Start with a Half Volley
Rule 1 of any exam should be: Relax The Candidate
27 January 2026
When I’m playing cricket, I'm always a bit nervous before I go out to bat. How fast will the bowling be? Will there be awkward bounce? Might the ball spin unexpectedly?
As the bowler runs in to bowl the first ball at me, what I’m hoping for is something easy to hit. A slow half volley outside my off stump, or a long hop that I can paddle away to the leg side. Basically anything that allows me to get bat on ball and, if I’m lucky, score a run so that I’ve opened my account, and won’t be heading back to the pavilion with a humiliating zero runs (a 'duck'). Then I can relax a little, and play my best game.
I believe that exams should be like this, too. The first question you are faced with should be something gentle that allows you to get off the mark. A question that anyone can answer if they have been paying some attention in class for the previous year, to demonstrate they understand the essential basics of their subject.
Imagine, then, an 18 year old taking their A Levels. They are studying Geography and History, two subjects they enjoy and feel comfortable with. They have also been encouraged to take maths because of the doors it might open later on. They aren't aiming to do a maths degree.
Their school has chosen the Edexcel exam board. There are three A Level exam papers, and the first of these is “Pure Maths”. They turn over the paper and see Question 1*:
To an experienced maths teacher, this might look straightforward and routine, and to a confident mathematician it might even seem easy. But for somebody less fluent in algebra, this is quite a jolt. They are expected to recognise that this involves the Factor Theorem, from which they are to infer that g[3]=0, substitute correctly, and solve for k**. It's a lot to process, and they know that this is Question 1 and that things are only got to get harder.
Of course there need to be challenging questions like this at A Level, and harder ones too. It’s not supposed to be a friendly game in the park. But does this opening question represent the foundation level of understanding that we expect of a school-leaver who has studied maths to A Level?
I like to think of the first question in an exam as the first exchange in an interview. “Welcome to my subject, how are you today, have you had a good journey?” A gentle half volley. It recognises that the best assessments test understanding, not the ability to overcome nerves.
For the student who isn’t a natural mathematician, I reckon that the g(x) question wasn't a half volley at all. It was a short-pitched delivery that whizzed past their outside edge.***
* This question comes from Edexcel's June 2024 Paper 1. Some Q1s in other years have been equally challenging.
** k = 12
*** POSTSCRIPT
I've had a lot of pushback on this from A Level teachers, who assure me that this really wasn't a difficult problem, and that in reality even the weak students scored well on it. The question was even praised by examiners as being a good opening question for the paper.
So why did the g(x) question make ME feel uncomfortable? I think it's because when you're away from a subject for a long time and come back to it, you see it through a different lens. At the back of my mind was: "What is the point of this question, what is it revealing about my knowledge of cubic equations?".
Let me step back. What algebraic skills do I expect mathematically qualified adults to have?
It's important to know how to rearrange and simplify equations, to know how functions behave, and what happens when you tweak them (sensitivity analysis). It's important to be able to turn a fuzzy real world situation into a mathematical model and to know the limitations of that model. I think it's vital to know how to simplify complex problems without over-simplifying them (eg small angle approximations), how to fit an equation to a pattern, and be able to sense when a pattern looks 'wrong'. And to develop those skills you do have to study algebra in some depth, in order to develop a hinterland of knowledge. The Factor Theorem has a place in this, but for me it is very low in the hierarchy of important algebraic knowledge, unless you're going on to do a maths degree.
What Question 1 would I have preferred? I'd have liked something that directly explores a student's understanding of how cubic equations work. For example, a plot of a cubic graph showing where it cuts the x axis, asking the candiate to write out the equation for the polynomial, broken down into its factors - answer [x-3].[x+1].[x-4]. And perhaps a part (b) that then pushed the concept a little further.
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