Welcome to the NRICH Advanced Problem Solving pages.

***For our new STEP preparation programme please visit maths.org/step.***

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.

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.

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

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

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

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

Our fifth module explains some key calculus skills.

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

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

This module highlights the importance of integration.

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

This module looks at how to solve problems involving vectors.

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

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

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

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

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

This module covers some techniques for dealing with complex numbers.

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

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