The Sixth Term Examination Paper (STEP) is a challenging mathematics admissions test used by universities such as Cambridge and Warwick as part of their offer conditions for mathematics and related degrees. Unlike many other admissions tests, STEP is typically taken at the end of Year 13 and is designed to assess a student’s ability to apply A-Level mathematics in unfamiliar and demanding problem-solving situations.

STEP questions are longer and more open-ended than standard exam questions. Rather than simply applying a method that has been recently taught, students must combine different areas of mathematics, think creatively, and develop clear logical arguments. The exam rewards mathematical reasoning and persistence as much as technical knowledge.

Each STEP paper contains 12 questions, of which students answer six. The questions are drawn from a range of pure mathematics topics typically covered in A-Level Maths and Further Maths, including algebra, calculus, sequences, trigonometry and geometry. Students are expected to show clear working and develop structured mathematical arguments rather than simply producing final answers.

Preparation for STEP often requires a different approach from school mathematics. Regular practice with past STEP questions helps students become familiar with the style and difficulty of the problems while developing the deeper problem-solving skills required for success. Starting preparation early allows time to build confidence and gradually develop the mathematical intuition needed to tackle these challenging questions.

Achieving a strong STEP grade demonstrates a high level of mathematical ability and problem-solving skill, which is why it is used by universities to identify students who are well prepared for the demands of studying mathematics at degree level.

Each STEP question is marked out of 20 marks, and for each paper a candidate’s final score is based on the six questions in which they perform best. Although all attempted questions are marked, it is generally advisable to focus on no more than six questions, aiming to produce clear and well-developed solutions rather than attempting a larger number with incomplete answers.

The mark schemes are designed to reward clear mathematical progress and sound reasoning. Candidates can gain credit for making substantial progress towards a solution, even if the final answer is not fully reached. Full marks are awarded for any correct and well-justified solution, regardless of the method used, unless the question specifically requires a particular approach.

STEP papers are graded using five possible outcomes:

• S – Outstanding

• 1 – Very good

• 2 – Good

• 3 – Satisfactory

• U – Unclassified

These grades reflect the depth of understanding and problem-solving ability demonstrated across the paper, rather than simply the number of complete solutions.

The following PDFs are extracts from the STEP specification outlining the formulae you are expected to know and use without them being provided in the exam, as well as the notation you should be familiar with when sitting the STEP examinations. If additional formulae are required for a particular question, they will either be provided in the question or you will be asked to derive them as part of the solution.

• Required Formulae
• Notation