I am thinking about buying a home that has a concrete patio (~16x20) that is sloping towards the home. There is a large tree next to the patio which might be the culprit (roots pushing up concrete). There are signs that the basement was wet in the past but it looks dry right now. The backyard also slopes but there are multiple drains in the yard which were probably put in to fix past problems. What I am wondering is what is the best way to fix the patio problem and is there anything else I should think about before buying this house? It would be helpful if you could tell me the range of how much this might cost to repair in the future.

First you will want to determine if the patio is something you really want to save. If not, remove it and properly prepare the area by removing tree roots, and poorly draining soils, adding crushed stone and sand while establishing a slope away from the house. If you would like to keep it, cut the tree roots that could be lifting the slab. They will die and allow the slab to eventually drop. If you want quicker results you could try having a contractor lift the offending side by drilling holes in the slab and injecting either expanding foam or grout. Either will cause the slab to lift but has to be done carefully so as not to crack the slab. I do not know how much such a repair would cost but you could have a local contractor give you a price.

Did you get a home inspection. That patio may be just the tip of the iceberg. Home owner disclosures require the seller to tell you about past problems such as flooding, have you gotten one yet?