Are there any tests more specific than a mammogram to detect breast cancer and what are they?

You are a medical student performing your gynecology rotation in a local physicians’ office. A 35 y/o woman presents to the office for evaluation. In performing her history, she relates a familial history of her mother having died from breast cancer.

Knowing that women normally do not have their first mammogram until the age of 50, what tests can be performed for this patient? Are there any tests more specific than a mammogram to detect breast cancer and what are they?