Subject matter expertise
Maths is not just any subject. It is a special and very interesting subject that needs proper care and attention to get a hold over it. If a student is scared of maths then he or she can find it difficult to learn, but if a student loves it then he or she can easily master it. An experienced maths tutor should be capable of enjoying the subject and should also make the students enjoy maths with her expertise.
Prior teaching experience
No one can become a teacher overnight. Initially there could be some distractions if the teacher does not have prior teaching experience. Hence those who have been teaching in public or private schools can decide to call for private tuitions.
Knowledge of syllabi
Teaching maths for different age group is a challenging task. Hence as a maths tutor, one must be well versed in all kinds of syllabi like A level, further mathematics, key stage 3 level, GCSE etc so that they can cater to any student request.
Also keeping the atmosphere relaxed, making the students interact with the teacher, solving their doubts and questions and acting like a friend makes the students invest faith in their tuition teacher. A private tutor is hired mostly to improve the student's skill set and caliber. So, to become a maths tutor, one has to learn to appreciate the subject well!