You have got to be kidding! The school failed to teach your daughter enough that she does not show a years worth of progress in Math and you have to hire a tutor so that she can be promoted? If she passed the class with a B, the B was a lie. The school is responsible for teaching her, and if they want her to pass the TAKS (she should really only have one shot at it-this is a measure of the SCHOOL, not the student) then they should pay for it.
Here is one strategy. Write a letter to the school's special education department and demand an evaluation for a learning disablity in math, since, obviously, she did not really learn the way that they teach, her B is a sham, and she did not make one full year of progress, something they are responsible for. Say that your daughter should not be held back due to their failure. In your letter, note that you would settle for compesatory tutoring, at the districts expense, such that she learns the matieral necessary to pass the TAKS and be promoted to 8th grade.
I would also file a complaint with the department of education. They might be interested to know that your daughter will get two more chances to take the state assessment.
M.