STEP Prep Archive

Welcome to the NRICH Advanced Problem Solving pages.


These resources are designed to help potential university applicants develop their advanced problem-solving skills and prepare for sitting examinations such as STEP. The material has been carefully selected to provide an accessible and supportive introduction to advanced problem-solving, and to help you build your confidence, fluency and speed.

Start by reading about the materials, or scroll down to get started on the modules.

The 24 modules below begin with general problem-solving skills and gradually introduce new techniques, ideas and advice to help you to solve advanced problems.

There is also a discussion forum to support Y12 and Y13 students preparing for STEP and other advanced mathematics examinations. You can ask for help and hints if you’re stuck, share what you have tried so far, offer advice to others and get expert guidance from Cambridge University students and staff. 

You may also be interested in Stephen Siklos's book, Advanced Problems in Mathematics: Preparing for University, which can be downloaded for free.

Advanced Problem Solving Module 1


Our first Advanced Problem Solving module provides a gentle introduction to being a problem-solver.

Advanced Problem Solving Module 2


The second Advanced Problem Solving module introduces you to mathematical notation and logical thinking.

Advanced Problem Solving Module 3


This Advanced Problem Solving module introduces some important aspects of mathematical proof.

Advanced Problem Solving Module 4


Our fourth module aims to give you a clearer understanding of the concepts underpinning calculus.

Advanced Problem Solving Module 5


Our fifth module explains some key calculus skills.

Advanced Problem Solving Module 6


In our sixth Advanced Problem Solving module, clever substitutions are the key to solving problems.

Advanced Problem Solving Module 7


This module contains advice and resources to help you prepare for university interviews.

Advanced Problem Solving Module 8


This module will help you to improve your trigonometry skills and understanding.

Advanced Problem Solving Module 9


In this module, you will learn about proof by induction and apply it to STEP questions.

Advanced Problem Solving Module 10


This module highlights the importance of integration.

Advanced Problem Solving Module 11


This module offers advice and practice on how to sketch graphs.

Advanced Problem Solving Module 12


This module looks at how to solve problems involving vectors.

Advanced Problem Solving Module 13


This module helps you to understand how to approach advanced geometry questions.

Advanced Problem Solving Module 14


This module explores what you need to know in order to tackle advanced Mechanics questions.

Advanced Problem Solving Module 15


This module looks at Statistics questions and what you need to know in order to solve them successfully.

Advanced Problem Solving Module 16


In this module, we explore how to tackle advanced Probability questions.

Advanced Problem Solving Module 17


This module offers advice and practice on dealing with questions involving Differential Equations.

Advanced Problem Solving Module 18


This module covers some techniques for dealing with complex numbers.

Advanced Problem Solving Module 19


This module offers some tricks and tips for dealing with questions involving equations and inequalities.

Advanced Problem Solving Module 20


This module looks at some of the things you need to understand about polar coordinates.

Advanced Problem Solving Module 21


This module offers advice on getting your head round "unusual" questions.

Advanced Problem Solving Module 22


This module looks at hyperbolic functions.

Advanced Problem Solving Module 23


This module looks at some of the key concepts involving series and sums.

Advanced Problem Solving Module 24


This module offers last-minute hints, advice and practice for preparing for advanced problem solving examinations.