I would definitely suggest that your daughter wait until after the SAT's to begin the MTX. If she's never taken it, you have no idea how she'll react. I'm not trying to scare you or her, but I wouldn't risk blowing the exams.
I'm using Enbrel and just now added MTX after having been off it for two years. The day after I take it I have a headache and feel tired and slightly nauseated. Some people have no reactions and some have severe nausea and/or vomiting that lasts for a couple of days.
Here are a couple of old threads from folks on these boards.
"New to Methotrexate and really unsure" https://www.healingwell.com/community/default.aspx?f=17&m=1155513&g=1155722#m1155722
"First time on methotrexate" https://www.healingwell.com/community/default.aspx?f=17&m=692213
Good luck to your daughter,