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STEP Support Programme

STEP Support - Assignment 3


This is the third of the 25 Foundation modules. We suggest working through the first assignment and second assignment before starting this.

STEP is a challenging examination, and is different in style from A-level, although the mathematical content is the same. STEP questions are longer: they are designed to take around 30 minutes, rather than the typical 10 minutes required for an A-level question.

Do not worry if the STEP problems appear difficult: they are meant to be! However, you should not be daunted. These assignments are designed to help you to develop the skills you need, over time, so that by the time you sit the STEP exam in the summer of Y13 you will feel well-prepared.

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 involves the sigma notation, and a proof of the formula for the sum of the terms of a geometric progression. For the last part, use the formula rather than summing the individual terms, and try to do this without using a calculator.

The main STEP question (2004 STEP 1 Question 2) introduces the “floor” notation. More information on this and related functions can be found here.

The final question involves a linear Diophantine equation, i.e. one of the form ax+by = c where a, b and c are are given integers and we are looking for a solution where x and y are also integers.

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)