A Level Mathematics: Preparing for the comprehension section for H640 OCR B (MEI)
15 May 2024
Steven Walker, Maths Subject Advisor
This blog was originally published in September 2020 and has been updated to include new resources.
In this blog I will look at the rationale for the comprehension section, the OCR resources available and useful links to third party websites to help students prepare for the comprehension section of A Level Mathematics B (MEI) H640.
The assessment structure for H640
The A Level Mathematics B (MEI) examination is made up of three papers:
 H640/01 – Pure and Mechanics
 H640/02 – Pure and Statistics
 H640/03 – Pure and Comprehension
One of the unique features of this qualification is the comprehension section on H640/03.
When considering how to prepare your students for this section in the exam, it is worth thinking about why it has been included in the first place.
Comprehension – it’s defined in the content criteria
All specifications for A Level Mathematics were accredited based upon covering the DfE Mathematics AS and A Level content April 2016, which includes in its aims and objectives that:
AS and A Level specifications in mathematics must encourage students to:
 read and comprehend mathematical arguments, including justifications of methods and formulae, and communicate their understanding.
 read and comprehend articles concerning applications of mathematics and communicate their understanding.
Reading – it’s an important skill to develop
A few months after taking their A Levels, a large proportion of the students will be in higher education. Students are expected to be able to learn for themselves through reading. For many students, including those studying any of the STEM subjects, social sciences, or the humanities, they will have to read some mathematics or statistics.
Where do students learn the skills to do this? The answer is – in preparing for the comprehension section of the MEI A Level.
It’s about equipping students to become independent learners. The comprehension section in the exam is a way of setting exam questions that encourages this independent learning skill.
Comprehension activities
These activities have been designed in the style of section B of H640/03, but only focused on AS/Stage 1 content.
Each one is comprised of a mathematical article, a set of questions based on the article and a mark scheme.
These activities can be used throughout the course once the respective mathematical content has been covered. This enables students to apply their understanding of the content whilst at the same time honing the skills necessary for tackling the comprehension section.
The activities could be completed as group work in class, independent homework tasks, or as more formal formative assessments.
The prerequisite maths for the four comprehension activities is outlined in the table below:
Activity 
Title 
Prerequisite maths

1

Poetic alternative to Pythagoras Theorem

Pythagoras’ Theorem, algebraic manipulation, quadratic equations. 
2

Heron’s formula for area of a triangle

Pythagoras’ Theorem, algebraic manipulation, surds and trigonometry. 
3

The mirror property of parabolas

Quadratic curve, line segments, gradients, simple differentiation, angle properties of parallel and intersecting lines, loci and perpendicular bisectors 
4

Three types of sequence and the Golden Ratio

Sequences, surds, quadratic equations and cubic equations where 0 is a root. 



The maths included is deliberately straightforward, but the way it is presented and the connections which are made between different areas of maths will be less familiar – and these are the skills that need to be mastered.
What else could be used?
Students should be encouraged to ‘read around’ the subject, which will support preparing for this section of the assessment. A good start is the intro sections of each chapter in the textbook. Also try the range of articles available on sites such as:
In looking for articles to use in class why not start with the Highway Code section on the thinking and braking distances?
Exam material
Students have access to the H640/03 exams using the past paper finder.
into your Teach Cambridge account to access the latest past papers and four sets of practice papers.
If you are a new OCR centre, you can signup for a trial access to Teach Cambridge.
Legacy 4754B assessment
From at least 2005 there has been a comprehension paper or section in the MEI A Level. There are plenty of examples to work from and the examiners have lots of experience at setting them, and was the comprehension item of the legacy 7895 MEI A Level Maths.
There are some slight changes in style between the reformed and legacy 7895 (Unit 4754 Core 4 Paper B) qualification comprehension assessment:
 H640 will only focus on maths content taken from the Pure Maths section of the specification.
 The H640 comprehension passage is shorter than the 4754B passage.
 The comprehension forms section B of the H640/03 2hour examination rather than a separate exam (H640/03 has 75 marks rather than 100 to reflect the ‘reading time’ needed for this section).
Recent examples include:
2016: Photomontages. This article applies trigonometry in a practical situation and would be appropriate for an extension task in GCSE and accessible for AS classes.
2018: Rain stopped play. This article looks at the various models used to estimate fair results in cricket. This task involves the application of mathematical formulae and substitution and demonstrates how mathematics can be applied in a nonmathematical context. This would be accessible for an AS/stage 1 class and would be appropriate as an extension task at GCSE.
Online professional development courses available
Take a look at the past events, held on Teach Cambridge, focused on the teaching and assessment of the comprehension requirement.
MEI has run online webinar sessions focused on preparing for the comprehension section, which can be found on the MEI Staffroom.
Stay connected
Share your suggestions of activities in the comment box below. If you have any queries, email us at maths@ocr.org.uk, call us on 01223 553998 or follow us on X (formerly Twitter) @OCR_Maths. You can also sign up to receive subject updates and receive uptodate email information about resources and support.
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 OCR in 2014 and worked on the redevelopment of OCR’s FSMQ and the A Level Mathematics suite of qualifications. Away from the office he enjoys cooking and travel.
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