STEP Preparation Resources

Welcome to the NRICH STEP preparation pages.

STEP is an additional mathematics examination, taken at the end of Y13, which forms part of conditional offers to applicants for mathematics and some related degrees at Cambridge and some other universities.

These resources are designed to help potential university applicants develop their advanced problem-solving skills and prepare for sitting STEP Mathematics examinations. 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.

Although these resources were developed with STEP in mind, there is plenty of useful material here for anyone interested in advanced problem solving in mathematics, including those intending to sit the Maths Admissions Test (MAT).

Start by reading about the STEP preparation 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 such as those found on STEP.

To complement these resources, we have also launched a new 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 who’ve taken STEP themselves. 

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

STEP Prep Module 1

Our first STEP preparation module provides a gentle introduction to being a problem-solver.

STEP Prep Module 2

The second STEP Prep module introduces you to mathematical notation and logical thinking.

STEP Prep Module 3

This STEP Prep module introduces some important aspects of mathematical proof.

STEP Prep Module 4

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

STEP Prep Module 5

Our fifth module explains some of the key calculus skills you will need for STEP.

STEP Prep Module 6

In our sixth STEP preparation module, clever substitutions are the key to solving problems.

STEP Prep Module 7

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

STEP Prep Module 8

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

STEP Prep Module 9

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

STEP Prep Module 10

This module highlights the importance of integration for STEP.

STEP Prep Module 11

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

STEP Prep Module 12

This module looks at how to solve problems involving vectors.

STEP Prep Module 13

This module helps you to understand how to approach geometry on STEP.

STEP Prep Module 14

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

STEP Prep Module 15

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

STEP Prep Module 16

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

STEP Prep Module 17

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

STEP Prep Module 18

This module covers some techniques for dealing with complex numbers.

STEP Prep Module 19

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

STEP Prep Module 20

This module looks at some of the things you need to understand about polar coordinates when working on STEP questions.

STEP Prep Module 21

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

STEP Prep Module 22

This module looks at what you need to know about hyperbolic functions for STEP.

STEP Prep Module 23

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

STEP Prep Module 24

This module offers last-minute hints, advice and practice for your final STEP preparation.

Citi Foundation logoWe are grateful to the Citi Foundation for their generous support for the development of this STEP preparation programme.