# Find Out What Topics You Should Be Teaching With This Question Level Analysis Of Edexcel Maths Past Papers (Foundation)

**The past eighteen months have been very challenging for the education sector, and lots of us are still trying to work out the implications for exam groups from 2022 onwards**.

The initial motivation for this Edexcel maths past papers blog was as research for another article on preparing Year 10 for GCSE, so I started by looking at the June 2019 Edexcel GCSE maths series in detail.

Please note, this blog focuses on Edexcel maths past papers, not the AQA or OCR exam boards, nor IGCSE maths. What’s more, the focus is on GCSE maths, not A Level maths or the maths Edexcel A Level.

This set of papers alone raised a few interesting and surprising statistics: for example, 42% of the ‘Shape’ marks from the mark scheme were for perimeter, area and volume, and many of these involved problem-solving in non-standard contexts.

Obviously, as a mathematician, I then wanted to investigate this further – an anomaly or a pattern? (As it turns out, the amount was slightly anomalous, but the assessment of perimeter, area and volume mainly as non-procedural questions was a pattern across all papers).

This led to the analysis below; a detailed look at the full set of six Edexcel GCSE maths Foundation papers from June 2017 through to November 2019. I have briefly discussed the methods used, then outlined any interesting points for each series of papers. Finally, I have looked at the full set of six papers, outlining common themes in each strand, and drawn conclusions about implications for teaching.

Throughout the blog, Third Space Learning will also show you how our GCSE maths revision programme aligns with Christine’s findings. While this blog is focused on the Foundation paper only, our tuition programme consists of ‘crossover’ GCSE lessons, which means they are relevant to students sitting either the Foundation or Higher paper, apart from a few specifically Higher lessons!

Because of the diagnostic element of our programmes (including Post Sessions Questions), there is a means by which students are directed to the most relevant lesson content for them. Tailoring our one to one intervention programme allows the lessons to be pitched at the right level, plug topic gaps and address misconceptions.**Read more:** How We Developed Our GCSE Maths Revision Programme & GCSE Intervention Strategies

### Edexcel maths past papers key findings

If you are short on time, here is a topic-based summary based on all of the papers. There is also a further breakdown for each past paper below. At the end of the blog, I will dive deeper into cross-paper patterns and how this can be translated into the classroom.

#### Number and proportion

- More focus on context-rich problem solving with basic arithmetic, fractions, percentages, ratio and proportion.
- Real-life contexts include bank accounts, utility bills, wage increases, recipes and best-buys.
- Place value, standard form, powers and roots, rounding and estimation, factors, multiples, HCF and LCM tend to be assessed in more of a procedural manner and could be ‘easy wins’.

#### Algebra

- Algebra at Foundation tends to be examined in a fairly standard procedural way.
- However, students find the topics themselves more challenging, so these are not necessarily ‘easier’ marks.
- Spend time ensuring students can apply standard algebraic methods accurately.
- Consider spending less time on simultaneous equations, quadratic expressions and equations, in favour of more time on graphs, sequences and functions.

**Read more:** 15 Algebra Questions And Practice Problems (KS3 & KS4)

#### Shape

- Context-based problem-solving on perimeter, area and volume, making sure students can flexibly apply these skills to other problems.
- Greater focus on time, particularly misconceptions around fractions of an hour, and use of a calculator for time problems.
- More time on scale drawing work and bearings, and linking this to other topics.

#### Probability and statistics

- Increased focus on ‘newer’ topics, such as Venn diagrams, sets and listing outcomes.
- Emphasis on frequency trees vs standard tree diagrams.
- Application of fraction and ratio skills to unfamiliar contexts for mutually exclusive events.
- Greater emphasis on presenting data, particularly looking at pros and cons of different types of graphs, and spotting errors in given graphs and charts.

Did you know that Third Space Learning’s GCSE revision programme covers these topics? We have a variety of lessons, ranging from standard form, powers and roots, and rounding and estimation, to solving equations, the volume of prisms, and Venn diagrams! Our one to one intervention lessons also features exam questions in context. Here’s a screenshot of our Teacher Selection programme!

