# Number theory

### 08-S1-Q1

Irrationality, proof by contradiction, C1.

[STEP I 2008 Question 1 (Pure)]

### 07-S1-Q1

Balanced number, sum of digits, C1.

[STEP I 2007 Question 1 (Pure)]

### 06-S1-Q1

Perfect square, inequality, factors, C1.

[STEP I 2006 Question 1 (Pure)]

### 05-S2-Q2

Euler totient function, prime factors, proof, counterexample, C1.

[STEP II 2005 Question 2 (Pure)]

### 05-S1-Q1

Sum of digits, C1.

[STEP I 2005 Question 1 (Pure)]

### 04-S1-Q5

Arithmetic progression, square, solution, C1.

[STEP I 2004 Question 5 (Pure)]

### 03-S1-Q7

Inequality, divisibility, sum of digits, C1.

[STEP I 2003 Question 7 (Pure)]

### 99-S1-Q1

Divisibility, average value, C1.

[STEP I 1999 Question 1 (Pure)]

### 98-S2-Q1

Cubic equation, factors, integer solution to equation, C1.

[STEP II 1998 Question 1 (Pure)]

### 97-S2-Q1

Sum of numbers, digits, product of primes, C1.

[STEP II 1997 Question 1 (Pure)]

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)