AS and A Level: Maths: Core & Pure Mathematics Coursework

"This is a fairly standard piece of coursework: a happy medium. Each of the three methods that were used (Newton-Raphson; iteration using rearrangement; decimal search) were employed with a great deal of understanding of what needs to be done to get the answer out the other end. To this end, the graphs were used well to demonstrate the author had a clear idea of what he had to find. However, what was slightly more disappointing is the very surface level on which each of the methods was described. There was no clear demonstration that the author understood why he was doing what was doing. The comparison section at the end lacked any real depth to it. The functions chosen were all simplistic polynomials, and indeed, some very easy to solve by hand (the first one chosen is a polynomial in x squared, for example.) TSR User:DavyS"

"An... interesting submission. First of all, even if it were excellent mathematics, the fact that all but the text (e.g. the graphs, mathematical formulae etc.) are missing because of the transfer to online media. However, even what little is there is quite poor. It is, essentially, gathering some secondary data and not consider what is going on, just playing about with excel and calling a few numbers up. The language is sophisticated, but it's not sure which of that is the author's work and which are merely copies of buttons on Microsoft Excel's graph wizard. TSR User:DavyS"

"From the beginning of the work, it isn't immediately clear exactly what the author is attempting to achieve - a brief introductory paragraph, along with some diagrams to illustrate the results that have been tabulated, would be a huge help to the clarity of the investigation write-up. In terms of the mathematical content itself, the logic following in reaching conclusions is clear and well explained, and the important step of testing of these conclusions is carried out. However, the final step of demonstrating a rigorous proof is omitted, a step which would lift the quality of the work substantially. It's good to see a number of cases investigated (squares, hexagons and cubes), but there doesn't appear to be any rationale given for why these shapes are chosen over other possibilities. An overall conclusion for a general n-sided shape would have been good to see, even if only for a 2D shape and not for 3D. TSR user: Illusionary"

"A thorough understanding of the theory of numerical methods (Newton-Raphson, Rearrangement and Decimal Search). The method itself, the limitations and the mathematics behind it are thoroughly explained for all three problems. The comparison of the method at the end was a bit problematic. A formula was chosen that didn't work with rearrangement and so this was ruled out of being the best unfairly (although, admittedly, correctly.) Also, the graphs have been distorted by being put online, which is a shame. TSR User:DavyS"

"A good attempt, but lacking in a few areas. The work starts off well, with a clear introduction explaining the scope of the investigation. It is clear that the original work included diagrams to illustrate the results determined from the initial data collection stage (which are a useful inclusion), and tables are used effectively to show these results. Clear conclusions are reached for a general formula for the number of squares, but the explanation given for the derivation of these formulae could be improved. In particular, while the formulae are tested, they are not actually *proved* in any case included here, and it is important to realise the difference between tests and proof in a maths investigation. TSR user: Illusionary"