Nikini, who went to King Edward VI High School (for girls), had taken French, maths, further maths and classical civilisation - a subject in which she came in the top five in the country.

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The subjects at which private-school pupils excelled were those demanded by the top universities: maths, further maths, English and physics.

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An early check of the A-level further maths paper on 31 May found an error and the paper was returned to the printers to be altered.

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And a clever redesign of the syllabus has made it easier to teach further maths over two years along with standard maths, thus boosting its popularity.

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