Proof by induction, Chebyshev polynomial, differential equation, polynomial, degree.
[STEP III 2010 Question 7 (Pure)]
Taylor series, differentiation, induction, differential equation.
[STEP III 2001 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)