skip to content

STEP Support Programme

STEP Support - Assignment 5


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.

Assignment PDF: 
Hints and Partial Solutions: 

Useful Links

Underground Mathematics: Selected worked STEP questions

STEP Question database

University of Cambridge Mathematics Faculty: What do we look for?

University of Cambridge Mathematics Faculty: Information about STEP

University of Cambridge Admissions Office: Undergraduate course information for Mathematics

Stephen Siklos' "Advanced Problems in Mathematics" book (external link)

MEI: Worked solutions to STEP questions (external link)

OCR: Exam board information about STEP (external link)

AMSP (Advanced Maths Support programme): Support for University Admission Tests (external link)