An annual update on UK University Entrance Examinations for Mathematics:
STEP (Sixth Term Examination Paper) Mathematics is a well-established mathematics examination designed to test candidates on questions that are similar in style to undergraduate mathematics. For students studying for STEP, try this excellent portal from stepmaths.co.uk which has (all free) access to STEP questions and solutions. Create an account, login and you have access to a complete library of resources.
The resources are very clearly presented. For each question you have access to a pdf with the question, Examiners’ Report and both an Official and thanks to Peter Mitchell a fully worked handwritten solution.
Note that you can also download a free copy of Stephen Siklos’ Advanced Problems in Mathematics and Core Mathematics. Advanced Problems in Mathematics is excellent preparation for any undergraduate Mathematics course. (Alternative source – free pdf)
Following each question, you will find a discussion and a full solution. The clear Contents page lists all 43 problems. Each problem has been given a title and a rough indication of the mathematical content which means you can pick out questions by topic.
An alternative (also free) source for worked solutions to STEP papers comes from MEI.
Also available are Advanced Extension Award worked solutions. The AEA qualification from Pearson is based on the A Level specification and designed for the top 10% of students to help differentiate between the most able candidates. Note that AEA papers can be found here and STEP papers here note the STEP resources including the searchable database.
Underground Mathematics has STEP questions within their Review Questions. Each question comes with a fully worked solution.
See also, from Cambridge University, their STEP Support Programme. From the home page, access the resources, you will see STEP Support Programme Foundation modules, STEP 2 modules and STEP 3 modules.
From Nrich, Prepare for University.
To further challenge yourself, MAT, STEP and AEA questions provide an excellent source of questions. Dr Jamie Frost has created such a useful resource with his STEP, MAT and AEA questions all aligned to new A Level chapters. This document is 156 pages of categorised questions (brief answers are given). Also available is a pdf file of just the STEP questions.
For mark schemes see:
- MAT (Maths Admissions Test), see the right-hand menu, question papers, followed by solutions as separate documents. For superb resources for these questions see these Underground Mathematics Review Questions where you will find not only the questions but suggestions and complete solutions.
- AEA questions and mark schemes.
- For STEP, see the beginning of this post for mark schemes and full worked solutions. STEP mark schemes can also be found on the Cambridge Assessment Preparing for STEP page.
Note the Underground Mathematics Review Questions include Oxford Mathematics Admissions Test questions and full solutions. TMUA is a newer admissions test only one question is available on the Underground Maths site, however, there is much overlap between the specifications for the TMUA and other tests such as the Oxford MAT, so these questions should provide useful resources for students taking this examination. Interestingly, Durham University states that “Those students already registered for MAT may substitute those results in place of our own test, if they do not wish to take both.”
Warwick University advise taking one of MAT, TMUA or STEP.
TUMA papers and mark schemes are available from Cambridge Assessment and I would highly recommend the presentation introducing the test, from Julian Gilbey. As suggested – try the questions first (pdf file) before watching the presentation.
Talking to Julian Gilbey, he recommends for the TMUA, the importance of working through the Extended specification notes on the website, to learn about the logic side. (See Test Specifications for the specification and enhanced specification.) He also stresses that the more Maths you can do, the more you work on stretching problems and think hard about maths the better you will get at maths. Examples he mentions for resources are any questions on the Underground Maths website, (not just the review questions already mentioned here), UKMT and olympiad problems, STEP problems (probably just STEP I initially).
“And essentially your ability to ‘think mathematically’ and to solve mathematical problems is all that these tests are testing”