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Step Exam Past Papers, Worked Solutions and Answers

Free STEP Cambridge Questions & Mark Schemes for all STEP Maths Past Papers

On this page you will find STEP Cambridge question and answer documents for all STEP past papers. We've also broken them down into topics to help you easily navigate questions that you want to practise.

We recommend using this STEP question bank to structure your STEP revision. You can maximise your chances of securing an offer at Oxbridge with our STEP Tutoring programme.

Want more information on the STEP exam? Check out our guides on What is the STEP exam and The Best STEP Resources for more advice.

Call us on 020 3305 9593 to find out more.

STEP Maths Past Papers 2010-2021

1 | 2021 | STEP Exam Past Paper

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2 | 2020 | STEP Exam Past Paper

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3 | 2019 | STEP Exam Past Paper

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4 | 2018 | STEP Exam Past Paper

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5 | 2017 | STEP Exam Past Paper

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6 | 2016 | STEP Exam Past Paper

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7 | 2015 | STEP Exam Past Paper

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8 | 2014 | STEP Exam Past Paper

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9 | 2013 | STEP Exam Past Paper

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10 | 2012 | STEP Exam Past Paper

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11 | 2011 | STEP Exam Past Paper

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12 | 2010 | STEP Exam Past Paper

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STEP Past Papers 1998-2009

1 | 2009 | STEP Exam Past Paper

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2 | 2008 | STEP Exam Past Paper

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3 | 2007 | STEP Exam Past Paper

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4 | 2006 | STEP Exam Past Paper

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5 | 2005 | STEP Exam Past Paper

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6 | 2004 | STEP Exam Past Paper

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7 | 2003 | STEP Exam Past Paper

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8 | 2002 | STEP Exam Past Paper

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9 | 2001 | STEP Exam Past Paper

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10 | 2000 | STEP Exam Past Paper

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11 | 1999 | STEP Exam Past Paper

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12 | 1998 | STEP Exam Past Paper

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STEP Maths Questions by Topic

| Analysis

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| Binomial Expansion

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| Circular Motion

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| Coin Toss

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| Collision

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| Complex Numbers

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| Continuous Random Variable

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| Coordinate Geometry

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| Curve Sketching

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| Differential Equation

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| Differential Equations

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| Differentiation

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| Elementary Probability

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| Equilibrium

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| Euclidean Geometry

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| Friction

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| Functions

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| Hooke's Law

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| Inequality

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| Integration

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| Integration by Substitution

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| Number Theory

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| Poisson Distribution

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| Projectile Motion

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| Proof by Induction

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| Pulley

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| SHM

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| Trigonometry

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| Vector Geometry

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Frequently Asked Questions
STEP

