STEP Maths Exam Guide: Everything You Need to Know

What is STEP?

The Sixth Term Examination Paper (STEP) is a specialist mathematics examination designed to assess candidates' mathematical aptitude beyond A-Level standard. Administered by Cambridge Assessment Admissions Testing, STEP papers challenge students with complex, multi-stage problems that require deep mathematical thinking, creativity, and rigorous proof-writing skills. Unlike standard A-Level examinations, STEP tests the ability to tackle unfamiliar problems, apply mathematical concepts in novel contexts, and construct logical arguments with precision.

STEP has been a cornerstone of university mathematics admissions for over fifty years, earning its reputation as one of the most demanding pre-university mathematics assessments available. The examination serves as a reliable indicator of whether a student possesses the mathematical maturity and problem-solving capabilities required for undergraduate mathematics at the most competitive institutions.

Which Universities and Courses Require STEP?

The University of Cambridge requires STEP for all Mathematics and Computer Science applicants. Most colleges specify STEP 2 and STEP 3 as conditional offer requirements, with typical offers ranging from grade 1 in one paper to grade 1 in both papers, depending on the college and course. Computer Science applicants at Cambridge typically receive offers requiring one STEP paper, whilst Mathematics applicants face requirements for two papers.

The University of Warwick uses STEP as part of conditional offers for Mathematics courses, often requiring a grade 2 or grade 3 in STEP 2 or STEP 3. Imperial College London and King's College London occasionally include STEP in conditional offers for Mathematics programmes, particularly for candidates whose predicted grades suggest they may benefit from demonstrating additional mathematical capability.

Several other Russell Group universities, including the University of Bath and University College London, may reference STEP in their admissions processes or recommend it for preparation, even when not formally required. Some universities accept strong STEP performance as evidence for reducing A-Level grade requirements or as part of contextual offers.

Why Universities Use STEP

Universities employ STEP to identify students who demonstrate genuine mathematical talent beyond examination technique. A-Level Mathematics, whilst rigorous, focuses heavily on applying standard methods to familiar problem types. STEP, by contrast, presents unfamiliar problems that cannot be solved through memorised procedures alone. The examination reveals whether candidates can think independently, develop original approaches, and maintain logical rigour under pressure.

For admissions tutors, STEP results provide a reliable differentiator amongst candidates with identical A-Level predictions. The examination also correlates strongly with success in undergraduate mathematics, as both require the same qualities: persistence with difficult problems, comfort with abstraction, and the ability to construct clear mathematical arguments. Universities recognise that students who excel at STEP are far more likely to thrive in the demanding mathematical environment of a top-tier undergraduate programme.

Test Format

STEP consists of three papers: STEP 1, STEP 2, and STEP 3. Each paper lasts three hours and contains twelve questions. Candidates attempt any six questions from the twelve available, with their best six answers contributing to their final mark. Questions are divided into three sections: Pure Mathematics (eight questions), Mechanics (two questions), and Statistics & Probability (two questions).

STEP 1 is based on A-Level Mathematics content, making it accessible to students partway through their A-Level studies. STEP 2 assumes knowledge of A-Level Mathematics and is typically taken by students who have completed or nearly completed their A-Level course. STEP 3 assumes A-Level Further Mathematics content, including additional pure mathematics, mechanics, and statistics topics. Most university offers specify STEP 2 and STEP 3, as these papers align with the mathematical background expected of incoming undergraduates.

Materials and Equipment

Candidates may use a scientific or graphing calculator during STEP examinations, though questions are designed such that calculators provide minimal advantage. Formula booklets are not provided, and candidates must memorise all relevant formulae. Students may bring clear water in a transparent bottle, but no other materials, notes, or electronic devices are permitted in the examination room.

STEP papers are printed with generous space for working, and candidates write their solutions directly onto the examination paper. Examiners expect to see full working and clear reasoning throughout each solution, as marks are awarded for method as well as final answers.

Question Types Explained

STEP questions typically follow a structured format, beginning with an accessible entry point before building towards increasingly challenging extensions. Early parts of a question may guide candidates through establishing preliminary results, which then become essential tools for tackling later, more demanding sections. This scaffolded approach rewards candidates who read questions carefully and recognise how different parts connect.

Pure Mathematics Questions

Pure mathematics questions cover algebra, calculus, trigonometry, sequences and series, proof techniques, and coordinate geometry. Questions often combine multiple topics, requiring candidates to draw connections between different areas of mathematics. A typical question might begin with an algebraic manipulation, develop into a calculus problem, and conclude with a proof involving mathematical induction or proof by contradiction.

