|The traverse is usually a "targeted, carved" traverse. The task we did during our clinic was across a medium steep hill, firm pack. the goal was to make a perfectly straight traverse with 2 medium spaced (10-12 inches apart) carved tracks aimed at a target across the hill. This shows very fine edge control with some steering. If you just carve the traverse, you would get an arc in the traverse so you have to lighten up the edge angle to get the ski to run straight. Terrain will dictate that you need to make very fine adjustments to your edge angles to keep this line straight. Also maintaining the 10-12 inch (or whatever the examiner demo shows) requires independent leg steering, proper weight distribution and matched edge angles. All a lot harder than it sounds as well.
How is it physically possible to make a straight traverse without any slideslip? The shape to the ski, even with little pressure would make the ski take a curved course over the snow. I don't think it's physically possible do do this without some slideslip.
In the east, the traverse tasks on the exams involve doing them on one ski. In the Level II exam it's the downhill ski, in the Level III it's the uphill ski.
In both circumstances the examiner is looking for balance and stance, and a carved (i.e. no skidding) path across the snow. It's really a balance exercise more than anything, and one that requires a lot of practice.
In the east we have a core set of about a dozen tasks that can be used in the exam. As with the traverse task above, they are the same tasks but executed slightly differently at each level. Of the dozen, the examiners decide which three will be used in that particular exam and each examiner tests for the same three tasks. One great task is "super slow skiing". As we all know speed hides a great many things and the super-slow is a great way to see if the person is executing correctly.
(Note that this is only for the skiing portion of the exam, which is a two days, i.e no teaching involved. If you pass the skiing portion you can then take the teaching exam.)