Before you do a deep dive you should learn at least a little something about air management ... actually, you should learn more than a little.
Do you know how fast you consume air? Has your instructor talked to you about SAC rate ... how to determine it, and how to use it to figure out how quickly you will consume air at depth?
Do you know what turn pressure means, and how to determine it?
Has your instructor discussed with you the importance of monitoring your air pressure regularly?
Can you determine that you will even be carrying enough air for the dive you are planning?
What about buddy skills .... has your instructor discussed the importance of keeping a safe proximity to your dive buddy? Watching your dive buddy for signs of stress or narcosis (have you even discussed what those are)? How to respond if you see those signs? Diving in a manner that allows you and your buddy to maintain visual contact at all times?
If the answer to any of those question is no, then you have not adequately prepared for a deep dive. You may be just fine, but that's because you will be depending on your instructor or divemaster to keep you safe, rather than going down with adequate knowledge to keep yourself safe.
Remember, once you are certified AOW you will want to do these dives without the assistance of an instructor or DM. Gas management and buddy skills are essential ... both to help you avoid the most common cause of trouble and to teach you how to deal with most common causes of distress. Your AOW class should be the vehicle by which you learn these skills.
There's far more to deep diving than just the experience of the dive. A little anxiety is normal ... but the proper training will include the skills to help you deal with it.
And FWIW - I don't ask my students to solve a puzzle or math problem at depth ... you will never do something like that after class. My students do an out-of-air drill at depth ... I just spit my reg out, flash my light in their direction, and see how they respond. That tells me everything I need to know about their ability to handle narcosis ... and it's by far the most probable emergency you will have to deal with at depth. Best to see under supervision how you will deal with it. Oh ... and kneeling on the bottom isn't allowed. If you are going deep, you need to have adequate buoyancy control to be able to handle common problems without losing buoyancy. If you do not, then you should work on your buoyancy control at shallower depths before attempting a deep dive. Losing buoyancy on a deep dive can quickly result in an uncontrolled ascent, which can land you in the chamber, or worse.
Yes, relax and have fun ... but make sure you have received the proper training in advance of the dive ...
... Bob (Grateful Diver)