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STEP Support Programme

STEP Support - Assignment 10


This STEP support module derives some of the compound trigonometry formula ($\sin(\alpha + \beta)$ etc.) and introduces a new function. 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 derives the trigonometrical identities for $\sin(\alpha \pm \beta)$ and $\cos(\alpha \pm \beta)$.

The main STEP question (2005 STEP 2 Question 2) introduces a function which will probably be unfamiliar to you. Don't be put off by this; the question starts by asking you to evaluate the function for some specific values so that you get a feel for what it does.

The final question consists of 4 questions taken from examination papers published more than 150 years ago. Needless to say, calculators should not be used!

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)