Abstract
This research comprises an investigation into the implications for the candidates of entering the Southern Examination Group's (SEG) Mathematics syllabus without coursework for 1988. The papers for this syllabus are arranged in a 4-in-a-row scheme. Candidates enter on one of three levels, and, owing to the nature of this particular level system, not all grades are obtainable on each level. Thus, candidates are being asked to choose between three levels of entry. The aim of this work is to model the examination system, and to evaluate it by considering the loss to a candidate of obtaining anything less than the highest A grade. Before proceeding to a structured analysis, a preliminary model was created based upon the Summer 1988 GCSE examination results of Yateley School, Hampshire. This model is developed, tested and evaluated in chapter 1. The insight gained from this mainly intuitive model is used in chapter 2 to set up a formal structure modelling the examination from the parameters of an individual candidate through a trial examination and GCSE examination to an expected loss. This model is then extended to evaluate the loss for a group of candidates where the information is given in the form of a probability distribution over the individual's parameters. In chapter 3 the model is tested and evaluated. It is used to obtain estimates of the group distribution, in the first instance by matching the overall loss to the group, then by matching the GCSE grades obtained by the group and finally by maximising the likelihood of obtaining the trial examination results and final grades.