cumulative. Vectors and complex numbers come early, then the techniques of differentiation and integration, differential equations, and the probability and statistics that students most often under-prepare. A gap in JC1 tends to surface as a wall in JC2.

H1 is narrower, and less forgiving of gaps, because there is less room in the paper to recover marks elsewhere.

Both are taught with the mark scheme in view: where method marks sit, what has to be shown, and which conventions examiners expect.

Both Analysis and Approaches and Applications and Interpretation are examined on technique and on explanation. IB candidates lose marks as often to unfinished justification as to wrong answers, which makes an examiner's perspective unusually useful here.

The Extended Essay and Internal Assessment are assessed on judgement as much as on mathematics: choosing a question that can be handled well, then writing it up against the criteria. That is the part of the Diploma most often left to chance.

N-Level students are sometimes taught as though the O-Level syllabus applies at a lower level. It does not. The G2 papers have their own emphases and their own pace, and treating them as a diluted O-Level is how students end up unprepared.

International A-Level candidates are usually working towards a different board and timetable from their school cohort. Teaching follows the specification they will actually sit.