Examiners look for rigorous mathematical reasoning, clear communication of ideas, and the ability to generalise from specific cases. Strong candidates demonstrate algebraic fluency, recognise underlying patterns, and construct logically complete proofs. Questions frequently require candidates to formulate their own approaches rather than applying standard algorithms, testing mathematical creativity alongside technical skill.

Mechanics Questions

Mechanics questions involve applying mathematical principles to physical situations, including projectile motion, forces and equilibrium, circular motion, and simple harmonic motion. Problems often require candidates to formulate equations from first principles, integrate differential equations, or optimise physical quantities subject to constraints.

Examiners assess whether candidates can translate physical scenarios into mathematical models, apply calculus to solve resulting equations, and interpret solutions in the original physical context. Strong responses demonstrate clear understanding of physical principles, careful mathematical execution, and thoughtful interpretation of results.

Statistics and Probability Questions

Statistics and probability questions explore discrete and continuous distributions, expectation and variance, hypothesis testing, and probability theory. Questions may involve calculating probabilities for complex events, analysing statistical models, or proving general results about random variables.

Examiners look for precise probabilistic reasoning, careful handling of summations and integrals, and clear explanation of statistical concepts. Candidates must demonstrate understanding of when different distributions and techniques apply, and communicate their reasoning with mathematical precision.

Scoring System

Each STEP paper is marked out of 120 marks, with each question worth 20 marks. Candidates' six best answers contribute to their total score. STEP results are reported as grades: S (Outstanding), 1 (Excellent), 2 (Very Good), 3 (Good), U (Unclassified). Grade boundaries vary by paper and year, reflecting question difficulty and candidature performance.

Typically, a grade 1 requires approximately 75-85 marks (63-71% of the total), whilst a grade 2 requires approximately 55-70 marks (46-58%). A grade S, awarded to exceptional performances, generally requires 95 marks or higher (approximately 80%). These boundaries adjust annually, but the distribution of grades remains relatively stable.

What Constitutes a Strong Score

Cambridge offers typically specify grade 1,1 or grade 1,2 in STEP 2 and STEP 3, depending on the college and course. Computer Science offers often require a single grade 1 in STEP 2 or STEP 3. Achieving two grade 1s places candidates amongst the strongest mathematicians in their cohort, demonstrating the deep problem-solving ability required for Cambridge's intensive mathematics programmes.

Universities use STEP grades as threshold requirements rather than considering individual marks. Meeting the specified grade requirement, even at the lower boundary, satisfies the condition. However, achieving grades significantly above the requirement provides reassurance during the sometimes unpredictable A-Level results period.

Registration and Timeline

Registration for STEP opens in March each year, with a closing date typically in early May. Candidates must register through their school or examination centre, or as private candidates if their school does not offer STEP. The registration fee is approximately £127 per paper (2024/25 rates), with reductions available for candidates eligible for free school meals.

STEP examinations take place in June, usually in the second and third weeks of the examination period. STEP 1 is typically scheduled first, followed by STEP 2 approximately one week later, and STEP 3 a few days after STEP 2. Results are released in mid-August, shortly before A-Level results day, allowing universities to confirm offers based on STEP performance alongside A-Level grades.

Candidates take STEP at registered examination centres. Schools that teach A-Level Mathematics usually offer STEP, but candidates whose schools do not can arrange to sit the examination at another centre or register as private candidates at an approved venue. The Cambridge Assessment Admissions Testing website maintains a list of centres accepting private candidates.

Preparation Strategy

Successful STEP preparation requires sustained engagement with challenging mathematics over several months. Starting preparation early—ideally in the autumn term of Year 13 for students taking examinations in June—allows time to develop the problem-solving skills and mathematical maturity STEP demands. Attempting to prepare in just a few weeks before the examination rarely yields strong results, as STEP tests deep understanding rather than memorised techniques.

Six Months Before

Begin by ensuring thorough mastery of A-Level Mathematics content, including areas often rushed in schools, such as proof by induction, parametric equations, and differential equations. Work through STEP 1 questions to build familiarity with the examination style. Focus on understanding why solutions work rather than memorising approaches. Spend time on each question, attempting different methods and exploring extensions independently.

Develop the habit of writing clear, complete solutions. STEP rewards mathematical communication as much as correct answers, so practise presenting arguments logically, justifying each step, and explaining reasoning explicitly. Work through questions untimed initially, prioritising depth of understanding over speed.

Three Months Before

Transition to STEP 2 and STEP 3 papers, focusing on whichever papers your offer requires. Attempt complete papers under timed conditions to build examination stamina and time management skills. Analyse your performance carefully: identify which topics require additional work, recognise patterns in questions, and develop strategies for approaching unfamiliar problems.

