Look at thoooose ratios!! Why didn't see I a full ap singed yet?
Well, here it is. Before commenting or rating, please check this build ingame. You will see how can't handle your swag.

Pros.

Great helath.
Great survavility.
Insane dmg over time with the Q.
Insane damage with E, because of that awesome Ap ratio.

Cons.

Low range of abilities.
Forced to stay nerbie of enemies if you want to deal some damage.
No hard CC until Rylai's.

Not much to say, this are some basic runes for an AP. I prefer flat mana recovery rather than the other ones because thay will be so useful in early game, when you use to be more mana hungry. Besides, it staks with 'Meditation', so... don't worry about your Q.

21-0-9, AP masteries. Because of the damage, the mana regen and because it rocks.

Nothing to say about Ghost, one of the most useful summoner spells on Singed.
About flash... well, singed until level 6-7 doesn't have a strong survavility compared to mid or late game, and flash will help him to get kills or scape from certain death.

Why you use a tank as an AP Carry (Yep, this build makes you an AP carry)?

Because of the ratios of his abilities and his huge damage over time. Besides, he can be played as a tank too with this build.

Why Mercury's? He's (almost) full AP, Y U no Sorcere's?

Because you can't no be stoppen, and that Tenacity will be so damn useful.

But your team will see you as a tank, as a initiator of teamfights.

Yep, problem? With this build, your enemies will not last enough to kill you with the health provided from an early RoA and a Rylai's. Chill out and kill while you run in circles.

This guide is in construction, but check it and try it. You will be surprised.

Ah, and sorry for my english.