Role Reversal

Something's wrong with my subjects this term, I think.

HL1: Maths
I had a test today. A rather okay paper for me, though quite firmly on the hard side relative to most IB HL Math papers that I've seen. I lost about 5 marks I think because my Volume of Revolution answer (the very last question) was terribly complicated (so probably wrong). Well, I just hope I can still pull out a rough 7... I'm assuming that's about 83, so 50/60. I hope I didn't lose 5 more marks, yet I'm quite sure I did. Somewhere or another.
Self-Predicted Grade: 6

HL2: Computer Science
About 5 + 3 + 2 = 10 marks gone out of 60; I had no idea how to create a virtual non-dedicated device (5 marks), ran out of time for the binary tree deletion algorithm (did most parts, except the i have 2 children deletion, so can probably get about 4 of 7) as well as didn't have time to answer a question on serial vs parallel connection in networking (2 marks). Well, I'm very sure I didn't perfect-run the rest of the paper, so...
Self-Predicted Grade: 6

HL3: Physics
Whee! Let's just fail.

Seriously, it was hard but probably not as hard as many people made it up to be. I screwed up countlessly; I misread a number from the GDC (10 power 7 and 10 power 8), and because of that lost about 7 marks I think. B fields question and circular motion, I ran out of time. So...
Self-Predicted Grade: 4

SL1: English A1
Ispahan Carpet was awesome. I was hoping for a little bit of marks on the high side to scratch the surface of a 7, but I guess not this time.
Self-Predicted Grade: 6 (7 is being too optimistic)
Actual Grade: 6

SL3: Economics
I saw the test paper and was quite relieved, though I felt a bit cheap choosing question 1 to dodge the new topic of Unemployment. They should just have set 2 questions, 1 on unemployment and 1 on inflation to stop people from doing this kind of stuff. Oh well, not difficult at all.
Self-Predicted Grade: 7
Actual Grade: 7

Wow. Unlike last year, where my HLs dominated my SLs (7 7 7 - 5 7 6), this term looks like an almost complete role reversal (6 6 4 - 6 [7] 7)!

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On another note, I created a very nasty mathematical problem based on what I learnt from Econs as well as Math...

Suppose you have two economies A and B producing two goods, X and Y. Partial units of goods are considered lost and the resources wasted. The PPC for economy A is modelled by 8x^2 + y^2 = 100 000 000 and the PPC for economy B is modelled by x^2 + 2y^2 = 51 840 000.

Consumers of the goods value them at the following rates:
the nth unit of good X produced has a utility 4/(3n),
the nth unit of good Y produced has a utility 3/(4n).

Find the maximum possible total utility achievable between the two groups of people supported by the two economies, assuming that free trade, with zero tariffs and zero transport cost, is allowed to take place between the two countries.

For a bonus challenge, be like Keynes and do this without drawing the graphs. Seriously, modelling impressive equations without drawing the graphs is awesome.

jk.