"I prefer it if people come up with their own topics. I want people, in their essays, to find things interesting and write about them. My questions, when I set them, point in that direction. But I think my wishes - find things interesting, write about them - are present in every question that's set. Obviously we're not looking for a definitive and final answer to any of them, so there is always a need for engagement from the student."
In setting you a title for your supervision essay, Supervisors have a range of options. They may set a title of their own devising, take or adapt a question from a past exam paper, or ask you to develop your own title in response to the topic or text you are preparing, perhaps suggesting a particular theme to explore. Each approach allows you the freedom to explore your own interests while developing the skills mentioned above, such as close and precise engagement with a set problem (particularly useful in an exam) or the ability to develop a critical and creative angle on a new subject (useful in portfolio essays or dissertations). Talk to your Supervisor to find out what their priorities are when they set you an essay.
As noted before, different types of assessment focus on different skills. Moreover, each Supervisor will have different priorities in setting you supervision work. Some prefer you to develop the ability to focus closely on a particular problem by developing your critical analysis skills, and will guide you to key aspects of a text or author by setting specific questions. Others will want you to explore your own response to the text and develop your own questions and directions, especially after the more constrained syllabus of A-Level.
Ultimately, however, the two approaches function together to produce work which is focussed and analytical, while producing a fresh and creative response. Depending on your own priorities and your supervisor's aims, you could choose to explore strategies for developing either of these approaches: