Mathematics – Using legacy A Level questions

In this blog we will look at the changes from the legacy assessment criteria compared to the requirements in the reformed qualification, and sourcing legacy questions that could be adapted for use with your current students.

Key changes

The reformed A Level criteria included explicit synopticity, increased mathematical reasoning and problem-solving, the use of technology and the use of a large data set. However, the underlying maths has not changed which means that the old questions can still be useful practice material in class and at home.

ExamBuilder – access free assessment papers

ExamBuilder is the question-building platform for a range of our qualifications, including GCSE and A Level Mathematics. In addition to the H240 practice papers and the 2018 assessment, you can also find questions from the legacy 3890-7892 unitised maths suite that have been tagged to the reformed A Level specification.

We also administer the MEI A Level Maths qualification and questions written for our H640 B(MEI) Mathematics and legacy 3895-7898 MEI Mathematics can also be found on this platform.

ExamBuilder is free for all centres with an OCR Interchange account and gives you unlimited users per centre. Visit our web page for more information on how to get your login, or talk with your Exams Officer.

Where to find withdrawn qualification material

In addition to the check-in tests, practice papers and ExamBuilder we have also included an archive of legacy suites of past papers on the Assessment tab of the qualification pages.

Use of questions from across a single year may be an easier option to obtain a balanced blend of questions across the grade boundary spectrum and ensure good specification content coverage.

In the spirit of ‘here’s one I made earlier’ log on to Interchange to download a set of our H240 A papers made up of legacy questions (A Level formative assessment). [and a set for H640 to follow shortly].

The questions have been edited to reflect the accessibility principles applied to the reformed qualification, and the corresponding mark scheme and the notes from the examiners’ reports match these edits.

Synoptic questions in A Level Maths

One of the concerns highlighted with the unitised approach to A Levels was that students were studying in silo, chucks of content and not seeing the whole intertwined beauty of the subject. The legacy A Level Maths overcame this to some degree with the caveat that the content of the previous units was assumed knowledge, and even within a unit there were always opportunities to make links between topics.

Summer 2012 4722 Core 2 Q9

Here’s a nice question bringing together sections 1.04 Sequences and Series with 1.06 Exponentials and Logarithms. Note that whilst this was originally part of an AS unit, in the reform it could only feature on the full A Level.

A key assessment requirement is that there should be opportunities for candidates to make links for themselves, without any prompts within the question.

Summer 2012 4729 Mechanics 2 Q3

This framework question, in its entirety, would be ‘off-spec’, however, part (i) assesses moments. A slight edit could make this a nice synoptic problem-solving question linking the 3.04 Moments section of Mechanics with 1.05 Trigonometry section in Pure:

A uniform beam AB of mass 15 kg and length 4 m is freely hinged to a vertical wall at A. The beam is held in equilibrium in a horizontal position by a light rod PQ of length 1.5 m. P is fixed to the wall vertically below A and PQ makes an angle of 30° with the vertical (see diagram). The force exerted on the beam at Q by the rod is in the direction PQ. Show that the magnitude of the force exerted on the beam at Q is  where K is a constant to be determined. [4]

Mathematical reasoning and problem solving

The reformed qualifications have defined Assessment Objectives (AOs) detailing a consistent proportion of marks for AO2 Mathematical Reasoning and AO3 Problem Solving (including mathematical modelling).

Summer 2012 4724 Core 4 Q7

This type of question, looking for students to expand the brackets and then use double-angle formulae to rearrange the expression into a form that can be integrated requires candidates to make problem-solving decisions and needs careful algebraic manipulation to avoid careless mistakes. In its current form, the request for an ‘exact value’ indicates that an answer of 0.119, found directly from the numerical integration calculator function would not gain credit (although a useful check against the exact ). If the question was focused more towards the assessment of mathematical reasoning then the phrase ‘Determine the exact value …’ (or perhaps use of the bold ‘In this question you must show detailed reasoning’ statement) could emphasise the need for a clear presentation of the mathematical argument in order to gain full credit. Alternatively, the question could be switched to ‘Show that ’ so a clear justification of the given answer would be needed (and not just verifying that both sides are approximately 0.119).

Use of technology

The specification makes clear that candidates may use their calculator for any function that they can perform and there is an expectation that technology should permeate the study of A Level Mathematics.

Summer 2012 4721 Core 1 Q7

This type of disguised quadratic is typical of the sort of question that can be quickly solved on a calculator, adding the bold statement ‘In this question you must show detailed reasoning’ does not prohibit the use of a calculator, simply that the logic applied needs to be explicitly stated. Candidates that clearly used the substitution  to find  by calculator and so  would gain full credit. Alternate approaches, i.e. using  equally fine, it’s the clear progression of the argument that is being assessed.

Large data set

One area that does require a more creative approach is in incorporating questions that make use of the Large Data Set (LDS). However, it should be remembered that the requirement that the exam boards provided an LDS was primarily as a teaching resource, and its inclusion into the assessment is so that candidates understand the context of the data source when interpreting results.

Summer 2012 4732 Statistics Q3

This question could be adapted to real data from the LDS

Data taken from the North West Local authority 2001 Age Structure data.

A question could then look at the changes in population within this region between 2001 and 2011 and interpret any outliers in the population growth data. For more ideas on using the LDS see the lesson activities on the teaching and planning tab of the qualification page.

In summary

We have produced four sets of practice papers and the 2019 past papers are held behind a password on Interchange. The sample assessment material and 2018 papers are available on the qualification page. These have all been written specifically to meet the accredited H240 OCR A qualification.

Additional questions can be sourced from legacy papers, an example has been compiled and is held on Interchange. For more details on the assessment principles see the Exploring our question papers – AS and A Level Mathematics A summary brochure.

Stay connected

If you have any queries or questions, you can comment below, email us at maths@ocr.org.uk, call us on 01223 553998 or Tweet us @OCR_Maths.

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About the author

Steven Walker, OCR Maths Subject Advisor

Steven joined OCR during the recent qualification reform period, working on the redevelopment of Entry Level, GCSE (9-1), FSMQ and the suite of A Level Mathematics qualifications. He now focuses mainly on supporting the Level 3 qualifications. Steven originally studied engineering before completing a PGCE in secondary mathematics.