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STEP Support Programme

STEP Support - Assignment 14


This STEP support module includes some useful factorisation results, and some work with Fibonacci numbers. 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 introduces the "difference of two cubes" and "sum of two cubes" factorisations, which (like the difference of two squares factorisation) are well worth knowing.

The main STEP question (2010 STEP 2 Question 3) involves Fibonacci numbers and an explicit formula for them (rather than the implicit one $F_{n+1}=F_n+F_{n-1}$).

The final question is a simplified version of a problem from a 1850 publication "The Lady's and Gentleman’s Diary".

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)