CIE IGCSE Maths Examiner Report June 2023: Summary

The June 2023 CIE IGCSE Maths Extended papers for Zone 3 (papers 21 and 41) contained 31 questions. It would be great as a teacher to be able to read every page of the examiners’ report, however there is a lot to read through and your time is precious.

Therefore, in this article I’ll be summarising the key takeaways from the CIE IGCSE Maths Examiner Report for those papers. 

Key Takeaways from the Edexcel IGCSE Maths Examiner Reports

My main takeaways for this set of papers are that students need to look out for the following common errors: 

• Incomplete or vague explanations cost marks (students often knew what to do but failed to explain fully, which led to the loss of method marks even when answers were mathematically sound)

• Calculator misuse and premature rounding (in both papers, candidates lost precision marks by rounding too early, misusing π, or being in the wrong calculator mode, especially during multi-step problems)

• Misreading of question wording (errors stemmed not from weak maths, but from misunderstanding what the question actually asked)

• Working not shown or hard to follow (many candidates missed method marks due to crossing out their working, jumping steps, or failing to structure their reasoning)

• Inconsistent or incorrect terminology and notation (Misuse of notation and informal language were penalised, even when the maths was correct)

• Strategic method selection was weak (especially in algebra and geometry, students often reached for complex methods (e.g. quadratic formula) when simpler ones would do)

Number

Common Strengths

• Basic time calculations, such as adding hours and minutes (Q2 Paper 21)

• Basic fraction operations (Q10 Paper 21)

Common Areas for Improvement

• Many candidates confused compound and simple interest, often failing to work with total value (Q13 Paper 21)

• Reverse percentage questions led to frequent errors from incorrect increases or decreases (Q1(a)(iii) Paper 41)

• Some candidates struggled with rounding or converting to/from significant figures (Q4 Paper 21)

Key Examiner Advice

Examiners noted that candidates frequently misread percentage-based problems, particularly those requiring reverse working to find an original value. There was a tendency to apply the usual “increase/decrease” strategy without recognising that the original was the unknown. 

This was especially apparent in questions involving discounts, exchange rates, or profit margins. In calculator-based tasks, premature rounding (e.g. using 3.14 for π or truncating intermediate steps) led to small accuracy losses, which were enough to drop method marks. 

In Paper 41, candidates often misjudged which quantity the profit margin should be calculated from — confusing profit based on cost versus selling price.

I have found it useful when teaching to incorporate reverse percentage activities with scaffolded steps, allowing students to reason from the “final” amount back to the original. Practice tasks can vary context (discounts, markup, tax) to build flexibility. 

It's also useful to set calculator-based exercises where students compare results using approximations (e.g. 3.14 vs π key) to develop a better understanding of the impact of rounding. Using shopping scenarios, budgeting tasks, and profit comparisons helps to anchor numerical thinking in real-life decisions.

Algebra and graphs

Common Strengths

• Finding and interpreting nth terms of linear sequences (Q8b Paper 21)

• Using the quadratic formula effectively to solve equations (Q7c Paper 41)

• Sound manipulation when expanding algebraic expressions (Q10a(iii) Paper 41)

Common Areas for Improvement

• Function notation and composition confused many candidates, especially with inverse functions (Q10a(ii) Paper 41)

• Candidates frequently made errors when rearranging formulae or expressing inequalities algebraically (Q7d and Q8a Paper 41)

Key Examiner Advice

Candidates showed competence in expanding brackets and simplifying, but often defaulted to the quadratic formula even in cases where factorisation was quicker and simpler. This suggests a lack of confidence in algebraic decision-making. Some students also misunderstood function composition or used incorrect bracket placement in simplification, indicating a need for clearer structural understanding of algebraic operations.

I like to encourage students to practice method selection by presenting quadratics in mixed formats and asking them to choose the most efficient route before solving. Regular exposure to algebraic logic puzzles — like “find the mistake” or step-by-step corrections — can also help sharpen procedural skills.

Coordinate geometry

Common Strengths

• Finding midpoints between coordinates (Q6b(i) Paper 41)

• Calculating gradients between two points (Q6b(iii) Paper 41)

Common Areas for Improvement

• Solving equations graphically was often misunderstood or ignored in favour of algebraic methods (Q20c Paper 21)

• Plotting or deducing coordinates of a square resulted in inaccurate or invalid shapes (Q6a Paper 41)

• Candidates occasionally confused midpoint with mean of differences or used unsuitable points (Q6b(i) Paper 41)

Key Examiner Advice

Candidates should ensure accuracy when plotting or deducing points, especially when forming geometric shapes. Careful diagram work is essential, as misplaced points or misidentified coordinates often led to incorrect conclusions. 

Candidates are advised to practise using formulae for midpoint, gradient, and length, as these were generally well understood but sometimes mishandled due to arithmetic or sign errors. It is also important to distinguish between visual reasoning using grids and formal algebraic methods — both should support one another for full accuracy and confidence.

