Algebra and Graphs rewards precision, and that’s exactly where students trip up. Below are the recurring Algebra and Graphs mistakes that pull grades down on Cambridge 0580 — with why they happen and how to avoid each one.
1. Sign errors when expanding negative brackets. Students forget to multiply the negative sign by every term inside the bracket, often only applying it to the first term. For example, writing -2(x - 3) = -2x - 6 instead of the correct -2x + 6.
2. Incorrect cancelling in algebraic fractions. Students cancel individual terms instead of common factors. You can only cancel a factor that divides the entire numerator and the entire denominator. For example, writing (x + 3)/(x + 5) = 3/5 by cancelling the x terms, which is completely wrong.
3. Forgetting to factorise completely. Students find one factor but do not check whether the remaining expression can be factorised further. For example, factorising 2x squared + 6x as 2(x squared + 3x) instead of the fully factorised 2x(x + 3).
The Bigger Picture
Algebra mistakes are the most costly in IGCSE Mathematics because algebra skills are needed in almost every topic. The key to avoiding errors is to show every step of your working clearly. Never skip steps or do calculations in your head. Check your answers by substituting back into the original equation. For quadratics, always rearrange to zero before factorising. For algebraic fractions, always factorise before cancelling. These habits will eliminate the majority of common algebra errors.
These three are the worst offenders, but they aren’t the whole list. For the full set of algebra and graphs mistakes — with more worked examples — see our Algebra and Graphs common mistakes resource, or work through the Algebra and Graphs topic hub.
One Question Students Always Ask
What are the most common algebra mistakes in IGCSE exams?
The most common algebra mistakes include sign errors when expanding negative brackets and incorrect cancelling in algebraic fractions. These errors account for a significant proportion of lost marks. Understanding why they happen and practising the correct methods will help you avoid them.
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