The questions you listed at the beginning of the passage are clearly answered or assumed in the rest of your paper, which is applaudable. Your introduction is very thoughtful, introducing a lot of your perspectives on this problem. However, your introduction should provide additional explanation on certain choices made in the model. For example, what motivated the choice of scores of 20 and 80? How do you define the total length of the test? What does it mean by “the top students can finish”? How many percentages of students are considered as top students?
In addition, the time formula, T1 = 4e^[(A-D11)^2]+1, needs to be modified. Currently, if the student’s ability is much higher than the problem difficulty, it will take him more time to solve this problem than if the student’s ability is only a little bit higher than the problem difficulty. This might not be a realistic description of the situation. An alternative way is to put A-D1 in the denominator and further manipulate the formula. That way it will take students of higher abilities less time to solve the problem than students of lower abilities. On the other hand, for the students who cannot solve the problem, it will take them more time to realize that they can’t solve it if their abilities are higher but still lower than the problem difficulty than if their abilities are much lower which means they will probably give up sooner.
Moreover, there are few issues with your variable definitions. According to your definitions, each problem should be worth the same amount of points. There is no need to add the difficulty of the problem to the total score. Make sure your assumptions are constant throughout the paper and your model clearly matches your explanation. The term “unit points” is never explicitly mentioned besides in the “definitions” section. There’s also a small list in section 2.1, the purpose of this list is abstruse. Please state them in complete sentences to be more understandable.
Formatting is really good. Many keywords are in bold and graphs are all aesthetically pleasing. The paper could be strengthened by including references, like where you found out that the absolute height of the positioning satellite is usually 4 times than the absolute height of the Earth in problem 2.
Sensitivity analysis needs some touching up: one cannot tell how you varied the initial values based on your explanation. Make sure to be clearer on this. You need more that just a graph to explain the robustness of the model.
Problem 2 could be improved by adding discussion on the development on the model and its formula. It would have been interesting to read more about the sensitivity of your model as well. It is important to actually show the code. For example, how the program checks whether four lines will pass through it without intersecting with the earth. If this is done, and more math is clearly presented on your paper, this will be a great solution.
A final remark, all justifications should be in complete sentences to show professionalism and clear reasoning.
In general, your approach is very creative and a lot of great assumptions made can actually simplify the problem a lot (such as dividing the earth into 4096 regions).
Association of Computational and Mathematical Modeling