Extended Essay: Exemplar Commentary 

Subject 
Maths 
If applicable, theme for WSEE 

If applicable, category for language essays 

If applicable, subjects used for WSEE 

Title of essay 
The Mathematics of the Rainbow 

Essay number 
A 
Examination session 
May 2014 
Assessment of extended essay 

Criteria 
Mark awarded 
Commentary 

A: Focus and method [6] 
4 
There is a clearly focussed topic and research question, but the methodology a little lacking—it’s all rather repetitive. In a sense it’s one short essay repeated four times, and this repetition should be avoided. Both the research question and the methodology needed greater thought. A more effective essay would have gone on to explore some other aspect of rainbows, perhaps after the secondary rainbow. Exploring the “ends” of the rainbow, perhaps. 

B: Knowledge and understanding [6] 
5 
Good knowledge and understanding shown, and an effective commentary runs through the essay. The use of mathematical terminology is good. 

C: Critical thinking [12] 
8 
This is a good, well written essay, but Snell’s Equation, which was crucial, was stated without justification or example. Basically, the same approach is taken four times in looking at four types of rainbow, so it’s rather repetitive. That Snell’s Equation is taken from physics doesn’t make this inappropriate as a maths essay, as the candidate has taken a situation from physics and analysed it in a mathematical manner. The repetition keeps the essay out of the 1012 range, but the clear analysis and discussion puts it firmly in 79. 

D: Presentation [4] 
4 
Well presented. All requirements are here. 

E: Engagement [6] (not included) 

The assessment of an accompanying RPPF will affect the overall mark awarded and the grade achieved. 

Total marks awarded 
21/28 
As a maths essay it’s a little flawed, but as a learning process with a successful outcome it is very good. Please note: as a result of modifying existing extended essays for illustrative purposes, not all exemplars have an accompanying RPPF for assessment under criterion E (this is a mandatory element for all essays as of 2018). As a result, this essay has been marked out of 28 rather than 34. 
Extended Essay: Exemplar Commentary 

Subject 
Maths 
If applicable, theme for WSEE 

If applicable, category for language essays 

If applicable, subjects used for WSEE 

Title of essay 
Fractals 

Essay number 
B 
Examination session 

Assessment of extended essay 

Criteria 
Mark awarded 
Commentary 

A: Focus and method [6] 
5 
A clearly developed research question is communicated well in a good introduction. Some relevant sources are used, but it’s all a little overambitious and the candidate’s mathematics skills clearly aren’t up to it—but that doesn’t affect a good mark here. 

B: Knowledge and understanding [6] 
3 
There is rather poor use of mathematical terminology. Knowledge and real understanding seems limited, and too often results are quoted with no real understanding evident and no attempt at justification. Fractals is a topic for the most mathematically able, not the case here. 

C: Critical thinking [12] 
4 
Adequate is perhaps a little generous; the research is appropriate, but the analysis and discussion are mathematically adequate at best. An overambitious choice, the candidate’s mathematics skills weren’t up to the task. There’s too much imprecise discussion that is not backed up by mathematical evidence. 

D: Presentation [4] 
2 
Some very poor graphs and poorly presented mathematics. 

E: Engagement [6] (not included) 
4 
Based on the evidence in the essay and on the RPPF, this is a good reflection, where the candidate’s desire to link maths and art leads to an exploration of fractals and hence to a refined RQ to explore the Mandelbrot and Julia sets and then to try to link them together. Good level of personal engagement shown. 

Total marks awarded 
18/34 
The reflection probably doesn’t acknowledge that the student has taken on too much and his mathematics isn’t up to the task. A good try, but the mathematics here is very difficult—an over ambitious choice. 
Extended Essay: Exemplar Commentary 

Subject 
Maths 
If applicable, theme for WSEE 

If applicable, category for language essays 

If applicable, subjects used for WSEE 

Title of essay 
Area under a Curve 

Essay number 
C 
Examination session 

Assessment of extended essay 

Criteria 
Mark awarded 
Commentary 

A: Focus and method [6] 
2 
The research question was never clearly expressed; it’s a fairly poorly done investigation into standard area under a curve methods, which is too broad a topic. There is no effective research question, so there is limited methodology to solve it. 

B: Knowledge and understanding [6] 
3 
Limited real understanding is shown, it’s all rather standard bookwork. Verifying the Trapezium rule for a straight line and Simpson’s rule for a quadratic is simply ridiculous—the answers have to be correct. Little real understanding evident. It is a lightweight essay, but the mathematical terminology used is accurate, lifting the mark to a 3. 

C: Critical thinking [12] 
3 
A poorly thought out and poorly stated research question meant this became basically just bookwork, poorly and inadequately explaining the methods used. There is clearly a lack of real reflection as the candidate failed to come up with any effective question to explore. Poor and limited research analysis and discussion. 

D: Presentation [4] 
2 
Graphs are poor—there are far better ways of drawing a straight line than opting for a calculator screen dump—particularly from a very poor GDC that draws a straight line as a step graph! 

E: Engagement [6] (not included) 

The assessment of an accompanying RPPF will affect the overall mark awarded and the grade achieved. 

Total marks awarded 
12/28 
A disappointing EE. Had the student used the reflection document to really think about what he was doing, he would surely have been able to formulate an effective RQ. As it was, he has just listed, inadequately, methods for area under a curve. A poor essay. Please note: as a result of modifying existing extended essays for illustrative purposes, not all exemplars have an accompanying RPPF for assessment under criterion E (this is a mandatory element for all essays as of 2018). As a result, this essay has been marked out of 28 rather than 34. 