A syllabus is a floor, not a ceiling. Some students clear it early and then spend eight months being asked to prove it again. This is what we do with those months.
School mathematics names the technique in the question. Olympiad mathematics does not, and that single difference is what develops a mathematician. We work through the standard ladders, at the level the student is actually ready for.
Olympiad physics asks a student to model a situation before touching a formula, which is exactly what engineering asks. It is also the most reliable preparation for university physics that exists at school age.
A student who has carried one real piece of work from question to conclusion has something to talk about for years. These are chosen to fit the child, and they are supervised the way an engineering project is supervised, with real reviews.
Two honest notes. This is not a shortcut to an examination grade: it is the opposite, a deliberate detour away from the paper. And it is not for every strong student. Some capable children want depth; others want the grade and their evenings back. Both are legitimate, and the assessment is where we work out which one you have.
The assessment includes one problem deliberately above grade level. How a child handles being stuck tells me more than how they handle being right.
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