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This is an archive resource. For our current 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.
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.
You may also be interested in Stephen Siklos's book, Advanced Problems in Mathematics: Preparing for University, which can be downloaded for free.
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.
This module contains advice and resources to help you prepare for university interviews.
This module will help you to improve your trigonometry skills and understanding.
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.
This module offers advice on getting your head round "unusual" questions.
This module looks at hyperbolic functions.