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The Gradient Function Coursework
- Essay length: 3186 words
- Submitted: 20/02/2008
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Reviewed by:
groat
The first 200 words of this essay...
The Gradient Function Coursework
In this piece of coursework I am going to do research on the gradient of various graphs at various points, in order to find a function, which will determine the gradient of these points without drawing or using approximations. I will only need to know the coordinates of the point as well as the type of graph I am considering, to submit them into the gradient function and determine the gradient at this point. The formulae I will use and produce will have particular parameters. Now I am going to explain them.
a: this letter will stand for the coefficient of x in the function y=ax^n and
determines how steep the graph will be.
n: this letter will be the power to which x is raised in the function y=ax^n and
determines the shape of the graph.
m: this letter will stand for the gradient at any point of any graph. I can say for
example the gradient at the point P(1;1) of the graph y=x is 1. Therefore here m=1.
The first range of graphs I am going to investigate will have
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Review of essay
Rating: 5 star(s)
Response to the question
This piece of coursework superbly explores the gradient of basic polynomial curves. The argument posed is logical, and diagrams and screenshots of excel are used to support this argument.
Level of analysis
The analysis in this piece is strong. I liked how they begin by trying to work out the gradient of a function at a point, and then showing the understanding that this isn't accurate enough. They use plenty of excel screenshots to give evidence for their hypothesis, but what I really liked was the proof by first principles (shown under the more about calculus section). Using and understanding limits at GCSE level shows high level analysis and I imagine showing this technique will help secure top marks in any piece of coursework. This piece of coursework even goes further to understanding how differential equations and integration may be useful in a real-life application. If I were to make one suggestion, it would be to explore the notation a bit further.
Quality of writing
This piece of coursework is structured well, and spelling and grammar are strongly utilised. Although pieces of formal coursework are becoming less common in mathematics at GCSE, I would note that this piece could be made more sophisticated by removing the frequent use of the first person. Other than that, it should be admired!
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