Concrete slab on pressure treated lumber

Your best bet for a good finish relies on doing three things:

• Making sure that the foundation for the extension is well compacted and onto good material
• Cut back and scable the joint with the existing 10x10 slab so that there is a good bond when the new concrete is cast.
• Drill and fix dowel bars into the existing slab across the joint with the extension.

The number and type of bars will vary depending on the load from the new shed but you should be fine with something like 8mm (3/8") bars at 200mm (8") centres.

You should probably note that this will give you a full structural connection and so may be too much for your particular problem unless you want to be absolutely sure that the slab and the extension don't separate.

Yep, if there wasn't insulation &/or gravel under it, that would cause hollow sounding areas. But, he definitely screwed-up on not doing a control joint...every 10' is normal as well as required for exterior slabs.

However, your best course of action is to cut that crack open. Not actually all of the way through, but at least an inch deep. Control joints are meant to crack & making them in the first place usually ensures that any cracking will happen within them.

Since you only have 1 crack though, then you really don't have any other choice but to take that crack's lead. It would be reasonable to expect that there wouldn't be any other cracks in the future after that stress relief & stress relief focusing measure.