Personalised online lessons to prepare your KS4 students for maths GCSEs

Weekly online one to one maths revision lessons delivered by specialist tutors and designed for the students who need it most.

### Edexcel maths past papers methodology

#### Categorising by topic

One thing I found particularly challenging about this blog was getting the level of detail right. When I began my analysis on the first set of papers, it became apparent that I would not be able to go into the fine-grain level of detail that I usually do on exam feedback spreadsheets, both due to time constraints and the fact that this would give hundreds of sub-topics across a few sets of past exam papers.

I decided to apply a broader approach to categorise each question, with the potential later on for drilling down further into particularly interesting topics or those which attract a large number of marks.

A few years ago, as part of our GCSE scheme planning for the changes in 2015, I took the KS3 and 4 Programmes of Study and divided them into ten key areas, with each area split further into topics and sub-topics. We used this for our scheme of work, and I still use this now to organise my electronic resources. I decided to use this structure for my analysis, as it’s already closely aligned with the categorisation that the exam boards use.

Classifying some of the multi-mark, deeper problem-solving questions presented a bit of a challenge; I decided to pick a main topic for each question and classify it under that heading, rather than try and assign marks for topics within questions. So, for example, June 2019 P1 Q18 required candidates to use skills working with four operations and decimal calculation as well as area; however, as the question is inaccessible without some knowledge of the area of a rectangle, I classified this as ‘perimeter, area and volume’.

It should be noted that the proportional reasoning category only covers standard proportion and ratio-type problems – so recipes, conversions, splitting into ratios and so on. However, many ratio problems do include fractions, percentages or both.

**Read more:** 15 Ratio Questions And Practice Problems (KS3 & KS4)

#### Categorising by complexity

In order to simplify the analysis process, I decided to classify the high-mark problem-solving questions by their main topic; this does lose a little bit of detail but makes it easier to look for trends across a larger data set.

I also wanted an idea of the difficulty or complexity of each question; I decided to base this broadly on the GCSE assessment objectives:

- A01 – using and applying standard techniques (50%);
- A02 – reasoning, interpreting and communicating mathematically (25%);
- A03 – solving problems in mathematics and other contexts (25%).

It should be noted that this is a very rough basis, as longer or multi-step questions often award marks for more than one assessment objective. My complexity classifications can be stated as follows:

**C1**– standard procedural problems, often worth one or two marks;**C2**– problems asking candidates to explain their reasoning, interpret information from tables, diagrams or other contexts, or ‘show that’ type questions;**C3**– non-standard multi-step problems, often requiring the application of skills from a variety of topics, worth three, four, or more marks.

This is also not a ‘difficulty’ measure – it should be noted that ‘higher grade’ topics, such as simultaneous equations or estimating the mean, are often examined as standard procedural.

All series have roughly a third of the marks on the mark scheme allocated to C3 problems; there is some variation between proportions of C1 and C2. From the six series analysed, the November series seem to favour a higher ratio of C1 to C2 questions, particularly in the last two years that we have exam papers for.

### Notes on the Edexcel maths past papers

As I began working through the papers and compiling the data, I also noted some features of each set of papers. I did not really have a hard-and-fast method here; these were just the things that jumped out at me once I had completed the data crunch of each GCSE maths past paper set.

#### June 2017

- Number and proportion =
**35%** - Shape =
**27%** - Algebra =
**23%** - Probability and statistics =
**16%**

Generally, this ‘feels’ like a difficult paper, with the first few questions being markedly more challenging than more recent papers. This was the first set of examined papers for the new specification and the issue of difficulty with the front end of the question paper (compared to the old specification) was addressed in the Chief Examiner’s Report in June 2018.

More recent papers have settled into a pattern of the first five or six questions being one- or two-mark C1 questions on easier topics. There was also more algebra content in the June 2017 series than the following five (23% vs 17-18%).

