How To Get Into Cambridge University

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Cambridge University Entrance Exam 2018 (STEP) – Full Textbook (180 pages) of Complete Worked Solutions – DOWNLOAD BELOW


What is STEP?

If you decide to apply to Cambridge University to study mathematics, you will have to sit the STEP (Sixth Term Examination Paper) exam.  Your offer from Cambridge will be conditional on your A-level and STEP results, so it is very important to prepare for your STEP exam in the same manner as your A-levels.  You will sit the STEP exam in June and you will be given the results in August.

You will also sit the STEP exam if you apply to Warwick University.  Many other universities will recommend that you complete the STEP questions in the book below for the sake of learning good mathematical technique, even if you do not take the exam.

STEP has been around for 30 years, and has remained a staple to test the very brightest maths students.  There are three STEPs, called papers I, II and III.  Each paper has thirteen questions, including three on mechanics and two on probability/statistics.  You will be assessed on six questions only.

The pure mathematics question in Papers I and II are based on the core A-level mathematics syllabus, with some minor additions, which are listed at the end of this book.  The pure mathematics questions in Paper III are based on a ‘typical’ Further Mathematics A-level syllabus.

The mechanics and statistics questions in STEP are aimed at students who have a particular interest in these topics.  If you take a look at the statistics questions, you will find they require knowledge of probability rather than statistics (for example, there are very few questions on statistical tests of given data).  This is because the underlying theory of statistics is not covered at A-level.


How Can I Do Well in The STEP Exam and be Offered a Place at Cambridge University?

The best preparation you can do for the STEP exam is to slowly work through STEP exam style questions.  You must go through all the possible questions that could come up in your STEP exam, and you must save your solutions so you can review them as part of your revision.  It is important to start as early as possible, so you do not get overwhelmed with the workload.

The following book contains STEP questions which have been specifically selected to take you through the entire STEP syllabus for Papers I, II and III.  Each question is followed by a comment and a full written solution, teaching you step-by-step how to do questions similar to it.  You will learn the methodology required to tackle advanced STEP questions that you will encounter in the STEP exam.


I am making this book freely available to download for the time being, but I reserve the right to remove it and make it available only for my students.


Please click the link below to download now.