### Introduction

This STEP Support module includes a proof of a circle theorem, sketching inequalities in 2 variables and a couple of logic puzzles. 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 leads you through a proof that the angle at the centre of a circle is twice the angle at the circumference.

The **main STEP question (1995 STEP 1 Question 1)** starts off with a cubic inequality and then leads into inequalities in two variables on the (x,y) plane. It is a nice example of a STEP questions where each part builds upon the one before.

The **final question** consists of two logical thinking puzzles. The first one needs careful thought – consider carefully what could be on the other sides of the cards. For the second puzzle you might like to think about what times you could measure. The fact that they are non-uniform means that they do not burn evenly throughout; you cannot bend it into quarters and see how long it takes for three of the quarters to burn through.

### Further reading

This Advanced Problem Solving Module discusses some more aspects of Mathematical proof.

### Hints, support and self evaluation

The **“Hints and partial solutions for Assignment 4”** file gives suggestions on how you can tackle the questions, and some common pitfalls to avoid, as well as some partial solutions and answers.