Algebra and Graphs
Algebra is a key topic in the Cambridge IGCSE Mathematics 0580 syllabus and appears consistently across all exam sessions. Understanding how algebra questions are structured in past papers gives you a
Algebra is a key topic in the Cambridge IGCSE Mathematics 0580 syllabus and appears consistently across all exam sessions. Understanding how algebra 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 Algebra and Graphs
| Pattern | Frequency | Papers | Marks |
|---|---|---|---|
| Solving linear equations | Very Common | Paper 2, Paper 4 | 2-3 marks |
| Factorising and expanding expressions | Very Common | Paper 2, Paper 4 | 2-4 marks |
| Solving quadratic equations | Very Common | Paper 4 | 3-5 marks |
| Simultaneous equations | Common | Paper 4 | 4-5 marks |
| Changing the subject of a formula | Common | Paper 2, Paper 4 | 3-4 marks |
Solving linear equations
Collect terms with the variable on one side and constants on the other. Perform inverse operations systematically, showing each step clearly.
Factorising and expanding expressions
For expanding, multiply each term in the first bracket by each term in the second. For factorising, look for common factors first, then try grouping or the difference of two squares.
Solving quadratic equations
Try factorising first. If it does not factorise neatly, use the quadratic formula. Always check for two solutions and give answers to the required degree of accuracy.
Simultaneous equations
For two linear equations, use elimination or substitution. For one linear and one non-linear, substitute the linear equation into the non-linear one and solve the resulting quadratic.
Changing the subject of a formula
Use inverse operations to isolate the required variable. Be careful with squares and square roots, and remember to consider both positive and negative roots where appropriate.
Year-by-Year Trends
Over the past five exam sessions, algebra questions have remained consistent in both style and difficulty. The May/June sessions tend to feature slightly more challenging algebra problems compared to October/November. Recent papers show an increased emphasis on multi-step problems that combine algebra with other topics, particularly in Paper 4. The total marks allocated to algebra have remained stable, typically comprising the same proportion of the overall paper.
Mark Allocation
In Paper 2 (non-calculator), algebra questions typically carry 4-8 marks and test conceptual understanding without complex arithmetic. In Paper 4 (calculator), algebra 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
- An equation with the unknown on both sides
- A word problem requiring forming and solving an equation
- A quadratic expression to factorise or solve
- A formula rearrangement with squares or fractions
- Simultaneous equations set in a real-world context
Examiner Insights
- Show every step of working — marks are awarded for method even if the final answer is wrong
- When factorising quadratics, check your answer by expanding
- In simultaneous equations, always find both variables and clearly label which is x and which is y
- Read the question carefully to check whether exact or decimal answers are required
Worked Examples
Full solutions for Algebra and Graphs
Revision Notes
Key concepts & formulas
Common Mistakes
Avoid these errors
Frequently Asked Questions
What algebra topics come up most often in IGCSE Maths?
Solving linear equations, expanding and factorising, and rearranging formulas appear on nearly every paper. On Extended, quadratic equations, simultaneous equations, and algebraic fractions are very common.
How many marks is algebra worth?
Algebra typically accounts for 15-20% of the total marks, making it the highest-weighted topic. It appears on both calculator and non-calculator papers across all sessions.
What is the hardest algebra question type?
Non-linear simultaneous equations and algebraic fraction equations tend to be the most challenging. These appear in the second half of Paper 4 and can carry 5-7 marks.
Can I use a calculator for algebra on the IGCSE?
Paper 2 is non-calculator but includes algebra questions testing your manipulation skills. Paper 4 allows a calculator but many algebra questions still require algebraic working rather than numerical answers.
Are functions only on Extended?
Yes, functions (composite functions, inverse functions, domain and range) are Extended-only content. Basic function evaluation may appear on Core but the deeper function concepts are exclusive to Extended papers.
What function topics appear most often?
Finding inverse functions and evaluating composite functions are the most common. These appear in nearly every Paper 4 exam session, typically carrying 3-5 marks each.
How do I find the inverse of a function?
Replace f(x) with y, swap x and y in the equation, then rearrange to make y the subject. For example, if f(x) = 2x + 3, write y = 2x + 3, swap to x = 2y + 3, then rearrange to y = (x-3)/2, so f⁻¹(x) = (x-3)/2.
What sequence questions appear on Core vs Extended?
Core tests continuing sequences and finding nth terms of linear sequences. Extended adds quadratic sequences, geometric sequences, and more complex pattern problems.
How do I find the nth term of a quadratic sequence?
Find the first and second differences. If the second difference is constant (say 2a), the nth term formula starts with an². Subtract an² from each original term to find the remaining linear part, then combine.
How many marks are sequence questions worth?
Sequence questions typically carry 3-6 marks per question. They appear on both papers and are a reliable source of marks if you know the methods well.
What inequality topics are on Core vs Extended?
Core covers solving simple linear inequalities and representing them on number lines. Extended adds graphical inequalities, quadratic inequalities, and more complex algebraic inequalities.
When do I reverse the inequality sign?
Reverse the inequality sign when you multiply or divide both sides by a negative number. For example, -2x > 6 becomes x < -3 when you divide by -2.
How do I shade graphical inequalities?
Draw the boundary line (solid for ≤/≥, dashed for </>) then test a point like (0,0). If it satisfies the inequality, shade that side. The final answer region satisfies ALL inequalities simultaneously.
Is differentiation on Core or Extended?
Differentiation is Extended-only content. It does not appear on Core papers. On Extended, it appears exclusively on Paper 4 (calculator paper).
What differentiation do I need for IGCSE?
You need to differentiate polynomial expressions using the power rule, find gradients at specific points, locate and classify stationary points, and find equations of tangent lines. You do not need integration, chain rule, or product rule.
How many marks is differentiation worth?
Differentiation typically carries 6-10 marks on Paper 4, usually as one or two multi-part questions. It is a relatively high-value topic for the amount of content to learn.
How do I classify stationary points?
Find d²y/dx² (differentiate again). If d²y/dx² > 0, it is a minimum. If d²y/dx² < 0, it is a maximum. Alternatively, check the sign of dy/dx just before and just after the stationary point.
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