Try to turn off the spotlight search, go to restriction and turn off ping. Double tap the home button often to reveal the multitasking bar and so to completely close recently opened apps. If you can, then buy memory manager from the app store, there is also a free version too, I just never used the free version so I don't know how it works but the paid version is great. Hard reset your iPhone once in a while. Those should help your phone to speed up a bit.