A Level Maths: strengthening algebra to kick start term 1
14 October 2025
Steven Walker, Maths Subject Advisor
Starting A Level Maths can be both exciting and daunting for students. One of the biggest challenges they face is the leap in algebraic fluency required. While GCSE lays the foundation, A Level demands a deeper, more flexible understanding of algebraic techniques. In this blog I look at where early intervention may help avoid some of the mistakes and misconceptions that seem to persist through to the final summer exam.
Revisit core skills early and often
Encourage students to consolidate key GCSE algebra topics such as expanding brackets, factorising quadratics, and working with indices. These are the building blocks of A Level topics like functions, calculus, and proof.
Question 1 Maths A H240/03 2024
Most candidates scored full marks on both parts of this initial question. However, in part (a) a significant number did not apply the cube to both parts of the bracketed expression correctly, either incorrectly stating 8a5 or 2a6 as their result for this. In part (b) some candidates did not spot the difference of two squares in the numerator, whilst others stated the quadratic expression factorised to (x – 1.5)(x + 4), presumably having attempted to reverse engineer their result from the quadratic solve function.
Key thought: Regular practice as starter activities might be useful to keep these fundamental skills fresh.
Promote mathematical discussion
Rather than rote procedures, focus on developing students’ ability to reason algebraically. Ask them to explain steps, spot patterns, and justify methods. This builds confidence and prepares them for the more complex calculus, proof and trigonometric problems later in the A Level course.
Question 1 Maths A H240/02 2022
Encourage students to look at a question like this and identify where candidates might have made mistakes. In part (a) care is needed ensure that the negative sign is applied to all terms in the second fraction. In part (b) students need to recognise the significance of expressing x6 in the form (x3)2 . The first step in part (c) is to consider 243 in the form 3a.
Key thought: Encouraging mathematical discussions in addition to the silent working through exercises reflects the world of mathematics beyond the school gates.
Use dynamic graphing software
Multiple low-stakes quizzes and worksheets can be demotivating for those students that didn’t feel too confident in year 11. Platforms such as Desmos, Geogebra, Autograph or a graphical calculator such as the Casio CG100 can be used to create and then investigate common exam question scenarios.
Question 7 Maths A H240/01 2024
Students are often comfortable with numerical solutions but struggle when faced with algebraic terms. In part (a) care is needed when rearranging to make h the subject of the gradient equation. Part (b) was generally answered well, although a few students did not read the question carefully and found the midpoint of AB rather than using the stated information that B was the midpoint of AC. Part (c) again requires students to be manipulating a quadratic equation involving variables.
This question is best tackled with an initial sketch. The use of graphing software helps link algebra to graphs, but to fully realise the power of the software students need to develop good algebra skills. This desmos example shows the elements of this question for students to investigate not only the solutions to the problem, but also consider how to create the equations themselves.
Key thought: Encourage students to create graphs using software so that they can recognise the importance of a visual representation.
Encourage practice with purpose to build a positive mindset
Many students feel they “just aren’t good at algebra.” Reinforce the idea that fluency comes with time and effort. Celebrate small wins and progress. Provide varied practice that moves beyond repetition. Include problems that require students to choose methods, spot errors, or apply algebra in unfamiliar contexts.
By embedding these strategies into the first term of the course (and beyond), students can build a strong algebraic foundation – setting them up for success throughout the A Level course.
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About the author
Steven originally studied engineering before completing a PGCE in secondary mathematics. He has taught secondary maths in England and overseas. Steven joined Cambridge OCR in 2014 and worked on the redevelopment of the FSMQ and the A Level Mathematics suite of qualifications. Away from the office he enjoys cooking and to travel. You can follow Steven on BlueSky or Linkedin.
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