# STEP Prep Archive

### ***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.

### 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 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.