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STEP Support Programme

STEP Support - Assignment 20


This STEP support module includes some differentiation by first principles and an introduction to induction. 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 uses differentiation by first principles to derive the derivatives of some well known functions.

The main STEP question (1996 STEP 2 Question 3) is about proof by induction, a Further Mathematics topic which appears on the STEP 1 specification (as well as STEP 2 and 3). There is also a second STEP question (2006 STEP 3 Question 8) about induction.

The final question is a puzzle involving a triangle and some angles.

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)