The Sixth Term Entrance Paper (STEP) is used by the University of Cambridge to determine entry to their undergraduate mathematics degree. STEP questions are significantly more challenging than those found in typical secondary school examinations. In particular, they are similar in style to the mathematics students will experience at university. Here is a text to help students bridge this gap, and develop confidence in tackling more demanding mathematics: Advanced Problems in Mathematics by Siklos.
You can find past STEP papers here: STEP Past Papers