In Exercise 1, we're mainly going to be dealing with eighth notes here with the exception of bar 8.
In all of these exercises, be very mindful of all the notes that require palm muting. Anytime you see the "P.M." markings, be sure to palm mute the associated note(s). I've stressed this in many of my other metal tutorials, and I'll stress it again...your palm muting must be extremely tight in order to properly pull off metal rhythm playing. So don't play these exercises faster than you can handle. Go slowly as you develop the ability to palm mute effectively. Once you start to feel comfortable with it, begin building speed.
In this exercise, bars 5-8 is pretty much a variation of bars 1-4. However there are some fairly significant changes, particularly with the increased use of legato. Be careful with all the slides in bar 7, and practice bar 8 very slowly as you get used to the tapping passage. The tapped notes are indicated by the "T" markings. I'd recommend using your picking hand's middle finger to tap the 6th string and your ring finger to tap the 4th string.
Once you have this riff down, head on over to the next page for Exercise 2!