Having passed the HAT and now in my second year of History and Economics in Oxford, I am in a position to comment on what tutors are looking for in a good examination script.
The crucial point to make, is that in the HAT test as well as in history and economics essays at Oxford, tutors are interested primarily in the argument made, and not in how much the student knows, in terms of information. A successful candidate will strive to think creatively about the big picture the question is asking him or her to consider, will plan an answer that contains several key and interrelated arguments, and then proceed to insert facts that support these essential arguments into the essay.
A less successful candidate, however, often focusses too much on displaying what he knows (facts, dates, names) at the expense of providing a logical and coherent answer.
This is easier said than done, and requires practice in thinking creatively of key arguments that can be made and how these relate to opposing arguments. It often helps to think in terms of categories when thinking about causation in history, for instance, exploring political, social, bottom-up, top-down, structural and individual perspectives, for instance.
Through my tutoring of both the HAT test as well as of History, Economics A level, International Baccalaureate, and GCSE, I will help students to learn to see the big picture and plan a coherent and argument-driven essays. This will involve the use of certain tried and tested methods such as mind-mapping, drastically improve essays if employed in the right way.