Exploration of questions from GCSE Maths A 2 - Identifying the most and least demanding question types

Oct 20, 2026

Examines how GCSE Maths A Higher Tier candidates find different question types within set topic areas most and least demanding. The study uses detailed statistical analysis of live test data from 2008-2011 AQA exams, converting raw marks to mean percentage scores per question. Difficulty is interpreted using mastery learning: candidates were assumed to have mastered a question when they averaged 80% of available marks within grade bands.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages19

Reading Time48 min

AccessFree to download

Introduction

Methodology

Interpreting the outcomes of the analysis

Further work

Figures

Figure 1: Percentages

Figure 2: Quadratic equations

Figure 3: Fractions

Centre for Education Research and Policy Exploration of questions from GCSE Maths A: identifying the types of question that candidates find the most and least demanding, within a topic. Melissa Jackson and Rachel Lismore-Burns Introduction Following each live examination session, senior examiners for GCSE and A-level produce reports on candidate performance in that examination. This paper explores how such reporting might be further enhanced, through the inclusion of the outcomes from detailed statistical analysis of live test data. The qualification selected for this initial piece of work was the AQA GCSE Mathematics A specification, at Higher Tier. As a Higher Tier qualification, grades A* - D are available. The data analysed came from the 2008-2011 examinations. This qualification is linear, with candidates completing their examination at the end of two years of study. The topic areas selected for this study were: • Percentages • Quadratic equations • Fractions • Probabilities It is important to note that there are two potential sources of difficulty in an examination. The first is the difficulty of the topics; the second is the difficulty of the specific questions asked. It would, for example, be possible to ask an easy question about a difficult topic, or a difficult question about an easy topic. For that reason, the topics selected for this report were selected because the format of the questions had been consistent over time. Methodology Candidates’ raw marks were first converted into mean percentages, to give the cohort average score per question. For example, a score of 60% signifies that, on average, 60% of the total marks available for a question were obtained by candidates. As questions were taken from different years, this definition of ‘difficulty’ assumes that candidates’ abilities remained unchanged in this period. It also assumes that the question order did not affect the difficulty of the questions. To relate these percentages to the grading standard, a concept of mastery learning was adopted. Candidates from each grade band were assumed to have mastered a topic when, on average, they gained 80% of the available marks for a question. Interpreting the outcomes of the analysis Figures 1 – 4 represent the difficulty of questions within each of the four topics selected, and the level of student ability, represented by grade, at which mastery of each question was achieved. The height of each question box relates to the average percentage score of the candidates in that cohort. Thus, the lower the height of the box, the more difficult the question. The colour of the question box represents the grade at which the question appeared to have been mastered. So, for example, in Figure 2 on quadratic equations, the question ‘factorise x2 + 3x’ was less demanding for candidates, with a mean percentage score of 72%, thus it has a greater height. It was mastered at grade B. The question ‘solve 2x2 + 3x - 7 = 0’ was more difficult for candidates, with a mean percentage score of 25%, so the height is much lower. It was mastered at grade A* . Further work Following this initial exploratory study, it would be useful to consider issues such as: • To what extent do the teachers’ perceptions of the specific difficulties faced by their candidates align with the outcomes from this analysis? • To what extent are the assumptions of key stakeholders about what students at different grades are likely to know, understand and be able to do, supported by the outcomes from this analysis? A more comprehensive review, incorporating additional data and seeking to understand in more detail the specific underlying difficulties experienced by candidates would clearly be of interest here. Exploration of questions from GCSE Maths A 2 Melissa Jackson and Rachel Lismore-Burns Figure 1: Percentages | Maths A Higher Tier June Series 2008-2011 | | | | | --- | --- | --- | --- | | 100
75
50
25

FAQs

What problem does the report address about GCSE Maths A question difficulty?

It investigates the types of questions candidates find most and least demanding within specific topic areas.

How is “difficulty” measured in the analysis?

Raw marks are converted to mean percentages to estimate the cohort average score per question, assuming ability and question order did not change across the years studied.

How do the figures show mastery and difficulty across topics?

Each question box height reflects the mean percentage score (lower height means more difficult), and the box color indicates the grade band where mastery is achieved.

Oct 20, 2026

Uploaded by Taylor Morgan