How to store user defined scoring formulas?
You can have a table of weights -- that is, an association of user with each question and how much that answer is weighted. Then you can give each user their own weight for each answer.

create table Weights(
    UserID     int not null references Users( ID ),
    AnswerID   int not null references Answers( ID ),
    Weight     int default 1, -- For Ux: Ax * Weight,
    constraint PK_Weights primary key( UserID, AnswerID )
);


I've shown the weight as an integer but you can change that if you want fractional values (A1 * 3.5 + A2 * -2.75 + A3 * 7 + A4 * 3.1415 = SCORE ).