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Algebraic formulae - OCRRearranging formulae - higher

Formulae are used in everyday life, from working out areas and volumes of shapes to converting units of measurement. Knowing how to use and rearrange formulae are very useful skills.

Part of MathsAlgebra

Rearranging formulae - higher

More advanced techniques are required to rearrange any formulae that involve any powers or roots. Further techniques are needed if the variable which needs to be the subject appears twice.

Example

Rearrange the formula \(T = 2 \pi \sqrt{\frac{L}{G}}\) to make \(L\) the subject.

If a formula contains a power or a root then this must be isolated before performing the inverse operation.

Firstly, isolate the root:

\(\begin{array}{ccc} T & = & 2 \pi \sqrt{\frac{L}{G}} \\ \div 2 \pi && \div 2 \pi \end{array}\)

\(\frac{T}{2 \pi} = \sqrt{\frac{L}{G}}\)

Now 'square' both sides:

\(\left(\frac{T}{2 \pi}\right)^2 = \left(\sqrt{\frac{L}{G}}\right)^2\)

Lastly, multiply by \(G\):

\(\begin{array}{ccc} \left(\frac{T}{2 \pi}\right)^2 & = & \frac{L}{G} \\ \times G && \times G \end{array}\)

\(G \left(\frac{T}{2 \pi}\right)^2 = L\)

Question

The formula for the surface area, \(A\), of a closed box is given by:

\(A = 2wb + 2wh + 2bh\)

Rearrange this formula to make \(b\) the subject.

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