→ How many questions does the STEP paper have?
There are two sections on the STEP exam, the STEP 2 and STEP 3 (STEP 1 was discontinued in 2020). 12 questions are given to students on each STEP paper. Test-takers are advised to choose no more than six questions to answer. However, there is no restriction on which questions to choose. The questions carry equal marks and the overall score is formulated on the six questions that have gained the highest marks.
→ What were the most difficult STEP questions according to last year's students?
Each STEP paper consists of 8 pure, 2 mechanics, and 2 statistics/probability questions. STEP 2 is based on A-Level Mathematics and AS Level Further Maths. STEP 3 is based more on A-Level Further Mathematics and may therefore seem more difficult. Even according to the University of Cambridge, the test is meant to be challenging and is aimed at the top 5% of mathematics students in the country.
→ Who are the Oxbridge Mind STEP Maths tutors?
Our Oxbridge STEP tutors are all previous or current Oxbridge Maths students who excelled in their Maths applications and graduated in the top 10% of their cohort. Our Oxbridge Maths tutors are subjected to a thorough background check to verify that they are competent, responsible, and courteous. All tutors are DBS verified, and all lessons are recorded to provide a safe and friendly learning environment. Throughout the process, your Maths tutor will establish a bond with you, functioning as a teacher, facilitator, and friend!
→ Why is it important to get Oxbridge Maths application help?
We understand how tough it is to apply to prestigious Oxford or Cambridge programmes, especially in Maths. Your time is limited, and you might find it tough to focus on your school exams and Oxbridge Maths application. Oxbridge Mind will assist you with your Oxbridge Maths application including STEP exams, ensuring that you complete it correctly the first time and freeing up time to focus on other aspects of your life (such as exams!).
→ What materials do Oxbridge Maths Tutors use?
Our Oxbridge Maths Tutors provide a wide selection of Maths (MAT/STEP) resources to their students. We've built a Maths course just for you, based on years of research and examiner knowledge. All of our instructors will cover the whole Oxbridge Maths course. While teaching Maths can be hit or miss, we make sure that our resources and Maths tutors are specifically targeted to your needs.
→ How many hours of Oxbridge Maths Tuition do you provide?
It's entirely your decision! Although there is no time limit on our Oxbridge Maths course, we recommend that you prepare for it for 20 to 40 hours. We're adaptable, and we want to make the STEP and interview as simple as possible for you so that you may receive the Cambridge/Oxford offer of your dreams by providing you with the best platform and award-winning tools. We ensure that you have access to a wealth of resources, including tutorials, STEP past papers, and much more!
→ Do I get to choose from your Oxbridge Maths tutors?
We want to make sure that you and your STEP tutor are on the same page and that you and your Maths tutor are working well together. If you have any gender, age, or other preferences, such as a Cambridge or Oxford undergraduate or postgraduate Maths tutor, please let our Oxbridge team know, and we will do our best to accommodate you! Get in contact with our Oxbridge team today to discover more!
→ What is unique about our Oxbridge Mind Oxbridge Maths Tutoring?
There are several Oxbridge Maths preparation courses to select from, and figuring out which one is right for you might be difficult. As part of our Oxbridge Maths preparation, our Oxbridge Mind Maths team delivers up-to-date STEP and interview tools. We have structured tutorials for Maths Interviews, and each session will be tailored to you and the specific areas you need to focus on to improve your performance. You can arrange your lessons via a personal WhatsApp chat with your tutor.
→ Is the Oxbridge Maths Tuition online or face-to-face?
We provide all of our Oxbridge Maths courses totally online since we understand how packed your schedule is. We've prepared some amazing presentations and will share our screen with you during the session to make learning more engaging and productive. With our flexible online Maths tuition, we can work around your schedule and teach you from the comfort of your own home at a time that is most convenient for you. Lessons and tutorials are recorded so that you can review them later if you forget something. When you don’t have a lesson, we set homework tasks for students to keep them motivated and thinking and track progress in between lessons.
→ Do you offer free consultation for Oxbridge Maths Course?
Without a doubt! Contact our Oxbridge staff today to learn more about our Oxbridge Maths programme and to schedule a FREE consultation.
→ Do I have to pay for all the 1-1 Oxbridge Maths Tutoring upfront?
Certainly not! We're a really adaptable team! We offer a variety of payment alternatives to help you manage the costs of studying for the Oxbridge Maths course; please contact our Oxbridge team for more details!
→ I’m an international student and live outside of UK, is that an issue?
Simply not! Students from all over the world are welcome to apply to our Oxbridge Maths programme! We are committed to helping overseas students achieve admission to prestigious universities such as Cambridge and Oxford. The following is a comprehensive overview of the services we provide worldwide: Maths Tutors in London, Maths Tutors in Australia, Maths Tutors in Singapore, Maths Tutors in India, Maths Tutors in New Zealand, Maths Tutors in Canada, Maths Tutors in the US, Maths Tutors in Dubai, Maths Tutors in Hong Kong, Maths Tutors in Melbourne, and more!
→ What is your success rate?
We've taught over 50,000 students and provided over 200,000 hours of one-on-one tutoring through Oxbridge Mind and Study Mind. We have a long history of achievement and student delight, which has earned us the title of TrustPilot's Top 5 Tutors in the UK. Our success rate at Oxbridge is more than double the national average in the United Kingdom.
→How does enrolment and payment work?
You will meet with one of our Oxbridge specialists to discuss your application and assess your suitability when you apply for a program. If you are accepted into the programme, you can pay either in full or in 12 monthly installments. We offer a variety of payment options that can be explored with a member of our team.
→ How long does the Maths programme last?
You can use your one-on-one Maths tuition hours for any topic throughout the course of three years, including your Maths Application and A-levels (all subjects). The majority of students will begin our programme between March and August 2022 for 2023 entrance, however we have many students who begin earlier or later! We may adjust the programme's structure to your needs, and we'll create a personalised strategy and timeframe for you right away.
→ Which package do you recommend I choose?
The platinum package is our most popular, and it leads to the most improvement in your Oxbridge Maths interview performance and overall application results. With over 70 hours of one-on-one mentorship, you'll get the greatest possible help to increase your chances of success. Our other packages are also highly effective, but we have less time to dig in-depth into topics or areas of weakness than we do with the Platinum Package because we have less hours of tuition.
→ Do you provide Personal Statement and Interview support too?
Without a doubt! We have prepared lesson plans for the Maths Interview, Oxbridge Maths Personal Statement, and other areas of your application in the Maths programme. You can use your 1-1 hour as you see fit across the application.
→ What happens if I have any issues, concerns or questions?
With your Maths tutors and the Oxbridge Mind support team, you'll have your own WhatsApp group. You are free to ask questions there at any time, for example, to organise lessons or for revision guidance. Our customer service team is always available, and we are pleased to speak with you over the phone.

