Oxford University Mathematician takes Cambridge Entrance Exam (STEP Paper) PART 1 @TomRocksMaths

Oxford University Mathematician takes Cambridge Entrance Exam (STEP Paper) PART 1 @TomRocksMaths

Uploaded March 2023 | Updated September 2026, 2 weeks ago

Oxford Mathematician Dr Tom Crawford completes the STEP Exam which is used by Cambridge University as part of the admissions process to study Undergraduate Mathematics. Part 2 is here: youtube.com/watch?v=f0Fm97oM608

The exam taken by Tom is the STEP Paper 2 from 2021. The exam forms part of the entrance requirements for admission to the University of Cambridge to study Undergraduate Maths.

You can download the test for yourself here: tomrocksmaths.files.wordpress.com/2023/03/step-2-2021-question-paper.pdf

And the mark scheme is here: tomrocksmaths.files.wordpress.com/2023/03/step-2-2021-examiners-report-and-mark-scheme.pdf

The exam is based on material covered in A-level Maths and AS-level Further Maths which are taken by 17-18 year old students in the UK as part of their high school education.

Produced by Dr Tom Crawford at the University of Oxford.

Tom is an Early-Career Teaching and Outreach Fellow at St Edmund Hall: seh.ox.ac.uk/people/tom-crawford

For more maths content check out Tom's website tomrocksmaths.com

You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.

facebook.com/tomrocksmaths
twitter.com/tomrocksmaths
instagram.com/tomrocksmaths

Get your Tom Rocks Maths merchandise here:
beautifulequations.net/collections/tom-rocks-maths

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$The OLDEST Maths Books in Oxford Oxford Mathematician Dr Tom Crawford looks through some of the oldest maths textbooks at the University of Oxford with assistance from the @StEdmundHall Librarian James Howarth. Link for Maple Learn worksheet below. Maple Learn worksheet on Parallelograms here: https://learn.maplesoft.com/doc/6p665268db/trm-parallelograms Sign-up for Maple Learn Premium using the code TOMROCKSMATHS for a discounted subscription. Head to https://getlearn.maplesoft.com/ for more information. List of books covered in the video: 1. Euclids Elements 2. William Leybournes Cursus Mathematicus 3. Galileos System of the World 4. Keplers On The Six-Angled Snowflake 5. Robert Hookes Micrographia 6. Isaac Newtons Principia Mathematica 7. Lewis Carrolls The Game Of Logic Highlights include: Galileos drawing of the heliocentric solar system with planets orbiting the sun; Robert Hookes drawings of snowflakes seen under a microscope for the first time; and Lewis Carrolls game of logic meant to be played by children. Some notes from James on the books. Fol. C 8 Mathematical collections and translations: the first tome. London: Printed by William Leybourn, MD CLXI [1661]. Translations of Galileo, Kepler etc. First volume only, almost all copies of vol. 2 destroyed in the Great fire of London. Fol. O 13 William Leybourn Cursus Mathematicus, London: Printed for Thomas Basset, Benjamin Tooke, Thomas Sawbridge, Awnsham and John Churchill,1690 9 book, 900 page course in mathematics – tons of diagrams including practical ones for calculating field area or height of buildings etc. Full title is fun: Cursus mathematicus. Mathematical sciences, in nine books. : Comprehending arithmetick, vulgar, decimal, instrumental, algebraical. Geometry, plain, solid. Cosmography, cœlestial, terrestrial. Astronomy, theorical, practical. Navigation, plain, spherical. 4° G 18 (1-7) Sammelband of 7 mathematical pamphlets including Kepler on Snowflakes. Two of the tracts we have the only copy in Oxford, two where it’s only us and the Box. Given by Timothy Goodwyn who transferred to Oxford from Leyden and became Bishop of Kildare. JJ94, John Newton, The scale of interest: or The use of decimal fractions, and the table of logarithmes, in the most easie and exact resolving all questions in anatocism, or compound interest; with tables of simple interest also at 6. per cent. per annum. Together with their use in the measuring of board, timber, stone, and gauging of cask, &c. very necesary for all carpenters, joyners, masons, glasiers, and all tradesmen whatsoever. Check your working using the Maple Calculator App – available for free on Google Play and the App Store. Android: https://play.google.com/store/apps/details?id=com.maplesoft.companion&hl=en Apple: https://apps.apple.com/us/app/maple-companion/id1466659419 Don’t forget to check out the other videos in the ‘Oxford Calculus’ series – all links below. Full playlist: https://www.youtube.com/playlist?list=PLMCRxGutHqflZoTY8JCm1GRzCdGXvZ3_S Finding critical points for functions of several variables: https://youtu.be/Leomuu82-u8 Classifying critical points using the method of the discriminant: https://www.youtube.com/watch?v=5M_ts8Q2LEM Partial differentiation explained: https://youtu.be/RVwcBGzQcT8 Second order linear differential equations: https://youtu.be/F54yhRB9qDI Integrating factors explained: https://www.youtube.com/watch?v=ftqKuOfOX3E Solving simple PDEs: https://youtu.be/uztjxrGY6Jw Jacobians explained: https://www.youtube.com/watch?v=YqMelRryG8U Separation of variables integration technique explained: https://youtu.be/zk41c0vs9XQ Solving homogeneous first order differential equations: https://youtu.be/uqvqjbAcbL8 Taylor’s Theorem explained with examples and derivation: https://www.youtube.com/watch?v=DULzJmUHN5g Heat Equation derivation: https://youtu.be/rz3cdzZXQms Separable Solutions to PDEs: https://www.youtube.com/watch?v=hcm-CgHFbwI How to solve the Heat Equation: https://youtu.be/l6spigOZCOs Fourier Series Derivation: https://youtu.be/LEonZYoW6sk Find out more about the Maple Calculator App and Maple Learn on the Maplesoft YouTube channel: https://www.youtube.com/channel/UCq2MmZQ8-kqEVAnmL2GSMsQ Produced by Dr Tom Crawford at the University of Oxford. Tom is an Early-Career Teaching and Outreach Fellow at St Edmund Hall: https://www.seh.ox.ac.uk/people/tom-crawford For more maths content check out Toms website https://tomrocksmaths.com/ You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths. https://www.facebook.com/tomrocksmaths/ https://twitter.com/tomrocksmaths https://www.instagram.com/tomrocksmaths/ Get your Tom Rocks Maths merchandise here: https://beautifulequations.net/collections/tom-rocks-maths$

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Oxford University Mathematician takes Cambridge Entrance Exam (STEP Paper) PART 1