What extra topics should the GCSE maths sylabus offer

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Since the mid 1980s the amount of material on the GCSE maths course has been drastically cut back
on. Algebra handling has been reduced and calculus, geometric proofs, indices and logarithms, set
theory, transformations, polynomials, sequences and series and certain financial topics have been
removed from the course. Also vectors, three dimensional trigonometry, matrices, and functions are
only offered on some exam boards.

Which of these should be made to reappear either as compulsory or as extra optional choices for
those taking the higher level exam ? What other areas of maths that have never featured in the GCSE
or O level course should also be made available, for example mathematical modelling, algorithms,
polyhedra and 3D structures or certain parts of the A level stats course like regression and
correlation ?
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