It can be reasonably argued that having a good memory helps in any academic subject, or in almost any area of life. You will need to be able to memorize a large collection definitions and formulae in many school subjects.
There are many who feel that memory plays a less important role in mathematics since the subject is more about using different techniques to solve different types of problems and being able to come up with the right strategy on the spot. Of all the academic subjects that you study in school, arguably mathematics is the least associated with rote memorization work.
However, memory work does play a key role in mathematics. While a formula sheet is always provided in school math exams at the secondary level and above, not all formulae can possibly be listed. Being able to memorize commonly used formulae such as the trigonometry formulae also saves you a little bit of time in examinations.
But memorization is not confined to just formulae and definitions. In mathematics, there are many problems requiring a specific strategy, for example, using the discriminant to determine the range of coefficients of a quadratic function if you are told that it intersects a given line at two distinct points. You have to remember these basic strategies by heart. There are also other problems that may require a specific algebraic factorization, or certain types of integration problems that require a specific substitution, for instance.
Being able to remember such techniques or formulae requires constant practice over time. That’s why you require constant revision in order to do well in mathematics. Having tuition in math can certainly help keep you focused on your revision plan and in identifying areas where you may lack specific knowledge, skills, or problem-solving techniques.