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This course covers some particularly difficult topics from STEP 2 and STEP 3, with full solutions. We focus on topics that are very easy to make mistakes in.


  • Confront forbiddingly technical new series and summations
  • Evaluate increasingly advanced definitions and properties of sequences
  • Establish byzantine factorial identities with the binomial theorem
  • Master all the intricacies of inverse trigonometric functions
  • Picture and understand functions you have never seen before
  • Quickly unpack parametric equations for sketching and calculating
  • Sketch every detail of functions with multiple turning points and varied asymptotes
  • Manipulate three-dimensional vectors to study lines, planes, and other figures
  • Extend your understanding of trigonometry to problems in three dimensions
  • Analyse 3D solids using your knowledge of geometry

Unique system of hints and solutions

Along with each past question, we provide a series of escalating hints, each giving you more information or clues as to how to proceed.

In this way, you can attempt each question yourself and, if stuck, receive only as much help as you need, so you can practise working alone as much as possible.

Full video solutions are still provided for you to see how an expert approaches the question.

Advanced Sequences and Series

We practise manipulating recurrence relations and series representations of functions

Factorial identities and binomial expansions

Manipulating factorials is not much covered at A-level but is a frequent subject of STEP questions, often introduced via the binomial theorem

Inverse Trigonometric Functions

It is very easy to miss a trick when dealing with one of these functions, most commonly because it can be difficult to account for their restricted domains, but they are a common sight in STEP 2 and 3

Challenging combinations and definitions of functions

You will often be asked to analyse and sketch unfamiliar functions; they might be complicated compositions of other functions, or have parametric definitions, but either way you will need to learn how to find their turning points and other important features quickly

Geometry in 3D

It can be hard to build an intuition for working in three dimensions, but geometry, vectors, and trigonometry questions can all take place there, so it is important to learn how to analyse these problems and make them comprehensible


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