Topic outline
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Top universities need to distinguish between a surplus of applicants, all of whom have excellent predicted grades and therefore needed to be differentiated based on their Personal Statement and perhaps an Entrance Examination or Interview. Hopefully the resources contained here will give you the opportunity to further explore your subject which you can use in your statement or interview and give you experience that might prove useful in performing well on subject-related questions in an interview or entrance examination.
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Below are links for the MAT past papers and the syllabus. There are also some worksheets and answers for topics on the syllabus which are not well covered at A Level on Geometry, Combinations and Prime Factorisation with notes for the latter two, covering some key themes, albeit designed for a lower level than MAT.
In addition, you should be aware that at K.E.S. we will typically cover the Binomial Distribution (note this is different from the Binomial Expansion) at about the same time that the MAT takes place. Therefore, particularly if you haven't done GCSE Statistics, you should make sure that you are familiar with this part of the A Level syllabus (and note that, as you don't have a calculator, you need to know the probability distribution function for calculating formulae).
It is also worth noting that the Section A questions for the MAT (including those that go further back than the past paper page on the website) are available on drfrostmaths.
Students taking the MAT are also advised to look at the TMUA papers as these are similar to Section A.
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TMUA is a relatively new admissions test. There are some past papers at the link given below but it is also advised to work through Section A of past MAT papers. These can be found on the page linked from the MAT section and also, with some additional papers that are before those on the official collection, on drfrostmaths.
As well as the Geometry and Prime Factorisation worksheets in the MAT section, there are tow other parts of the TMUA syllabus that will require further study beyond what you have learnt at A-Level. The Remainder Theorem is a generalisation of the Factor Theorem and a link is given below to some tuition videos. There is also a section of the syllabus on Logic and Proof for which notes are provided by the University of Cambridge and these are also linked below.
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STEP is a challenging examination. However, they are taken after A Levels (compared to late October/early November of Year 13 for MAT and TMUA) so you have more time to prepare and are a better mathematician (hopefully!) by that point. In addition, there is a selection of questions and you don't need to answer "that many" in order to achieve a Cambridge offer.
Cambridge Maths offers are typically based on STEP 2 and STEP 3. STEP 2 is based on A Level Maths and AS Further Maths and STEP 3 on both full A Levels. However, you might want to consider starting your preparation with some STEP 1 problems (just based on A Level Maths) and maybe even entering that exam to help you 'get into the zone.' Part of the recipe for success with STEP is in choosing the right questions for you and that comes with plenty of past paper practice. It should also be mentioned that, as all the questions are longer than A Level, you should have a higher threshold of thinking 'this seems a bit messy/long-winded' for instance, long algebraic expressions.
Another critically important aspect of STEP is working at it over a long period of time. Even though at the end of Year 12 or beginning of Year 13 it seems a long way away, the time quickly passes when you have to write a Personal Statement, attend interviews, complete mock examinations and then prepare for A-Levels. The sooner you start preparing, the better, but it expect that it will be hard in the beginning and don't let that put you off!
Below is a link to the Stephen Siklos (long-time Chief Examiner for STEP) book which is a must-read. There also a book which has lots of nice extension problems for Further Maths (useful for STEP 3 in particular), a link to an online STEP course and MEI's collection of worked STEP solutions which are often much easier to understand than the official mark-schemes which are written for marking rather than learning. There is also a document about what is called the "half-angle substitution" which is no longer on the A Level syllabus but might still form the basis for some STEP questions where they expect you to work it out on the fly.
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Below are some resources that might give you inspiration for things to talk about in your Personal Statement or at interview. You do not need to read everything or attempt every resource on these pages in order to be successful with your application! Instead pick some things that interest you.
Project Euler below is at the intersection of Maths and Computing. You need to be proficient at computer programming in order to be successful. If you don't already have these skills you might decide that it is a chance to learn some of the basics!