IGCSE Maths Number — Past Paper Question Analysis
Number is a key topic in the Cambridge IGCSE Mathematics 0580 syllabus and appears consistently across all exam sessions. Understanding how number questions are structured in past papers gives you a s
Number is a key topic in the Cambridge IGCSE Mathematics 0580 syllabus and appears consistently across all exam sessions. Understanding how number questions are structured in past papers gives you a significant advantage. This page analyses question patterns, mark allocation, and examiner expectations so you can prepare strategically. Teacher Rig uses past paper analysis as a core part of exam preparation, ensuring students are familiar with every question type they may encounter.
Question Patterns in Number
| Pattern | Frequency | Papers | Marks |
|---|---|---|---|
| Percentages: increase, decrease, reverse | Very Common | Paper 2, Paper 4 | 3-5 marks |
| Ratio and proportion | Very Common | Paper 2, Paper 4 | 3-5 marks |
| Standard form calculations | Common | Paper 2, Paper 4 | 2-4 marks |
| Bounds and accuracy | Common | Paper 4 | 3-5 marks |
| HCF and LCM problems | Common | Paper 2, Paper 4 | 3-4 marks |
Percentages: increase, decrease, reverse
For percentage increase/decrease, use multipliers (e.g., 15% increase = x 1.15). For reverse percentage, divide by the multiplier to find the original amount.
Ratio and proportion
Find the total number of parts, then find the value of one part. For direct proportion, y = kx; for inverse proportion, y = k/x. Find k using given values.
Standard form calculations
Write numbers as a x 10^n where 1 <= a < 10. When multiplying, multiply the a values and add the powers. When dividing, divide the a values and subtract the powers.
Bounds and accuracy
Upper bound = value + half the accuracy. Lower bound = value - half the accuracy. For maximum results, use upper bounds in the numerator and lower bounds in the denominator.
HCF and LCM problems
Use prime factorisation. HCF = product of common prime factors with lowest powers. LCM = product of all prime factors with highest powers.
Year-by-Year Trends
Over the past five exam sessions, number questions have remained consistent in both style and difficulty. The May/June sessions tend to feature slightly more challenging number problems compared to October/November. Recent papers show an increased emphasis on multi-step problems that combine number with other topics, particularly in Paper 4. The total marks allocated to number have remained stable, typically comprising the same proportion of the overall paper.
Mark Allocation
In Paper 2 (non-calculator), number questions typically carry 4-8 marks and test conceptual understanding without complex arithmetic. In Paper 4 (calculator), number questions can carry up to 10-12 marks and often involve multi-step problems with real-world contexts. Part (a) questions usually carry 1-2 marks for straightforward recall, while later parts build in difficulty and carry 3-5 marks each.
Common Question Setups
- A percentage increase or decrease in a real-world context
- A ratio problem involving sharing quantities
- Numbers to convert to or from standard form
- An upper and lower bounds calculation
- A prime factorisation leading to HCF or LCM
Examiner Insights
- Reverse percentage: to find the original, divide by the multiplier, not subtract the percentage
- In bounds questions, clearly state your upper and lower bounds before calculating
- Standard form: the first number must be at least 1 and less than 10
- For compound interest, use the formula A = P(1 + r/100)^n rather than calculating year by year
Worked Examples
Full solutions for Number
Revision Notes
Key concepts & formulas
Common Mistakes
Avoid these errors
Frequently Asked Questions
What number topics come up most often?
Percentages (including reverse percentages and compound interest), ratio and proportion, and standard form appear on nearly every paper. These are high-frequency topics across both Core and Extended.
How many marks is the Number topic worth?
Number skills typically account for 15-20% of the total marks, making it one of the most heavily weighted topics alongside Algebra.
Is bounds an Extended-only topic?
Upper and lower bounds with calculations are primarily tested on Extended papers, though basic rounding and accuracy questions can appear on Core.
How do I handle reverse percentage questions?
If a price after a 20% increase is £60, the original price is £60 ÷ 1.20 = £50. Divide by the multiplier (1 + percentage/100 for increase, 1 - percentage/100 for decrease). Never subtract the percentage from the final amount.
Master Number Past Paper Questions
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