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Finding questions fit for the new A Level: Part 1

Finding questions fit for the new A Level: Part 1

Why legacy past papers are not enough

It seems like resources for the new A Level will be tight. Yes, you can reuse papers from the legacy specifications and mix things up from different exam boards. There are still topics such as proof that are new within the A Level Maths remit. Furthermore, moving away from questions that have predictable forms is a key change to the A Level.

Questions will not so easily fall into topic specific boxes like a ‘quadratics question’ or a ‘Trig question’. Several topics will be tested within one question as a way to exercise the Problem Solving muscle. In my opinion, simply using legacy syllabus past papers will not be enough, they provide too much of a comfort zone!

Cast a wide net

Last month I attended a free and wonderfully enlightening CPD session at the King’s Maths School called ‘Problem Solving at Key Stage 5’. This was run by Dan Abramson, the Headteacher and expert all things to do with the teaching of the A level Maths curriculum.

When discussing resources for the new style of exam questions, he was refreshingly optimistic and pointed us to the TMUA, MAT, AEA and STEP papers. These have existed for years and students have been stretched in the same ways that the new A Level has only just started to catch up to. He even exemplified an A Level paper from 1973 as one that could be used for preparing for 2018 exams!

He encourages departments to look to these exams for inspiration and even write questions as part of preparing a truly representative bank of resources that prepares students for this new breed of exams.

The TMUA papers

& why I recommend using them

The Test of Mathematics for University Admission (TMUA) exams have been running for two years. There are two papers in each exam series sat by students wishing to study highly mathematical courses at universities such as Warwick, Durham and Lancaster. Each exam is 60 minutes long and all questions are multiple choice.

Use these during the year to make students ‘the good kind of uncomfortable’ and challenge existing expectations of questions. In other words, these are very good curve balls to throw at students to teach them how to tackle ambiguous questions.

Why you should do these papers yourself

I did them and quickly realised just how much ‘tunnel vision’ I had developed over the years of teaching the same past papers. We as teachers are potentially MORE stuck in our ways than students because of the prolonged use of the same resources.

Doing these papers will excite you and refresh your perspective on what the new A Level is really about. You will see why the routine past papers are not enough, even if the questions are a little challenging. We need to make ourselves a little uncomfortable and worried in order to understand how to best prepare our students for an entirely new style of assessment.

What’s great about them

1. Relevant content coverage

The specification for this exam (which can be browsed here) does not go beyond the old AS Mathematics specification, except for a few bits on statements and logic which are easy enough to work around (if not include!). This means we can be absolutely certain that the topics being tested are relevant to A Level students.

The specification states:

The content of Part 1 is almost all covered within the pure mathematics specification of an AS level in mathematics, and the content of Part 2 is almost all covered within a Higher Level GCSE mathematics course. There is some duplication of content across Parts 1 and 2. 

2. Unrecognisable & Unpredictable Questions

Try this question on quadratics:

This is a simple question that does not test any complicated mathematics. What it does do, is challenge familiarity. Quadratics have been tested in predictable ways for years, we will need resources that shake things up a bit and make students a little uncomfortable.

With a little problem solving and contemplation, students of all abilities have no reason to struggle with this question.

When I would set this:

At the end of the academic year, as a starter in a revision lesson, once quadratics feel like a long and distance memory. Let them forget the basics a little so that they learn the answers do not always have to be complicated!

3. Proof and Mathematical Argument is tested (my personal favourite)

This question requires bravery - students will need to dive into exploring sketches of quartics, with absolutely no hints of sketching provided in the question.

When I would set this:

As a written homework after covering Sketching Curves. This is a great opportunity to see how students will present mathematical arguments in written form. Explaining the solution here is far easier than composing a written set of arguments - this is one of the key overarching themes in the new A Level.

4. They focus on Problem Solving

Problem Solving is the skill of knowing what to do when you have no clue what to do. This is the best description I have come across so far. Try this question WITHOUT A CALCULATOR to see what I mean. It is a thing of beauty. 

Imagine this as a question in which working needs to be shown - a graphical calculator would not be enough! Curve sketching is going to be a subtly tested skill in the new A Level - this question links differentiation with curve sketching, which was almost unheard of in the old specifications!

When I would set this:

During year 2, while they are studying completely unrelated topics to the ones tested here. Students will need ways to keep the material from last year fresh in their minds, while still developing their problem solving skills. Which means that pure recall or predictable questions just won’t do it. It lends itself well as a ‘Problem Solving’ activity for students to do individually under timed conditions (as the solution is short!)

5. They encourage Investigative Skills

You could even try this one with your GCSE students!

When I would set this:

At the very start of their A Level studies as a group activity. This question requires no more than basic GCSE prime factors and an understanding of what integers are. It does however set a tone from the very start that students will need to investigate deeper into problems and use their reasoning skills to do well in the A Level. It will show them exactly the kind of ‘step up’ that the next two years will be!


Where you can find the questions

You can find direct links to papers below or via this link

Specimen Paper 1

Specimen Paper 2


2016 Paper 1

2016 Paper 2




A Checklist for Every Topic in the New Maths A Level

A Checklist for Every Topic in the New Maths A Level

Let's Talk About Logs (in the new A Level)

Let's Talk About Logs (in the new A Level)