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What mathematics do you need for university in the UK?

Prior to the election of a new UK government, the Qualifications and Curriculum Authority (which oversees assessments set by different providers) hosted discussions about reforming the A-level mathematics curriculum as studied by 16-18 year-olds in post-compulsory education. This report describes an exploratory investigation aimed at discovering whether there is evidence to indicate that reform is actually needed. The investigation was undertaken from the viewpoint that the purpose of A-level mathematics is to lay the mathematics foundations for study of quantitative subjects at university. A-level mathematics is generally mandatory for entry to courses in traditional STEM subjects (mathematics, physics, and engineering), but there is another group of quantitative subjects (chemistry, computer science, economics, business and finance, etc.), nationally taking in many more students, where A-level mathematics tends to be required for entry at only the highest ranking universities (Osmon 2009). The investigation focussed on the large number of students beginning courses in these subjects without mathematics beyond GCSE (the examination normally taken at age 16). They typically take ‘top-up’ module in their first undergraduate year, to build up their pure mathematics knowledge up to the level necessary for a first degree course in that subject. Comparing the content of these modules with A-level content provides evidence of how well these students would have been prepared if they had actually taken A-level mathematics. By proceeding in this indirect way, and using only modest resources, it proved possible to collect evidence relevant to the reform issue. In the two parts of A-level (AS and A2) the pure mathematics constitutes a prescribed core taking up two of the three modules in each part (Ofqual 2002). The investigation compared AS core with top-up in three popular quantitative subjects at two differently ranked universities: University of Manchester and City University, London. Manchester has detailed descriptions of its quantitative subject modules on its website (University of Manchester 2010), and City University provided the author with detailed descriptions of top-up mathematics modules for all its courses (City University 2010, personal communication). AS seemed about right quantitatively because the time allocated to top-up mathematics generally about 12.5% of the first undergraduate year equates approximately to the time a post-16 student would spend on an AS-level. Very strong patterns were evident: economics, business and finance courses provided very similar top-up at both universities, and moderately