G51MC2 Feedback 2003

Much of the material used for teaching this module was directly reused from previous years (most notably 1998). This created several problems, the major one appearing to be that a shift in the A-level syllabus meant the material assumed in several cases knowledge not possessed by the majority of the students. It was also clear that in several sections the students would have benefitted from more examples of the techniques in application and fewer proofs of the fundamental concepts. Since these sections are required primarily to support later modules where these techniques need to be employed it seems reasonable to shift the module to have a greater emphasis on practical application in future. The section on Program Correctness and a revision of proof by induction should ensure that the module continues to expose students to the concept of proof.

The Exam

Question 1

This was a compulsory multiple choice question and, one the whole, students did worse than anticipated on it. It was negatively marked which resulted in several very low scores indeed. I didn't have access to the proper facilities for doing a good analysis of the questions but most appeared to be answered correctly more often than not. The exceptions being one that asked if a graph remained connected after the removal of a vertex (I'm assuming this was caused by students misunderstanding the notation used). An a question on the assignment axiom in which the substitutions were the wrong way round - this one was answered incorrectly even by students who otherwise did very well suggesting that more emphasis needs to be placed on the directionality of the axiom in future.

Question 2

This was on induction and the marks were distributed with a large group getting first class marks for the question and an equally large group getting very few marks, suggesting people could either do induction or not.

Question 3.

Matrices. This was the most popular question on the paper despite being the area which appeared to generate the most confusion in feedback beforehand. On the whole the marks were quite low with many students able only to answer the first section (multiplication of matrices) and unable to apply matrices to 2D geometry. A lot of students lost marks because of basic errors in addition and multiplication.

Question 4.

Graph Theory. Performance on this question was generally better with most students who attempted it passing and demonstrating a basic understanding of graph theory notation and the concept of a subgraph.

Question 5.

Probability. Although people didn't do as well on this as the previous question performance was again acceptable. Most students could calculate a probability though most were unable to define a probability space or a sample space (the initial part of the question). A number got the technique for calculating the probabilities wrong. The initial task was to calculate the probability of someone winning 2 out of 3 tennis sets - with the match ceasing once 2 sets were won. Several people calculated the chance of winning 2 sets out of 2 and it was unclear whether this resulted from misunderstanding the question or not knowing how to create sample spaces. In either case an identical example was presented in the lectures and in the module notes and so basic revision should have prevented this occurring.

Question 6.

Program Correctness. This was attempted by a mere handful of students and had a similar distribution to the induction question.