Portal/Chamber 07

Chamber 07 uses pellets for the second time, with the pellet receiver powering a platform to take you to the chamberlock this time.

Walkthrough
The first portal simply needs to be placed where the pellet is making a burn mark in the wall opposite the pellet launcher; the pellet will go through the portal and come out the fixed orange end of the portal on the floor, heading into the pellet receiver. This will start the platform moving.

At first it might seem impossible to get onto the platform, but if you notice, there's a space on the ceiling above the platform at one end where a portal can be made. Fire the portal gun at the ceiling above the left side of the platform's movement range, then walk over to the fixed orange end of the portal on the floor.

Wait until the platform is directly beneath the blue end of the portal, and then fall through the orange end to land on the platform. Looking through the orange portal before falling through will help you adjust your portal placement or your fall so that you are more likely to land on the platform. Do not jump early, because the edge of the portal will limit your horizontal movement. Once safely on the platform, wait until you can jump over and proceed to the chamberlock.

No Cheating SpeedRun in One Segment for Mere Mortals
As for Chamber 06, there's nothing that most people are able to do to bypass or finesse anything in this chamber. There is a very difficult fling that can get you directly to the exit; look for YouTube videos if you're interested. Otherwise, just make sure not to waste any time. Don't wait until the first pellet makes a burn mark on the wall; memorize where the blue portal needs to go and put it there as you move into the room (but, don't pause moving forward because you need to reach the trigger that starts the pellet launcher). Turn to watch the pellet and as soon as the pellet passes through the portal move the blue portal over the platform. Immediately drop through the orange portal onto the platform. You don't want to have to wait while the platform travels to the other end and comes back. Move carefully to the back of the platform and judge the right time to rush forward and jump from it to the landing outside the chamber lock and go in.