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The Boy Who Essay

1984 words - 8 pages

MEI STRUCTURED MATHEMATICS
Marking C3 Coursework
10 tips to ensure that the right mark is
awarded

MEI Conference 2013 Marking C3 Coursework Page 2
Marking C3 Coursework
C3 coursework is very prescriptive. Providing assessors follow the criteria carefully there is no problem with the assessment. However, there are difficulties for the External moderator.
• Errors are made in the marking • Work is not checked but assumed to be correct. • Credit is given for work that is not evident.
It is not a question of "what is a good piece of coursework?" but "how can I ensure that I give an appropriate mark?" 1 Terminology This task is all about solving equations. Therefore, candidates should write equations. Persistent errors should be penalised in domain 5. Examples which should be penalised: I am going to solve the equation x3 − 4x − 1. I am going to solve the equation y = x3 − 4x − 1. I am going to solve the equation f(x) = x3 − 4x − 1. Correct terminology: I am going to solve the equation x3 − 4x − 1 = 0. Or I am going to solve the equation f(x) = 0 where f(x) = x3 − 4x − 1. 2 Illustrations All three methods require a graph and an illustration for both success and failure. A graph of the function is not an illustration of the method. Example I am going to solve the equation x3 − 4x − 1 = 0 Here is a graph of y = x3 − 4x − 1.

MEI Conference 2013 Marking C3 Coursework Page 3
You can see from the graph that there is a root of the equation in the range [1,2] which I shall find. This is not enough - only the graph has been drawn. For the change of sign method there needs to be some annotation or some "zoom in" graphs. Example For the Newton-Raphson method there needs to be two clear tangents showing convergence. This is not clear enough! This is better.
At x = 2 the function is +ve.
At x = 1 the function is −ve

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For the rearrangement method a cobweb or staircase diagram should be clear. E.g. Consider the solution of the equation x3 + x − 5 = 0 which rearranges to 3 5x x= − .
Note that general theory is not necessary or credit-worthy. It is not necessary to derive the Newton- Raphson formula and certainly not acceptable to credit such work as an illustration of the method. Each illustration should match the iterates used. 3 Iterates Every example of success and failure needs some iterates. Often these are missing yet credit is given for general theory. The iterates must match the illustrations. For example, the diagrams above illustrating the Newton-Raphson Method were of the function y = x3 + 3x2 + x − 0.5. This is the function that should be used when finding roots to demonstrate success. Excel screen shots are acceptable but the algebra must be shown. E.g. I am going to solve the equation x3 + 3x2 + x − 0.5 = 0. The graphs above illustrate the method. f(x) = x3 + 3x2 + x −...

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