Review official worked solutions after attempting each question. Don't simply read solutions passively—compare your approach with the model solution, understand why the official method works, and consider whether alternative approaches exist. Many STEP questions can be solved through multiple methods, and understanding these different perspectives deepens mathematical insight.

One Month Before

Focus on consolidation and exam technique. Practise recent past papers under strict examination conditions, including the full three-hour duration. Develop strategies for selecting which questions to attempt first, recognising when to move on from a difficult part, and maximising marks within the time available. Review challenging questions from earlier in your preparation, ensuring you can now solve them confidently.

Maintain regular practice right up to the examination. STEP problem-solving skills deteriorate without consistent reinforcement, so continue attempting questions even in the final week. Focus on areas of weakness whilst maintaining strength in confident topics.

Practise Resources

Cambridge Assessment Admissions Testing provides all past STEP papers from 1987 onwards, free to download from their website. These papers represent the most valuable resource for preparation, offering authentic examination questions with official mark schemes. Start with older papers for practice and reserve the most recent papers for timed mock examinations closer to the test date.

The STEP Support Programme, run by the University of Cambridge, offers free online preparation materials, including detailed worked solutions, topic-focused modules, and discussion forums. The programme provides structured preparation pathways and connects candidates with experienced STEP tutors through online masterclasses and livestreamed sessions.

Recommended Books

Advanced Problems in Mathematics by Stephen Siklos remains the definitive STEP preparation book, providing hundreds of STEP-style questions with detailed solutions and commentary. The book organises questions by topic, allowing focused practice on weaker areas whilst building towards full papers. A Concise Introduction to Pure Mathematics by Martin Liebeck strengthens foundational understanding of proof and abstract mathematical thinking.

Additional texts worth considering include Understanding Pure Mathematics by A.J. Sadler and D.W.S. Thorning for reinforcing A-Level content, and The Art and Craft of Problem Solving by Paul Zeitz for developing general problem-solving strategies applicable to STEP and beyond.

Online Resources

The Mathematics Education Network maintains a comprehensive collection of STEP resources, including solution banks and topic guides. Physics & Maths Tutor provides annotated STEP papers with student-friendly explanations. The STEP database, accessible through various mathematics education websites, allows searching for questions by topic, difficulty, and examination year.

YouTube channels run by experienced STEP tutors offer worked solutions to past papers and technique-focused tutorials. However, passive watching provides limited benefit compared with attempting questions independently before reviewing solutions.

How Taylor Tuition Can Help

Taylor Tuition offers specialist STEP preparation taught by tutors who have achieved exceptional results in STEP themselves and hold mathematics degrees from Oxford or Cambridge. Our tutors understand the examination intimately, having navigated the same admissions process and excelled in undergraduate mathematics at the UK's most demanding institutions.

We provide structured preparation programmes tailored to each student's timeline, target grades, and current mathematical level. Lessons focus on developing the problem-solving techniques, proof-writing skills, and mathematical intuition essential for STEP success. Rather than teaching memorised methods, we help students learn to approach unfamiliar problems systematically, recognise underlying mathematical structures, and construct rigorous arguments independently.

Our Teaching Methodology

STEP preparation at Taylor Tuition begins with diagnostic assessment to identify strengths and areas requiring development. We then create a personalised study plan covering all relevant STEP topics whilst building the broader mathematical skills—including algebraic fluency, logical reasoning, and creative problem-solving—that underpin success across all question types.

Lessons emphasise active problem-solving rather than passive instruction. Students work through challenging questions with guidance, learning to develop solution strategies, recover from false starts, and refine their mathematical communication. We provide carefully selected practice questions between sessions, with detailed feedback on written solutions to develop examination-quality mathematical writing.

As examinations approach, we conduct full mock tests under timed conditions, replicating examination pressure and developing time management strategies. Our tutors analyse performance question-by-question, identifying patterns in mistakes and refining technique to maximise marks on examination day.

Flexible Programmes

We offer STEP tuition across multiple timeframes, from intensive Easter revision courses to year-long preparation programmes beginning in the autumn term. Early starters benefit from deeper exploration of challenging topics and greater opportunity to develop mathematical maturity. Students beginning preparation later receive focused tuition prioritising high-yield topics and efficient examination strategies.

All programmes include access to our curated question banks, organised by topic and difficulty, and our library of STEP resources, including annotated solutions and topic guides. Students receive ongoing email support between sessions, ensuring they never remain stuck on difficult problems.

To discuss STEP preparation options and create a personalised study plan, please visit our enquiry page. Our admissions team will match you with a specialist STEP tutor whose background and teaching style align with your learning preferences and target grades.