# Mei Maths Coursework

## Coursework Support for Curriculum 2005 (legacy)

Coursework is an important part of the MEI Curriculum 2005 (legacy) A Level specification. It allows some areas of mathematics to be assessed that written examinations may not assess so well. It also allows candidates to show what they can do in a context other than a timed written paper. Working on coursework helps students to develop skills that are highly valued in higher education and by employers; it also helps students to develop a deeper understanding of the mathematics involved.

Coursework is mandatory in three units:

- 4753 Core 3
- 4758 Differential Equation
- 4776 Numerical Methods

Packs for the three modules requiring coursework (C3, NM and DE) can be downloaded from the Teachers' Resources section of the Integral Mathematics Resources. If your centre does not subscribe to the online resources please contact Stella Dudzic to obtain a copy.

Please use the links below to navigate to pages containing more information about the following:

MEI AS/A level syllabus (2004-)

Teaching Advanced Mathematics (TAM)

OCR(MEI) Coursework Key Documents

6

Maurice Yap 6946 – Core 3 Mathematics Coursework – 4752/02 Methods for Ada!ced Mathematics

Using numerical methods to find roots of and solve polynomial equations

This report will explore and compare the advantages and disadvantages of three different numerical methods used to solve polynomial equations, where analytical methods cannot easily be used. It will explore instances where, for some reason, they fail and also examine their ease, efficiency and usefulness in solving polynomial equations.

Change of sign decimal search method

The change of sign! method can be used to find an approximation of a root to an equation to a specified accuracy, using a decimal search."olynomial equations can be illustrated graphically as the function y # f$x%, as shown below in figure &. The points where the curve intersects the x'axis are the real roots of the equation f$x% #(, because the x'axis is where y # (. If the curve crosses this line, the values for f$x% when x is slightly larger and smaller than the root will be positive and negative, either way round $given that the values chosen for x are not beyond any other roots%.) logical and systematic way to use this to solve an equation to a certain degree of accuracy is a decimal search, where having already identified integer intervals where roots occur, the interval is divided into ten, and f$x% for each of the ten new values for x is found. ) search for a change of sign $* or '% is conducted and the process is repeated in the interval where the change of sign occurs until the level of accuracy desired is achieved. )fter this, the same technique is applied to find the other roots and thereby solving the equation.

+xample of an application of the change of sign method

or example, consider solving the following equation, by first finding the greatest root to five significant figures-

6

x

5

−

9

x

4

−

4

x

3

−

20

x

+

26

=

0

It is shown in figure & that there are three roots to this equation. That which is labelled root c! will be attempted to be found.

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