The Rule of Product

Allow me to use Mathematics to shed some light on the IELTS band scores for you.

There is this thing in Mathematics called The Rule of Product: If there are n(A) ways to do A and n(B) ways to do B, then the number of ways to do A and B is n(A) × n(B). 

Stated simply, there are 18 ways you can score for each skill of the IELTS test (ranging from 0 to 9, but man-oh-man please don't tell me there are ppl who dare to sit the IELTS test knowing they will perform below 5, because it would be 4,664,000vnd throwing out the window). So, I will just pick 7 ways you can score for each skill. As such, there will be 7x7x7x7 = 2,401 possible combinations of scores.

But many of those combinations are real funny: it is impossible for the vast majority to get L9-R9-W9-S9, and while a combination of L8.5 and W5.5 is possible, it is very highly unlikely. And so, eliminating those funny possibilities, we get left with 458 (if you wonder how I got it, come to class I show you how).

Now, because I have said I would use Mathematics to "shed some light", you might wonder where the "light" has got in. Most of us see the IELTS in a rounded band score. We see 7.5 as 7.5, a 7-point-5 that is inferior to an eight, yet we fail to see that 7.625 is 7.5, and 7.75 is also an 8 (but how different are 7.625 and 7.75? So negligible I can only say both scorers are equally competent). I call a score like 7.625 is a score with lots of regret, because you only need 0.5 in any of the skills to reach a new milestone. 

Of the 458, there are 118 combinations like that (anything ending with 0.125 and 0.625 can cost you a heartbreak). It inflicts you the pain that lingers for days on end, putting you into the thinking of how things would have been differently if you had made one or two more correct answers.

You could argue otherwise, that it is what appears on the report that matters. It is true, which I hope I can shed another ray of light for you: aim a little higher: say you aim for 8, then study to an 8.125 before you sit the exam. Because factoring in other variables, eg. your mental state under exam pressure - we cannot be so certain that the score turns out like how we practice at home.