I provide private lessons, tailored to each student’s needs, with a particular focus on exam preparation

A lot of the way I teach is based on conversations I've had with some of the best teachers I have had whilst at school. The best method I've found for getting across new and difficult concepts to students is using visualisation and spaced repetition. When teaching calculus for example, I find it helps to refer to constantly refer back to the graphs of the functions you're operating on because it drives home the concept of what different operations in calculus actually do. In my experience, developing this deeper, more fundamental understanding of the maths you're doing, while taking a little longer than just rote learning specific methods, helps tremendously when moving on to harder but related topics. On a similar note of developing a deeper conceptual understanding, I am a big proponent of, at times, going off syllabus and challenging my students to solve problems on the topic we're covering but which go beyond the difficulty they might encounter at school. This develops the ability to think critically and deepens understanding of the material covered, making the problems they face at school seem a lot easier.
Making my lessons engaging is probably the thing I spend the most time on in my preparation for the lessons. How I do that will always depend on the student I am teaching, and it may take two or three lessons for me to tailor my teaching style to who I'm teaching. To help with this I will always ask for feedback about each lesson - what was good and interesting, and what didn't go quite so well.