## Blind spots in the new A Level Maths

I write exam style questions from scratch as part of my role at MarkIt. By putting myself in the shoes of the examiners and keeping up with all that has been written about the new specification for Maths, I have noticed some blind spots that we as teachers will need to be extra aware of this year onwards. Without my extensive research into the overarching themes and the specimen papers, I am certain I would not have thought of these so I encourage you to read on.

**Quadratics: the completing the square blind spot**

*Legacy A Level :*

At A Level, or even GCSE, completing the square has been examined primarily as an algebraic and algorithmic exercise. You do the ’stuff’ and you get something that looks like the form the question asks for. At most students were asked to find maximum and minimum points. As seen in some specimen papers, examiners have their eyes on this familiarity trap - here’s why:

*New A Level :*

Mathematical modelling is a key overarching theme and completing the square, as a process, comes alive because of it. Adding context to exam questions, for example supply and demand as a function of price, makes the algorithmic process of finding a maximum value and the corresponding input feel meaningful.

This year onwards, we must actively hunt for questions where completing the square is a medium to understanding a hefty real life context. Students will then see when and why it can be used to draw conclusions.

**Binomial Expansion: the nCr blind spot**

*Legacy A Level :*

The nCr formula was only really tested in the OCR MEI specification. For all other exam boards, students simply used their calculators to find coefficients and do exam questions that have hardly varied from the typical expansions and approximations that have come up for the last decade or so. This is a familiarity trap to be aware of - we should make a point to teach the use of the nCr formula. Here’s why:

*New A Level: *

Mathematical proof being one of the overarching themes means that examiners will be actively fishing for places to test it. Also given that every exam now allows a calculator, there will be questions written to specifically test non calculator survival skills, something I am a huge fan of - see my rant about it here. So the nCr formula, hardly focused on before, will be a key target and we should teach students to apply the formula in general cases, bringing the use of factorials into the mix. Give the formula some TLC this year!

**Geometric Series: S-infinity blind spot **

*Legacy A Level :*

S-infinity was simple. Geometric series questions were broken down into parts, where students found or were given the right variables and simply used the formula to find S-infinity. Understanding the constraint on the common ratio that allows S-infinity to exist in the first place was rare and often completely forgotten by the time students got to the exams. Can we blame them? Past papers hardly ever brought this detail up. So why would it come up now?

*New A Level :*

Mathematical proof and language will seep into exam questions across chapters. S-infinity is a great opportunity for students to explain themselves using sound mathematical reasoning. We should not gloss over or underestimate the importance of teaching the constraint on *r* when covering S-infinity. This is a chance for them to learn the ‘why’ and be able to communicate it, which are the newly important muscles to exercise this year onwards.

**What should we do to prepare? **

### Have high standards for practice questions

When setting exam style practice at the end of a chapter, have high standards and do not simply rehash the hard questions from the old specification. Even though the content has not changed much in the new specification, there has been a shift in tone. Students will need to show mathematical reasoning and present clear arguments for proofs. Without these elements, exam practice on any chapter is inadequate.

I've come up with some examples of blind spots in the legacy specification that all of us will need to be hyper aware of to make sure students are not falsely comfortable. Look for these, and other familiarity traps in the worksheets you set.