Unlike sisters Eliza and Margaret Adam, and sisters Penelope and Ann Albertson, I have no idea whether any or all of the Alexander girls were related. I don't know much about them, period, and such a common last name doesn't bode well for learning more, but here goes.
Frances Alexander attended the Mordecai school for one session, the first half of 1810.
Jane Alexander of Mecklenburg Co., VA attended the Mordecai school for three-and-a-half years, mid-1814 to the end of 1817. The name "Mark Alexander" is associated with hers in the ledger.
Sarah Alexander of Mecklenburg Co. VA attended the Mordecai school for five sessions, not continuous: she was there from mid-1812 to mid-1814, and then again for the second session in 1815. A "Col. Alexander" is associated with her account in the school ledger.
Mecklenburg County VA borders Warren County NC. Mark Alexander isn't a difficult name to track down in Mecklenburg County. A Mark Alexander (1792-1883) was a Congressman from that county, born on a plantation near the county seat Boydton, an alumnus of the University of North Carolina at Chapel Hill (1811). He seems a bit young to be the father of any girls at the school; but maybe he's an older brother?
The Congressman Mark Alexander was married to Sallie P. Turner, the daughter of North Carolina senator and governor James Turner. Sallie Turner's older half-sisters Mary and Rebecca Turner definitely attend the Mordecai school, 1812-1815. More on them later.
Mark Alexander's father was also Mark Alexander (d. 1824), and his mother was Lucy Bugg (d. soon after 1792). He seems to have had a half-sister Lucy Jane Alexander (1803-1862), who was called Jane or Jenny, and who married Lawson Henderson Alexander (c.1789-1842, apparently a cousin) in 1823 and settled in Arkansas later in life. She apparently had four children, Nancy, Lucy, Marcus, and Sarah Jane. Is this the Jane Alexander who attended the Mordecai school? Seems very likely.
Would love to hear from any Alexander family historians who can disentangle any of this!
UPDATE 5/15/13: I have heard from an Alexander family historian! Frances and Sarah Alexander might be the daughters of Mark Alexander's brother, William Lee Alexander, who died in 1806.