Regular coordinate geometry practice, that progresses from calculating slopes and midpoints to full equation writing, is something I have always found useful in the classroom. Use diagrams to reinforce the geometric interpretation of perpendicular slopes, and encourage verbal reasoning (e.g. “the slope of this is negative one over…”). Challenge students to sketch and annotate lines using only partial data (a point and a slope, or midpoint and intercept).

Geometry

Common Strengths

• Applying scale factors correctly to solve similarity problems (Q9 Paper 21)

• Clear understanding of congruent triangles when correctly interpreting diagrams (Q12a Paper 21)

Common Areas for Improvement

• Geometrical reasoning was often vague or non-mathematical, especially with parallel lines (Q3 Paper 21)

• Circle theorems were poorly used or misunderstood, especially when involving diameters and tangents (Q12b(i–iii) Paper 21)

• Some students incorrectly assumed non-parallel lines or made unjustified geometric inferences (Q1 Paper 21)

Key Examiner Advice

In geometry, precise use of mathematical vocabulary is essential, especially when justifying answers with geometrical reasoning. Candidates often lost marks by using vague terms or mixing up concepts such as co-interior and opposite angles. 

Success was more common when students clearly identified properties of shapes, like similarity or congruence, and applied these logically. Circle theorems in particular require both conceptual understanding and careful interpretation of diagrams — candidates are encouraged to revise standard theorems and practise applying them in unfamiliar contexts.

In lessons, I like to encourage students to verbalise geometric deductions step by step, using structured language. Incorporate mini whiteboard tasks where they must explain why an angle is equal before calculating. 

Geometry flow diagrams and circle theorem flashcards (with a name and diagram) can reinforce correct language. Use multi-mark reasoning chains as regular practice so students get comfortable justifying each step clearly.

Mensuration

Common Strengths

• Volume calculations using given formulas (Q6 Paper 21)

• Surface area and perimeter tasks (Q4c(i–ii) Paper 41)

Common Areas for Improvement

• Many failed to apply correct unit conversions, especially cm³ to m³ in density problems (Q2e Paper 41)

• Arc length and area problems involving parts of circles often resulted in incorrect subtractions or fractions (Q4c(i) Paper 41)

• Some students used incorrect formulas or made premature rounding errors in volume problems (Q4b Paper 41)

Key Examiner Advice

Candidates generally performed well when formulas were provided, but many struggled with unit conversions, particularly when moving between cm³ and m³ or converting to grams. It's crucial to understand the relationship between linear, area, and volume units and to apply these accurately in real-world contexts. 

Candidates are advised to show all working clearly and avoid premature rounding, which frequently led to loss of accuracy marks. When dealing with compound shapes or circular sectors, a systematic approach — breaking the figure into familiar parts — often leads to more reliable results.

When available, I always try to use 3D nets or physical models to help clarify volume and surface area calculations with 3D shapes. You can create a “π precision lab” activity where students compare answers across π approximations to understand the importance of using the calculator key. Reinforce correct units (cm² vs cm³) through marking peer work and correcting deliberately flawed answers.

Trigonometry

Common Strengths

• Applying trigonometric ratios correctly in right-angled triangles (Q6b Paper 21)

• Competence using sine, cosine, and Pythagoras in composite 3D problems (Q2b Paper 41)

Common Areas for Improvement

• Many candidates drew inaccurate cosine graphs with poor symmetry or incorrect turning points (Q19a Paper 21)

• Solving trig equations often resulted in only one solution or incorrect use of inverse operations (Q19b Paper 21)

• Bearings questions were commonly mishandled due to angle misinterpretation or incorrect rule choice (Q18 Paper 21)

Key Examiner Advice

Candidates showed competence with basic applications of sine, cosine, and tangent in right-angled triangles, but struggled when problems required multi-step reasoning or involved bearings. Graph sketching, particularly of trigonometric functions, often lacked accuracy and a clear understanding of key features such as turning points and symmetry. 

Solving trigonometric equations sometimes resulted in only one solution being given, despite multiple solutions being required within a given interval. To improve, candidates should practise interpreting trigonometric graphs and revise how to apply both trig rules and graph behaviour when solving equations.

When teaching trigonometric functions, I always have my students regularly practise sketching sine, cosine, and tangent graphs by hand, focusing on key points such as maxima, minima, and axis crossings. 

Matching activities where students pair trigonometric equations with their correct graphs or identify transformations from visual cues can also be useful. To reinforce equation-solving, introduce loop-card games or stations where students solve for all valid angles in a range, encouraging them to check for multiple solutions using symmetry. 

Bearings and 2D/3D application problems can be tackled through map-based tasks or interactive group challenges where students calculate angles and distances from real-world-style diagrams.

