Rearranging Formulae
Rearranging formulae requires students to change the subject of an equation, using the same inverse-operation skills as solving equations but with multiple variables. Harder questions involve subjects that appear twice or under roots and powers.
What You'll Learn
- Rearranging simple formulae to change the subject
- Rearranging when the subject appears in a fraction
- Rearranging when the subject appears under a square root or squared
- Rearranging when the subject appears more than once
Watch Out For These Mistakes
Students make these errors again and again. Knowing them in advance gives you a head start.
Performing inverse operations in the wrong order
Forgetting to square both sides when the subject is under a square root
Not factorising when the new subject appears in multiple terms
What Examiners Say About Rearranging Formulae
Insights pulled from Cambridge IGCSE (0580) examiner reports — the exact mistakes candidates make every year.
- Misconception●●●●●
You can ONLY cancel FACTORS (things multiplied), not terms added/subtracted. Factorise numerator and denominator first, then cancel matching brackets. Never cancel x² from x² − 25.
Source: CIE 0580 · May/June 2021 · Paper 4 · Q7a
- Presentation●●●●●
In 'show that k = 8' questions, you must DERIVE 8, not assume it. Starting from 'k = 8' and working both ways is circular and scores zero. Work from the given info towards the target.
Source: CIE 0580 · May/June 2021 · Paper 3 · Q5
- Common Mistake●●●●●
When raising a power to a power, MULTIPLY the exponents: (x³)³ = x⁹, not x⁶. But for coefficients like (4x³)³, the coefficient is raised: 4³ = 64, not 4 × 3 = 12.
Source: CIE 0580 · Feb/March 2024 · Paper 2 · Q21b
Based on 3of 500+ insights extracted from CIE 0580 examiner reports (2018–2024).
Exam Coverage
This topic appears in the Cambridge IGCSE past papers. Our AI tutor can help with it on any question.
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Related Topics
Solving Linear Equations
Linear equations are one of the most frequently tested algebra topics at Cambridge IGCSE level. Students must isolate the unknown variable by applying inverse operations, handling brackets and fractions along the way.
Algebraic Fractions
Algebraic fractions combine fraction skills with algebraic manipulation and are a step up from basic fractions. Students must simplify, add, subtract, multiply and divide fractions that contain variables, often needing to factorise first.
Functions
Function notation formalises the input-output relationship. Students evaluate, combine, and find inverses of functions, building skills that are directly extended in further study.
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