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STEP Support Programme

STEP Support - Assignment 1


Welcome to the STEP Support programme. This is the first of 25 Assignments designed to develop your advanced problem-solving skills.

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 manipulating surds and simplifying them. The answers to the last part can be expressed surprisingly neatly!

The main STEP question (2005 STEP 1 Question 3) is all about the solutions (or roots) of quadratic equations, and whether an equation has 0, 1 or 2 real roots. As is often the case with STEP questions, the coefficients in the equation are not numerical (they are in terms of parameters such as a, b and c).

The final question gives a slightly surprising result. A clear diagram with all the given information shown on it is a good starting point.

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)