Number and proportion:

- P&C – Properties and calculations, including four operations, factors, multiples, powers, estimation
- FDP – Fractions, decimals and percentages
- PR – Proportional reasoning

Algebra:

- Basics – Skills such as algebraic manipulation, expanding, factorising, substitution
- Equations – Linear and quadratic
- SFG – Sequences, functions and graphs

Shape:

- C&M – Calculation and measurement, including units (including compound), scale drawings, area, volume, Pythagoras and trigonometry
- P&C – Properties and calculations, including reasoning with 2D/3D shape properties, transformations, congruence, vectors

Probability and statistics:

- Prob – Probability, including simple calculations, mutually exclusive events, theoretical and experimental
- Stats – Statistics, including drawing and interpreting statistical graphs and charts, and processing data to find averages

**Number and proportion**

Just over 6% of the total marks were for four operations, particularly basic calculation skills including order of operations, and all were C3. Candidates were asked to solve context-related problems to demonstrate their arithmetic skills; there were few ‘easy’ C1 marks for number crunching. This is a pattern common across most series of papers. There were, however, some very accessible C1 questions on factors, multiples, primes, percentages and fraction calculations.

There were 9 marks over three questions available for proportional reasoning, 8 of these marks were C3 with one C2. P3 Q10 required candidates to apply proportion skills to a problem involving line lengths, and P3 Q18 used fraction, percentage and ratio skills. There was a mix of complexity for ratio, but another big 5-mark question requiring the application of fraction knowledge and four operations (P2 Q18).

**Algebra**

Lots of the algebra content, including all algebraic manipulation questions, were C1, so these are standard procedural questions: simplifying, expanding, factorising and so on. P2 Q9 had a fairly straightforward application of linear equations in the context of angles around a point. P3 Q22 on non-linear graphs was a fairly straightforward reciprocal. Unusually, compared to the other series of papers, simultaneous equations appeared twice for a total of 7 marks.

**Shape**

20 marks (8% of the mark scheme) were available for units, measurements and drawings, but 11 of these were for time and compound units, with many C2 questions, asking candidates to explain their reasoning. Perimeter, area and volume questions asked candidates to demonstrate their understanding by reasoning in non-familiar contexts, and all questions were C2 or C3. Good examples of these are P1 Q15, involving the area of rectangles and triangles in a non-standard context, and P1 Q18, the area of a circle in the real-life context of grass seed on a garden.

**Probability and statistics**

All statistics were C1 or C2, with lots of smaller questions. There was more emphasis on interpretation and less on drawing diagrams. P1 Q14 required candidates to draw, then interpret a pie chart, and P1 Q21 on scatter graphs asked candidates to plot a point, identify correlation, estimate and then interpret a statement with reference to the graph. Plenty of newer content, such as Venn diagrams and listing outcomes, was examined on this set of papers – this was mostly C1.

#### November 2017

- Number and proportion =
**46%** - Shape =
**23%** - Algebra =
**17%** - Probability and statistics =
**14%**

**Number and proportion**

This series of papers had the highest number of marks allocated to number and proportion, and the lowest to probability and statistics, so it feels like a calculation-heavy series. These were allocated more evenly to topics than June 2017, with just under 5% (11 marks) four operations, 4% (10 marks) fraction calculations, and 7% (17 marks) percentages. These were a mixture of C1, C2 and C3, although over half of the percentages questions (11 marks) were C3, including a 5-mark question involving calculating a heating bill (P2 Q15).

There were 17 marks (7%) available on proportion questions. Again, while these were mostly C2 and C3, there were a couple of accessible C1 questions; P1 Q19 (a standard recipe for 3 marks) and P2 Q12 (a simple direct proportion problem). There were 25 marks (10%) over 11 questions categorised as ratio. This included 6 marks over 4 C1 questions – for example, P1 Q15 involved writing part of a ratio as a percentage, and P1 Q18 was splitting an amount into a three-part ratio.

**Algebra**

Of the 7 marks (4%) available for algebraic manipulation, 5 of these were on C1 questions. P1 Q6 on writing a formula was mathematically straightforward but very wordy, particularly that early on in the paper, so categorised as C3. Linear graphs, quadratic expressions, simultaneous equations and a quadratic equation all featured, but all at C1 and the quadratic equation was of the form ax^{2}=b (P2 Q24a).

