### Introduction

This STEP support module includes some differentiation by first principles and an introduction to induction. Previous assignments can be found here, but you can do this one without having done the others first.

STEP questions are difficult, they are supposed to be and you should expect to get stuck. However, as you tackle more and more STEP questions you will develop a range of problem solving skills (and spend less time "being stuck").

### About this assignment

The assignment is published as a pdf file below. Each STEP Support assignment module starts with a warm-up exercise, followed by preparatory work leading to a STEP question. Finally, there is a warm-down exercise.

The **warm up** for this assignment uses differentiation by first principles to derive the derivatives of some well known functions.

The **main STEP question (1996 STEP 2 Question 3)** is about proof by induction, a Further Mathematics topic which appears on the STEP 1 specification (as well as STEP 2 and 3). There is also a second **STEP question (2006 STEP 3 Question 8)** about induction.

The **final question** is a puzzle involving a triangle and some angles.

You can find further explanations of proof by induction, and more questions to try, in this NRICH Advanced problem solving module.

### Hints, support and self evaluation

The **“Hints and partial solutions for Assignment 20”** file gives suggestions on how you can tackle the questions, and some common pitfalls to avoid, as well as some partial solutions and answers.

Here is a Worked Video Solution to the first STEP question from this assignment.

Here is a Worked Video Solution to the second STEP question from this assignment.