## Sunday, 19 September 2010

### Drafts of answers to the "question of applied maths" Part 1

due to horribly long answer (over 1000 wds), I decided to present my answer (not model answer) into 2 parts.

part a,b: marking scheme provided

"score given" by another person
a)Define the term "score" in different perspectives. (15M)
-Another expression of "result"; simplified and quantificated - with explaination, each 2+3M
Score is defined as the integrated expression of a results after a certain process.(2 - "another expression") Results can be expressed in many forms in terms of visibility or sound (2 - Ex of another expression), but score is a rather simplied version of a results (2 - "simplicity"), which is presented with a number or a rank (set). (3 - Ex of simplicity)
At the same time one of the important difference between results and score comes from the compatability of scores. (2 - "quantification") Under the same system and process, scores are comparable while comparason is not so obvious as score (1 - Ex of another expression) .We can say that score is the quantification of results, with the help of ordered field (most probably real number) we can compare much more easily. (3 - Ex of quantification)
b)b)Consider the following cases, select an appropiate function f(x), state its domain and co-domain as well as the brief explaination to the process f. You may select f as a overall score (insert x and directly takes f(x) as the score) and f as a partial score (f as a partial score, while the total score is equal to sum of f(x_i).)
i)Score = hits within a period of time
ii)RPG game final results
iii)Rhythm game, score from each hits is proportional to the combo and inversely proportional to the time offsets error. (12M)
Expected answer : explaination (1) + PS/OS (1) + domain (1) + co-domain (1)
i)
f(x)=x, since ability is strictly equivlent to the hitting speed. (1)
Obviously this is OS, or PS = 1, also f: N→N. (1+2)
ii)
f: N^n →N, each number in the n-space vector divided by the corresponding growth factor and take their absolute value or mean. (2)
The idea comes from the limited growth chance. It's also a OS system, PS can't exist in this case. (1+1)
iii)
g = sum of f and f = x^2/e where x is the current combo and e as a measurement of error, it's obviously an PS system. (1)
f: N^2→Q, g: Q→Q, if integer function is considered than g: Q→N. (2)
This calculation alogarithm is obvious to sum up points from each hits to get an overall score. (1)
c)With reference to your answer in (a), state the nature of score and what can score show. Furthermore discuss, with examples, the compatability of score and its meaning, i.e., the growth factor / f'(x) VS the number of plays, cumulative scores, etc. (30M)