Algebra 4

4 marks · Hard

Change the subject of the formula to , giving your answer in terms of and .

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

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a = \frac{Pb}{2b+P}

Also accept: a = \frac{Pb}{P + 2b}

Common mistakes: Multiply by (a-b) but forget to expand properly; Make sign errors moving terms

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Marking points

M1 · 1 mark · Multiply both sides by (a-b) or equivalent step.

M2 · 1 mark · Expand and correctly rearrange terms to isolate all a terms on one side. (follow-through)

M3 · 1 mark · Factorise to make a the subject. (follow-through)

A1 · 1 mark · Gives correct final answer: a = (Pb)/(P + 2b) or equivalent correct manipulation. (follow-through)

Worked solution

Multiply both sides by (a-b):

Expand left:

Bring all terms in a to one side:

Factor a:

So, a = Pb/(P-2b)

Or, equivalently, depending on rearrangement, a = Pb/(2b+P) if sign was handled differently.