The methods I teach my ESAT students, in one book

For schools

For a teacher or a school preparing a whole cohort, there are complete ESAT mock papers.

• Print-ready PDFs for a whole year group, with worked solutions and mark schemes.
• A free sample pack is published on this site, with nothing to register for.
• An unseen pack can be written for a single school, and is never issued to another.

What you get

• 11 moves, each a way of reaching the answer in fewer steps than the usual method, with its tips and a drawing that shows it at a glance.
• 90 worked examples across Mathematics 1, Mathematics 2, Physics, Chemistry and Biology.
• 50 practice questions, ten for each module, each on its own page with room to work and a full worked solution overleaf.
• 34 habits that apply to every question, a chart for choosing a move and an error log.

• A formula notebook with every formula and fact the ESAT syllabus expects you to recall, module by module, from Mathematics 1 to Biology, and the results beyond the syllabus that shorten real questions. The paper gives no formula sheet, so the notebook gathers them in one place to learn.
• Every later edition of the book as a PDF, at no extra cost, on the same page.

Why a book, when a chatbot answers anything

A chatbot answers any ESAT question correctly, free, in seconds. It has read every correct solution ever published and almost none of the wrong ones, because students do not publish their mistakes. I have spent years sitting with candidates while the wrong ones happened, asking them what they thought they were doing, and writing it down after every lesson. Each edition of this book takes whatever is new in those notes and adds it.

That is what a model cannot reach, and everything else here comes out of it. On a multiple choice paper the options are the values a particular slip produces, which is how a distractor gets written. This book names the slips I keep seeing, two percentage changes added rather than multiplied, a repeated loss treated as one multiple, a ratio turned upside down, and works each one through every example: 497 wrong values with the arithmetic that reaches each. A candidate who recognises the slip sees the trap before doing any arithmetic.

A paper allows 40 minutes for 27 questions, or about 89 seconds each. I timed the usual method across every worked example in this book and it averages 63 seconds, so 71 per cent of the budget goes on one question, twenty seven times in a row, before a single hard one. The moves reach the same answer in about 30. Candidates are rarely short of correct methods and often short of time, and a chatbot hands them a correct method by the longest route it knows.

Every one of the 90 examples also changes its question until the move stops being true, and shows the different answer it then gives. A shortcut you cannot falsify is worse than no shortcut, because under time pressure you will reach for it in the one case where it does not hold.

The 11 moves at a glance

Each move opens with a drawing that shows the idea before any example. These are the eleven drawings, as they appear in the book.

What each example contains

1. An ESAT style question with five to eight lettered options.
2. The answer, and the problem stated plainly and in one other setting.
3. The move, and the usual method step by step.
4. The slip that produces each wrong option.
5. A changed problem on which the move fails, with its new answer.
6. An exercise with a worked version to check against.

Preview

Eight of the book's 460 pages, each marked as a preview: how the book is laid out, how a move opens, a worked example with the usual method beside it, a page of the formula notebook, and one practice question with its solution. It is not the whole book.

Questions I am asked