**Shape**

Perimeter, area and volume featured highly, with 24 marks (10%) allocated over 8 questions, nearly all C2 or C3, again requiring candidates to reason in unfamiliar circumstances. P1 Q13 asked candidates to work out the volume of a cube given its surface area, with no supporting diagram or steps, and P1 Q26 involved calculating areas inside concentric circles, with an additional step involving fractions at the end. There was relatively little on 2D shape and angle properties, and nothing on 3D properties.

**Probability and statistics**

The probability content felt quite light in this paper. There were only 14 marks (just under 6%); 5 of these were on a frequency tree with follow-up questions (P2 Q12) and another 4 on a two-way table (P1 Q12). Both were straightforward C1 problems.

Statistics leaned more in favour of presenting data (12 marks) than processing data (7 marks). 3 of the 12 marks on presenting data were C2, involving interpretation of charts, but the remaining 9 marks were C1, including 4 marks for drawing a pie chart (P2 Q5b) and 3 marks for completing a pictogram (P3 Q6).

#### June 2018

- Number and proportion =
**40%** - Shape =
**24%** - Algebra =
**18%** - Probability and statistics =
**18%**

**Number and proportion**

This was a relatively number-heavy set of GCSE maths past papers. Just under 8% of the total marks were for four operations, particularly basic calculation skills including order of operations, and lots of this was C3. Again, candidates were asked to solve context-related problems to demonstrate their arithmetic skills. However, there were 14 marks (6%) for factors, multiples, primes, all C1 or C2, and fairly accessible.

This set of papers had less proportional reasoning (22 marks, 9%), although it should be noted that this category only covers standard proportion and ratio-type problems, so does not include percentages and so on. This set was very ratio-heavy, with all ratio C3, and only one C2 question on proportion. Again, candidates were expected to demonstrate their understanding of these topics by solving context-related problems.

**Algebra**

There were 8 marks (5%) for linear equations, all of which were C1. There was one challenging C3 quadratic equation, which required candidates to form and solve an equation using facts about the area of 2D shapes.

22 marks (9%) were for sequences, functions and graphs – this was half of the total marks for algebra content. There were 14 marks (6%) on linear and non-linear graphs, all C1, with 6 of these marks for drawing a quadratic graph and using the graph to estimate solutions.

**Shape**

28% of the shape content was perimeter, area and volume, much of this C2 or C3. Paper 2 had two tricky C3 5-markers, Q19 requiring the perimeter of a semicircle in a context-based problem around a farmer’s field, and Q26 on the volume of a triangular prism requiring application of Pythagoras’ theorem. A further 33% of the shape content was units, measurements and drawing, including some nice straightforward C1 questions on Paper 2: Q5 on metric unit conversions, and Q9 on speed, distance and time, not requiring any change of units.

**Probability and statistics**

All of the statistics content was C1 or 2. The majority of the presenting data content asks candidates to read information from or interpret pre-drawn graphs; for example, P1 Q12 involved reading information from a stacked bar chart, then answering some C2 problems relating to the real-life context, and P3 Q19 required interpretation of a scatter graph in a similar way.

In terms of probability, lots of the new content was included, with P1 Q18 on sets without a Venn diagram, and P2 Q7 listing outcomes. Frequency trees featured again (P2 Q14).

#### November 2018

- Number and proportion =
**40%** - Shape =
**22%** - Algebra =
**21%** - Probability and statistics =
**17%**

**Number and proportion**

This series contained a large amount of percentages work; 34 marks (14%) available with a significant number of these C2 or C3, expecting candidates to problem-solve in different contexts. For example, P1 Q22 was a challenging question about sharing bonuses worth 5 marks, and P2 Q23 involved comparing two bank accounts for 4 marks.

The remaining number content seemed fairly balanced, with 9 marks (4%) for four operations, 10 marks for place value and ordering, 10 marks for fraction calculations and 8 marks for factors, multiples and primes, and a mixture of complexity throughout.

This set of papers had less proportional reasoning (18 marks, just under 8%), although this is probably balanced out by the number of questions purely focused on percentages. With the exception of 2 marks for ratio, all of these were C2 or C3.