Vectors and transformations

Common Strengths

• Accurately describing rotations and using correct vocabulary like 'clockwise' and 'centre' (Q11b Paper 21)

• Handling basic vector arithmetic and expressions confidently (Q16b Paper 21)

Common Areas for Improvement

• Descriptions of transformations often included multiple changes or missed essential properties (Q11a Paper 21)

• Vector magnitude questions were frequently approached with incorrect methods or incomplete squares (Q16a Paper 21)

• Some used position vectors incorrectly or gave non-vector expressions (Q16b Paper 21)

Key Examiner Advice

In vectors and transformations, many candidates lost marks by describing more than one transformation when only a single one was required, or by omitting key details such as the centre of enlargement or direction of rotation. Precise vocabulary is essential — terms like "enlargement," "reflection," and "rotation" must be used accurately and not replaced with informal language like "flip" or "turn." 

Vector magnitude and component work was less well understood, with frequent errors in applying Pythagoras’ theorem or combining vectors algebraically. Candidates are encouraged to practise both geometric interpretations and algebraic representations to develop a clear, dual understanding of this topic.

I like to reinforce transformation language through annotation tasks where pupils describe mappings aloud or match diagrams to full descriptions. Use structured sentence starters like “This is a reflection in the line…” or “This is a rotation of 90° clockwise about…” to model full transformation descriptions. 

Grid-based card sorting or matching activities can strengthen vocabulary recognition. For vectors, it is very useful to practise multi-step journeys where students must track paths such as A → B → C and then simplify. Reinforce proper notation with repeated visual examples and writing practice.

Probability

Common Strengths

• Calculating simple probabilities as decimals, fractions, or percentages (Q5 Paper 21)

• Identifying favourable outcomes from basic set or frequency data (Q3a(ii) Paper 41)

Common Areas for Improvement

• Multi-stage problems without replacement were commonly mishandled or incorrectly structured (Q15 Paper 21)

• Tree and Venn diagram-based problems lacked clarity or used incorrect totals (Q15 Paper 21 and Q3a(ii) Paper 41)

• Some candidates treated probabilities as additive even when multiplication was needed (Q15 Paper 21)

Key Examiner Advice

Although most students managed basic probability questions well, compound events involving multiple stages were often misunderstood. Many failed to use tree diagrams, even when they would have clarified the situation, and some confused whether the scenario involved replacement. Inaccurate listing of outcomes and failure to distinguish between independent and dependent probabilities led to frequent errors. Some students appeared unsure whether to add or multiply probabilities across branches.

In teaching, I have found it useful to incorporate visual scaffold activities like colour-coded tree diagrams, gradually removing supports as students gain confidence. Using concrete scenarios (e.g. choosing sweets from a bag) is a way to explore replacement rules. Encourage verbal “walk-throughs” of tree paths: “First we pick blue, then green…” to solidify the idea of sequence. Finally, include revision grids where students must decide when to multiply, when to add, and when to use fractions versus decimals.

Statistics

Common Strengths

• Cumulative frequency and median calculations (Q5a(i) Paper 41)

• Interpreting lower quartiles and percentiles correctly using diagrams (Q5a(ii) Paper 41)

• Finding mean of grouped data when midpoints were correctly identified (Q3a(i) Paper 41)

Common Areas for Improvement

• Histogram bars were drawn without adjusting for unequal intervals, leading to wrong frequency densities (Q5b Paper 41)

• When interpreting a cumulative frequency diagram, a number of students failed to subtract or interpret correct class totals for age brackets (Q5a(i) Paper 41)

Key Examiner Advice

In statistics, candidates often performed well when calculating averages such as the mean and median, particularly from individual or grouped data. However, constructing and interpreting histograms proved more challenging, especially when dealing with unequal class intervals and the need for frequency density. Misreading cumulative frequency scales or failing to interpret percentiles correctly also led to lost marks.

To improve, students should practise extracting key statistical measures from a variety of visual representations and ensure they understand how to use midpoints, class widths, and frequencies appropriately in data analysis.

To strengthen students’ grasp of statistics, I like to set up activities where they calculate the mean, median, and mode from raw, grouped, and continuous data — including the use of midpoints and estimated means. Card-sorting or matching tasks where students pair histogram bars with frequency tables, emphasising the role of frequency density in unequal class widths, can also be used. Incorporate interactive cumulative frequency exercises where students plot curves from data and estimate median and quartile values directly from graphs. 

Finally, include real-world datasets (e.g. sports stats or survey results) to practise interpreting statistical diagrams and drawing reasoned conclusions from summary measures and graphical trends.

How to Use the Examiner Report in the Classroom

Although examiner reports are perhaps aimed primarily at teachers, with your guidance they can be a very useful tool for your students as well. For example, choose a question from a past paper and ask your students to suggest what some of the common mistakes might have been. Sharing the relevant extract from the report might then either surprise your students or confirm their suspicions, and lead to interesting follow-on discussions.

Improve Student Outcomes with Save My Exams

Here at Save My Exams, we have concise revision notes for Edexcel IGCSE Maths to help your students when revising. We have flashcards which you can use in the classroom to test your students’ recall of key knowledge. For homework, you could use our differentiated topic questions, then use our student-friendly model answers to have your students peer mark each other’s work.

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References

Paper 0580/21 Question Paper

Paper 0580/21 Examiner Report

Paper 0580/41 Question Paper

Paper 0580/41 Examiner Report