Ok here is how i would design the database for this, it is in the format
TABLENAME(primary_key**, foreign_key *, other field, other field)//notes
(each table has start_date and end_date at the end but i didnt put them in)
USERS(user_ID**) // just so that all the people are connected
STUDENTS(student_ID**, user_ID *, name, user_name, password)
TUTORS(tutor_ID**, user_ID *, name, user_name, password)
EXAM(exam_ID**, tutor_ID *, exam_name) //tutor_ID to keep track of who wrote the exam
QUESTIONS/ANSWERS(qa_ID**, exam_ID *, question_number, question, answer) //this
//keeps track of the question and answer for all exams.
RESULTS(result_ID**, student_ID *, exam_ID *, question_number, answer)//this keeps track of what answers each student gives.
This structure will allow all of the things you requested so long as you can deal with nested SELECT statements, if you need help with those just ask. I figure you can put 1/0 for true/false and just a/b/c/d for the other values in the answers section.
I have also included an attatched jpg of a quick sketch ERD from paint just so you can understand a bit better the structure.