**Algebra**

After June 2017, this series has the highest algebra content. There were 10 marks (4%) for linear equations, all of which were C1 with the exception of one C2 (P3 Q17a) requiring candidates to form an equation about the perimeter of a pentagon – but even this was a ‘show that’ question, so lead candidates through quite nicely. Apart from quadratic equations, all other algebra strands appeared in some form. P2 Q25 was a challenging 3 mark problem-solving question on the gradient of a line, a topic that does not feature highly on the Foundation series so far.

**Shape**

The shape content was quite balanced, with 14 marks (just under 6%) on perimeter, area and volume, and also on units, measurements and drawing, and 12 marks (5%) on 2D shape and angle properties. All of the perimeter, area and volume content was C3; again, candidates were asked to solve problems rather than carry out learned procedures. There was slightly more on transformations, congruence and similarity than on some series (7 marks, 3%), all C1 or C2. There was a challenging trigonometry question involving ratio (P3 Q25).

**Probability and statistics**

Most of the statistics content was C1 or 2, and again favoured presenting data over processing data, in fact, there were only 4 marks available for the latter, all on P3 Q23b, which asked candidates to estimate the mean in a ‘show that’ problem.

A third of the marks for probability were allocated to two questions on independent and dependent events, both of which appeared on the same paper: P1 Q17 on frequency trees and P1 Q27 on tree diagrams, both C1.

#### June 2019

- Number and proportion =
**31%** - Shape =
**31%** - Algebra =
**18%** - Data =
**18%**

**Number and proportion**

There were 9 questions (21 marks, 9%) involving four operations; unusually, some were C1, such as P1 Q3 on the order of operations and P1 Q11, which was a simple 2- by 2-digit multiplication. Some of this involved interpreting information from tables (P2 Q7, P2 Q11). Just under 6% of the marks were for fraction calculations, with the majority of these C1 or C2.

32 marks (13%) across three papers were for proportional reasoning questions (mainly proportion or ratio). These were all C2 or predominantly C3, meaning that candidates were required to tackle problems involving some depth of thought.

**Algebra**

Half of the algebra marks available were for topics like algebraic manipulation, simplifying, expanding, factorising, and substitution. All of the algebra content, except the substitution and formula questions, was C1, including some simple linear equations (P1 Q10), and a fairly straightforward linear graph (P2 Q21), although this did require candidates to construct their own table of values.

**Shape**

An unusually high proportion (42%) of the shape questions involved perimeter, area, volume and all were C3. For example, P2 Q13 involved the perimeter of squares and rectangles in a tiling-type problem, and Q15 required candidates to apply a percentage calculation in addition to working out area. 27% of the shape marks were for units, measurements and drawings, including problems involving time calculations.

**Probability and statistics**

Again, quite a lot of the statistics content was C1 or C2, and this seemed to favour presenting rather than processing data (13 marks to 3 marks respectively). This series did include 3 marks for data collection and sampling (P2 Q22), which does not feature at all on some series.

There were no frequency trees or tree diagrams, but sets and Venns still featured, with a 5-marker requiring candidates to complete a Venn diagram, then calculate a probability using that diagram (P3 Q24).

#### November 2019

- Number and proportion =
**37%** - Shape =
**24%** - Algebra =
**18%** - Data =
**21%**

Generally, this past exam paper felt quite challenging compared to the two or three previous sets. There were relatively few C2 questions, which tend to lead candidates more towards answers, and a higher amount of C3, with more questions requiring the application of topics in a wider variety of contexts, such as algebra embedded in shape questions.

**Number and proportion**

The four operations questions were split between C1 (5/14 marks, 3 questions) and C3 (9/14 marks, 3 questions). Marks for fraction calculations were very accessible, with 6/8 marks on C1 questions.

There were 20 marks available for proportion over 7 questions; these were all C3 with the exception of one C2, such as worded problems requiring candidates to find ‘one’ of an amount before scaling up, currency conversions, and a really challenging problem on inverse proportion with an algebraic formula (P2 Q28). Of the 9 marks for ratio, 8 of these were also on C3 questions, including applying ratio skills to a problem on angles in a triangle (P1 Q24).