Cambridge Mathematics Guide

Want to learn more about the Cambridge Mathematics course? Check out our comprehensive article on what to expect in our UCAS guide.

Cambridge Maths Entry Requirements

Course Structure

Learn all about the course structure, what you study from year to year and how the programme is taught

Colleges

Learn about which colleges offer a Mathematics programme and how to apply

Admissions Requirements

Want to know more about the admissions process and entry requirements? We have them all here

Common Careers

Check out common careers that are offered to alumni of Mathematics at the University of Cambridge

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1-1 Personalised STEP Tuition
Our team strongly believes in the power of personalised instruction when it comes to achieving a high score on the STEP exam. Carefully selected from prestigious universities like Cambridge, our Oxbridge STEP tutors have undergone rigorous interviews to ensure their expertise. These tutors specialise in mathematics and provide exceptional Cambridge STEP tuition, catering to students of all levels. With a focus on effective exam techniques, they will help enhance your speed and precision in solving STEP questions.
STEP Video Tutorials Online
Curious about the structure of the Maths STEP exam? Look no further! Our dedicated Oxbridge STEP tutors have designed an exclusive Cambridge Maths STEP course to assist you in acing the Maths STEP exam. Each step of the STEP questions will be broken down, offering insights into success strategies and how to attain the highest possible score in the Cambridge Maths STEP.
STEP Practice Questions Online
Seeking STEP past papers? Access the latest Cambridge Maths STEP practice questions at your convenience, enabling you to practise from the comfort of your home. Engage with our Cambridge Maths STEP practice questions to boost your STEP exam confidence, enhance performance, and achieve a remarkable 37% increase in average speed. For STEP 2 and STEP 3, expect 3 sections: Section A (Pure Mathematics) with 8 questions, Section B (Mechanics) with 2 questions, and Section C (Probability/Statistics) with 2 questions.
STEP Worked Solutions
Once you've tackled the Cambridge Maths STEP questions, we'll provide you with comprehensive solutions to the actual STEP exam questions. Collaborating with a Cambridge STEP tutor ensures not only test success but also a standout score that sets you apart and secures your place in Cambridge's esteemed mathematics programme.
STEP Homework
Seeking more STEP past paper practice? Depleted your supply of STEP questions? Make the most of the time between sessions to complete any assigned STEP homework, ensuring you're fully prepared for the Cambridge STEP exam. Extra assignments are designed to pinpoint weak areas and generate specific questions for subsequent sessions.
STEP Support + Feedback
Require further refinement of your STEP technique? You're in the right place. Utilise the additional practice time between sessions to complete homework assignments given by our exceptional Cambridge STEP tutors, ensuring thorough preparation for the Cambridge STEP exam. We'll delve into each STEP question meticulously to ensure comprehensive readiness. By identifying weaknesses and generating targeted questions, these extra tasks are instrumental in shaping your preparation for the forthcoming session.
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Upon the successful submission of their application, every student is matched with an Oxbridge STEP tutor who possesses expertise in their chosen field of study.

2.

In your initial lessons, your Oxbridge STEP tutor will collaborate with you to create a tailored study plan.

3.

For a guaranteed place at Cambridge University, take advantage of our online STEP exam study materials and engage in our enriching programmes. Attend our comprehensive full-day group seminars for invaluable insights on perfecting your application.

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