The 1892 Clifton College Fifth Form examination looks quite different from a modern GCSE paper. However, the comparison is unfair for two reasons. Modern examinations include a wider range of contexts and rarely allow any choice of questions.
They are also designed for a much wider ability range. Even today, an examination designed solely for 16-year-olds at Clifton College would probably look harder than a GCSE.
A better comparison would be with an AS-level paper.
Of the Higher Algebra questions, Q3 could be asked at GCSE while Q4 and Q5 might appear on the Pure 1 module at AS. It is difficult for an outsider to know quite what is required in the first parts of Q1 and Q2 - presumably the Clifton boys were drilled in the required proofs and definitions.
The remainder of these questions would need rewording for today's students and most would miss the geometrical connection in Q2.
The Higher Trigonometry questions involve fairly routine manipulatins of trigonometric formulae. There is a greater emphasis on proof, but Q1 and Q3 both ask for standard bookwork, so memory is tested rather than understanding. All the questions could legitimately be asked in an A-level examination - and according to rumour they soon will be!
What should we do to improve standards among our more able 16-year-olds?
The Department for Education and Employment's emphasis on accelerating able students ("GCSE in Year 7") and the QCA's removal of level 8 work from key stage 3 are both unhelpful in this respect (and contradictory). But there is certainly scope for more challenging work in KS3 to build a solid foundation for GCSE and A-level. At each level our students need more exposure to difficult problems (like those found in Maths Challenges) to develop deeper understanding.
Most notable about the Clifton questions is that few are trivial.
Steve Abbott is deputy head of Claydon high school, Ipswich and president of the Mathematical Association