Introduction
This STEP Support module involves some trigonometry and a question about a tetrahedron (and a question about socks!). 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 shows you how to obtain a couple of trigonometrical results which you will need for later questions.
The main STEP question (2006 STEP 1 Question 8) is about a tetrahedron (triangular based pyramid), and using the volume of the tetrahedron to find another length.
The final question is about finding out how many socks you need to remove from a drawer in order to get a matching pair, two matching pairs and $n$ matching pairs. You need to fully justify your answer for n pairs rather than just extrapolating from the previous results.
Further reading
If you are feeling creative, you might like to try folding polyhedra .
Some hints and tips for tacking Trigonometry problems can he found here, and this page links to a whole range of different articles on problems involving Trigonometry.
Hints, support and self evaluation
The “Hints and partial solutions for Assignment 5” 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 STEP question from this assignment.