Several leading universities either require, or strongly encourage, prospective undergraduates for degree programmes in maths to take university maths entrance tests in addition to their A levels. Some universities also use these tests for admission to computer science and physics degrees. Whether or not university maths entrance tests are a good thing is open to debate¹ – I can see both sides of the argument – but I do think the test questions can be a useful A level Maths teaching resource.

There are three maths entrance tests for English universities: 

• the Sixth Term Examination Paper (STEP), administered by Cambridge Assessment
• the Test of Mathematics for University Admissions (TMUA), also currently administered by Cambridge Assessment
• the Mathematics Admissions Test (MAT), administered by the University of Oxford. 

Some universities also use the mathematics Advanced Extension Award (AEA), administered by Pearson.

All teachers of A level Maths should be aware of these tests, but the purpose of this blog post is not to share information on them – you can find out all the details through the Advanced Mathematics Support Programme (AMSP), including details of excellent, fully-funded, support for teachers and students. My aim here is to encourage all teachers of A level Maths to consider how they might use university entrance test-style questions to enhance their A level Maths teaching. 

Unlike most A level Maths questions, those in university entrance tests are not focused primarily on enabling students to demonstrate whether they have mastered the relevant A level Maths techniques – that is assumed. The purpose of these questions is to enable students to demonstrate their ability to reason mathematically and solve mathematical problems. Incorporating such questions into teaching and learning can help your students develop these skills, becoming ‘mathematical thinkers’, as well as being technically proficient. 

I like the analogy that mastering mathematical techniques is like learning musical scales, and using the techniques to reason, solve problems and develop new insights is like making music. Mastering the techniques is crucial, and can be very satisfying for students, but the greatest pleasure in maths comes from reasoning, problem solving and developing deep understanding. Pitched at the appropriate level, students are very motivated by questions that encourage them to think creatively (yes, maths is creative!) about how to use the maths they have learned to solve mathematical problems, develop their understanding and reason more deeply. Many university entrance test questions, chosen and scaffolded appropriately, can be accessible to all A level Maths students. This makes them a valuable resource to enhance A level Maths teaching. You can view and download a couple of example questions, with some notes and solutions, to whet your appetite!

Engaging with the AMSP professional development on university maths entrance tests can have an impact on your teaching beyond just supporting your highest attainers to gain a place at a prestigious university – it can also help enhance your teaching in ways that enable more students to appreciate the pleasure of mathematical problem solving, understanding and reasoning, and help them to access the highest A level Maths grades.

If you teach A level Maths, and university admissions tests are new to you, I’d recommend attending this online course from the AMSP, which will provide a useful introduction and overview.

The list below gives links to relevant resources and sources of support. The past papers are a great source of ideas for reasoning and problem-solving questions to enhance A level Maths teaching. 

• AMSP support (information about the different tests, fully-funded professional development for teachers and tuition for students, access to resources)
• Information about MAT (as well as past papers)
• Information about the mathematics AEA (as well as past papers)
• ‘Skills for Success in University Admissions Tests for Mathematics’ ISBN 978-1-3983-2331-5

Cambridge Assessment Admissions Testing Service have withdrawn from administering various tests including STEP and TMUA. The following links to their website still contain useful information and access to past papers.

• Information about STEP, including past papers
• Information about TMUA, including past papers

From 2024, the STEP papers will be administered by OCR using the same syllabus, and it is expected that the TMUA will continue but be administered by another body.

¹ Additional mathematics papers for entry to English universities, JMC, 2020, Jennie Golding, UCL IoE