**Algebra**

Some of the algebra felt markedly more challenging on this set of GCSE maths past papers than any of the previous sets. For example, P1 Q17 asked candidates to solve a linear equation, then carry out a substitution, and P3 Q14 used algebra in the context of the perimeter of a triangle. Algebraic manipulation questions were all C1, as is the pattern across most papers, but 7/9 marks on substitution and formulae were C3. However, all of the work on graphs and most of the work on sequences and functions were C1.

**Shape**

11/19 marks for 2D shape and angle properties were C3, and as mentioned above, candidates were required to apply algebra skills to more of the shape problems. All 10 marks for perimeter, area and volume were C2 or 3. There was a standard construction question (P1 Q23, construct a perpendicular); there are very few of these across all the papers.

**Probability and statistics**

Frequency trees appeared again, making it 4/6 sets of papers containing one or more questions on frequency trees – this was a C1 problem, requiring candidates to complete the tree and then answer a probability question based on their tree. P3 Q15 was a percentage question that lent itself to a standard tree or frequency tree diagram, but this was not essential for solving the problem.

### What does this mean for teaching and exam preparation?

Looking at the six series of papers as a whole reveals some interesting patterns about the types of questions set and the complexity distribution for each topic. I have split the data set out into the four strands, ‘Number and proportion’, ‘Algebra’, ‘Shape’ and ‘Probability and statistics’, and added commentary below.

These combined findings from across all of the papers build on the lighter touch topic-based summary at the beginning of the blog!

#### Number and proportion

The first thing I noticed was that some of the topics within the ‘Number and proportion’ strand attract a significant number of C3 marks. In proportional reasoning, in particular, 75% of the proportion marks and 68% of the ratio marks asked candidates to reason in unfamiliar, non-procedural ways, or to solve multi-step problems. There were a few more procedural fraction calculations and percentage questions, but with percentages, in particular, 48% of the marks were C3.

Lots of the four operations questions were similar, with plenty of questions featuring real-life contexts – 58% of the marks were C3. There were very few basic calculations, and many of the C1 marks were for order of operations rather than arithmetic.

On the other hand, there are plenty of C1 marks up for grabs in the following topics: place value and ordering (89%), rounding and estimation (61%), and powers and roots (82%). Standard form takes a fair chunk of the place value and ordering marks, but candidates are rarely asked to work beyond standard procedural problems. Decimals is all C1, but that is more a function of my categorisations, as this only really includes fraction to decimal conversions, ordering decimals and pure decimal arithmetic.

Rounding and estimation is 39% C2; this is mostly asking candidates to explain the effects of rounding or estimation on answers, whether an approximation will result in an over- or under-estimate, and so on.

31% of factors, multiples and primes is C2; there are a few questions asking candidates to give examples or counter-examples for a given statement, such as June 2018 P1 Q11, a two-part question asking for examples to show that two statements about (a) factors of even numbers and (b) digits in odd numbers are incorrect.

**What would I teach based on this data analysis?**

- Context-rich problem solving with basic arithmetic, fractions, percentages, ratio and proportion.
- Real-life contexts, including bank accounts, utility bills, wage increases, recipes and best-buys.
- ‘Number-puzzle’ problems where students are asked to work out a missing amount when the other proportions are given as a mixture of fractions, percentages and ratios (e.g. June 2018 P1 Q14).

#### Algebra

Algebra is a stark contrast to number and proportion in terms of complexity; there are a lot of topics here that rarely go beyond standard procedural C1 marks, and some topics do not seem to attract C2 marks either.

Algebraic manipulation, perhaps because it is the algebra toolkit of simplifying, expanding, factorising and so on, is 85% C1 marks, with no C3. A lot of the harder topics have a higher proportion of C1 marks as well: quadratic expressions (79%), quadratic equations (63%), simultaneous equations (75%), linear graphs (88%) and non-linear graphs (95%).

