skip to content

STEP Support Programme

STEP Support - Assignment 11


This STEP support module includes some functions defined in a way you may not have seen before, and several equations (most of which can be solved with carefully chosen substitutions). 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 asks questions about two different functions - the first one is one that will be familiar to you, but you may not have seen it defined in the same way before.

The main STEP question (2013 STEP 1 Question 1) consists of three equations to solve. You are given a substitution for the first equation, doing something similar for the other two would be a good plan.

The final question has a couple of equations involving indices. Slightly different approaches are needed for these two.

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)