No. Zero is not the right answer; there is some cost basis in the property. When she inherited the home in 1985 the fair market value of the home then became her cost basis. Hopefully somewhere in the house documents there is a value back in 1985. You can also look at tax records for 1985 on the property to at least get some basis established.
Next, when your name was added to the deed 1/2 of the basis at that time became yours. If you lived in the home for at least 24 months in the last five years prior to the sale then you can claim an exclusion of up to $250K on your part of the gain.
Finally, I assume your mom did live in the home for 24 months in the last five years so she will have up to a $250K exclusion on her part of the gain on her taxes.
As you mention receipts are the best support of the cost of improvements. However, typically should you ever be audited on the sale, the IRS can accept reasonable estimates for the cost of improvements.
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