In substitution and formulae, there is slightly more of a balance (51% C1, 22% C2, 27% C3) – this is one of the main areas within the Foundation series where candidates are asked to solve problems using algebra, so looking at context-based formulae such as temperature or a formula for working out costs. The C2 marks within this topic include things like translating a worded context into an algebraic formula.

The 30% of C3 marks on linear equations were three questions over the full set of 18 papers; two of these were context-based on shape and angle problems, and the other one was a simple linear equation followed by a substitution.

Sequences and functions attract the highest proportion of C2 marks (32%); this is due to questions that ask candidates to show that n is or is not a term in the sequence or to critique a false statement made about a sequence.

**What would I teach based on this data analysis?**

- Ensure students can reliably apply algebraic method.

It is worth remembering that, while the complexity and degree of problem-solving expected for algebra at Foundation is relatively low, students find the topics themselves more challenging, and so these are not necessarily easier marks.

For borderline 4/5 grade boundary students:

- Spend less time on topics such as simultaneous equations, quadratic expressions and equations.
- Spend more time on topics such as graphs, sequences and functions.

Interestingly, it is noted in the 2018 Chief Examiner’s report that: “simple coordinate geometry work is not done well at Foundation tier. Beyond drawing a simple graph of an equation, there appears to be little understanding of the relationship between equation[s] and graph[s], between graphs of parallel lines, or finding an equation from a straight-line graph.”

Third Space Learning’s GCSE intervention programme is specifically aimed at deliverability for borderline 4/5 grade boundary students! We have online lessons on the topics listed above in the Chief Examiner’s report, such as understanding the relationship between equations and graphs.

#### Shape

Shape was the strand that surprised me the most when completing this analysis, particularly the huge amount of C3 marks (84%) within the perimeter, area and volume topic. It also felt like there was a heavier focus on reasoning with speed, distance and time within the units, measurements and drawing topic, linking to another context for proportional reasoning.

Of the 34% of the C3 marks within units, measurements and drawings, quite a few of these were allocated to four- or five-mark questions. For example, Nov 2019 P1 Q27 involved scale drawing, bearings and a time calculation, and June 2018 P3 Q12 required candidates to measure a scale drawing of a tennis court, then use a map ratio to work out the perimeter of the real court.

While 74% of the marks for Pythagoras and trigonometry were C3, it is worth mentioning that these marks were over three questions from the first three series of papers (June 2017, Nov 2017 and June 2018), and when this topic was examined in June 2018 and 2019, the questions were C1, and worth fewer marks.

As already mentioned, perimeter, area and volume was very context-heavy, with some series having all of this topic assigned as C3. As I mentioned in the question paper analysis, these included real-life contexts such as calculating a circular lawn area and fencing for a farmer’s field, and there was also some crossover with fractions work, such as showing that a certain fraction of a shape was shaded. Many of the 2D shapes involved in area work were standard: squares, rectangles, triangles and circles, with less on compound shapes.

We have content relating to the farmer’s field question, and crossover with fractions work, in our GCSE lesson dedicated to the application of perimeter and area.

Transformations, congruence and similarity feel the same as on previous specification papers; a mixture of ‘do this transformation’ and ‘describe this transformation’, with perhaps a little more work on congruence and similarity beyond just knowing the meanings of the words (see Nov 19 P1 Q29 for example).

2D and 3D shape and angle properties attracted the highest proportions of C2 marks (45% and 46% respectively), purely because many of the questions in these topics contain the statement: ‘give reasons for your answer’. Interestingly, quite a few of the C3 marks involved solving problems with the interior and exterior angles in polygons (see Nov 19 P3 Q29 and Nov 18 P1 Q28 for examples).

**What would I teach based on this data analysis?**

- Include far more problem-solving and context-based problems in units on perimeter, area and volume.
- Make sure that students could flexibly apply these skills to other problems, such as in the tennis court scale drawing problem mentioned above.
- Place a greater focus on time, particularly misconceptions around fractions of an hour, and the use of a calculator (rather than non-calculator) for time problems
- Spend more time on scale drawing work and bearings, and linking this to other topics.

