Quadratic equations and simultaneous equations
Pearson Edexcel International GCSE Mathematics · 4MA1
Paper 1F | Whole paper: Number, Algebra, Geometry, Statistics
Three ways to solve a quadratic and two ways to solve a pair of simultaneous equations — with a rule for choosing between them.
Specification coverage
2 Equations, formulae and identities — statements 2.6–2.9 (Foundation and Higher Tier)
Assessment objectives: AO1. Suggested learning time: 110 minutes.
Required knowledge
- Solve quadratic equations by factorisation
- Solve quadratic equations using the quadratic formula (Higher)
- Complete the square (Higher)
- Solve simultaneous linear equations by elimination and by substitution
- Solve a pair of equations where one is linear and one is quadratic (Higher)
Required skills
- Choose the efficient method: factorise if it factorises, formula if it does not
- Recognise when a question implies a quadratic even though none is given
- Check both solutions against the context and discard the impossible one
How it is examined
- Structured questions building from a routine start to a multi-step finish
- Problem-solving questions with no method given
- 'Show that' and reasoning questions where the working IS the answer
Common mistakes
- Giving only one solution to a quadratic. There are usually two, and the second is worth a mark.
- Losing a negative in the quadratic formula, particularly under the square root.
- Forgetting to find the second variable in simultaneous equations — half the marks are in the value you did not calculate.
- Keeping a negative length or a negative time when the context makes it impossible. Discard it and say why.