Did you do any math here?
I'll post her abilities here as you've changed them so I can show my work. Maybe then teacher will give me a gold star.
Q - Throws a dagger dealing 60/85/110/135/160 (+45% Ability Power) magic damage. The dagger bounces to the 4 closest enemies dealing 10% less damage with each bounce.Enemies hit are marked for 4 seconds. Katarina's basic attacks or spells will consume the mark dealing 15/30/45/60/75 (+15% Ability Power) additional magic damage. (unchanged)
W - Whirls daggers in a circle dealing 40/75/110/145/180 (+60% Ability Power) magic damage. If she hits an enemy Champion, Katarina gains 15/20/25/30/35% movement speed for 1 second. (AD Scaling removed, takes the place of AP scaling)
E - Teleports to a target's location. Deals 40/70/100/130/160 (+25% Ability Power) magic damage if the target is an enemy.After using Shunpo, Katarina takes 50% reduced damage for 1 second. (Damage Reduction increased)
R - Becomes a flurry of blades, throwing daggers at the closest 3 enemy Champions dealing 350 / 550 / 750 (+ 625% AP) magic damage over 2.5 seconds.Daggers apply Grievous Wounds, reducing incoming healing by 50% for 3 seconds. (Damage buffed to a point that only a monkey would greenlight.
At rank one with 100 AP, her ult would do 975 damage, assuming you did not use your W or Q in that. That's enough to kill an ADC just by hitting one button. Assuming you used your W (also at rank one, lets assume you're level 6), as well as procced your Q and E...ASSUME FOR THIS EXAMPLE KATARINA IS LEVEL 6 WITH 100 ABILITY POWER.
First Q Proc deals 170 damage
Assuming Katarina is smart, she then Shunpo's to the target, dealing 65 damage with her teleport and dealing 60 damage by consuming the mark.
We're up to 295 damage.
Any non-inbred Katarina would then proc her W, dealing 100 Magic Damage and giving her 15% increased movement speed.
395 magic damage
Now she ults and, presumably, gets a full channel in the confusion, since all of her abilities are nearly instantaneous with no skillshots among them.
Katarina has put out 1270 damage in roughly 4.2 seconds, with no hope of heals saving that champion due to the grievous wounds inflicted by her ultimate.
Assuming the poor little Jinx she targeted is level 5 (bot lane always levels slower due to shared EXP), she died all the way back halfway through the ult, because she only has a paltry 845.76 HP.
http://i.imgur.com/TKCXxkw.gif"