#### Probability and statistics

Over the six series of papers, the ‘new spec content’ (i.e. that was added in 2015), as opposed to ‘old spec content’ is strongly represented in the probability strand. Independent and dependent events were almost always examined as frequency trees as opposed to tree diagrams, although there was one question paper that unusually contained both a frequency tree and a tree diagram. Sets, Venns and two-way tables carried a third of the total probability marks, with the new topics of listing outcomes and completing a Venn diagram featuring highly.

Mutually exclusive events were most likely to be examined at C3 (46%), usually with an application of ratio or more complex fractions work (see Nov 19 P3 Q16 for a good example of this). The rest of the probability content had a high proportion of C1 marks.

The vast majority of statistics content is C1 and C2; presenting data and processing data have only 4% and 15% respectively allocated to C3 marks. Furthermore, nearly 67% of the statistics marks were for presenting data. A large proportion (42%) of presenting data is C2, meaning that candidates are almost as likely to be asked to analyse, read information from, or critique a graph or chart as they are to draw one. Pictograms seemed to feature quite highly, alongside pie charts, with slightly fewer bar charts.

In processing data, in addition to some easier C1 or C2 questions asking candidates to find an average or range from a small ungrouped set of data, estimation of the mean for grouped data comes up fairly frequently. Data collection and sampling is not examined at all on quite a few of the series and has so far always appeared on Paper 2.

**What would I teach based on this data analysis?**

- Increasingly focus on the ‘newer’ topics, as these seem to be examined frequently at the moment.
- Particularly adapt the teaching of tree diagrams to focus mainly on frequency trees.
- Give students plenty of experience in applying their fraction and ratio skills to unfamiliar contexts for mutually exclusive events.
- Give greater emphasis to presenting data, particularly looking at the pros and cons of different types of graphs, and spotting errors in given graphs and charts.

Third Space Learning’s GCSE maths revision lessons include fraction to decimal conversions, ordering decimals, shape and angle problems, sequences and functions, speed and distance, Pythagoras and trigonometry, and average and range. The intervention programme also features exam questions for students to practise their skills in context!

### Edexcel maths past papers conclusions

Writing this blog has been very interesting from a personal perspective; even as an experienced maths teacher, it has caused me to re-evaluate some of the ideas I had about exam preparation for the new GCSE, and to think carefully about the time weightings given to certain topics once maths revision begins.

It was clear from the Sample Assessment Materials and the messaging from exam boards that one of the goals for GCSE maths 2015 was to increase the demand in problem-solving, and also to ask more questions requiring connections to be made between topics.

Part of this needs to be allowed for in a scheme of work; for example, when teaching mutually exclusive events, give students plenty of problems requiring an understanding of fractions, decimals, percentages and ratios. This cannot be done as a quick fix at the end.

However, with regard to final exam preparation, there are a few things to consider. A significant amount of algebra, statistics and probability is procedural C1 content, so this suggests there is less value in spending a lot of vital exam preparation time on rich problems for these topics.

Furthermore, we need to consider the frequency at which topics like quadratic equations appear on Foundation papers. For borderline grade 4/5 candidates, we may in fact be better off spending more time on problem-solving using proportional reasoning or shape, returning to the low-frequency procedural topics in the very final weeks.

What students clearly do need is plenty of practice on number skills, so these are not limiting their ability to access the context-based problems, and plenty of time and opportunity to work with number and proportion skills in a wide variety of contexts.

They also need lots of time on context-based shape work, particularly perimeter, area and volume, and 2D shape and angle properties. This could in part be achieved by using all of the papers analysed above as practice papers, mock exams or elements of a worksheet, both in the classroom and at home.

Finally, it’s important to assess all of this with regard to your specific setting and students. For some, a grade 3 represents an outstanding achievement, and a careful selection of topics to focus on may help a student to achieve this. Other students may have ‘dropped down’ to Foundation at the last minute, so might need some rapid intervention to boost number and proportional reasoning problem-solving skills, particularly C3 questions, as GCSE maths revision in a Higher tier group may not have targeted these areas.

**Read more:** 25 GCSE Maths Questions Organised By Topic And Difficulty

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