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Welcome to GCSE Edexcel Maths revision.

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Topic M 9: Formulae and rearranging.

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This video covers Higher tier.

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It includes the shared content and the labelled Higher extensions.

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The subject of a formula is the variable on its own, usually on the left.

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In A equals l w, A is the subject.

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Changing the subject rearranges the relation without changing its meaning.

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Treat both sides equally and undo operations in reverse order.

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From y equals 3 x plus 5,

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subtract 5 from both sides,

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then divide by 3 to x equals the fraction with numerator open bracket y minus 5 close bracket and denominator open bracket 3 close bracket ,

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end fraction .

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Worked example: From v equals u plus at,

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subtract u and divide by t to a equals the fraction with numerator open bracket v minus u close bracket and denominator open bracket t close bracket ,

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end fraction ,

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where t is not equal to 0.

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Check the result by multiplying both sides by t and adding u.

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If the subject is inside a bracket, undo any outside operation first.

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For P equals 2 multiplied by open bracket l plus w close bracket ,

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l equals the fraction with numerator open bracket P close bracket and denominator open bracket 2 close bracket ,

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end fraction minus w.

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If A equals pi r squared ,

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divide by pi ,

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then take the positive root for a radius: r equals square root of open bracket the fraction with numerator open bracket A close bracket and denominator open bracket pi close bracket ,

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end fraction close bracket .

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Geometrical lengths cannot be negative.

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Worked example: A taxi charges 4 pounds plus 1 pound and 80 pence per kilometre.

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C equals 4 plus 1.8 d.

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If C equals 22, pounds then d equals open bracket 22 minus 4 close bracket divided by 1.8 equals 10 kilometres.

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Use consistent units in formulae.

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In distance equals speed multiplied by time, a speed in kilometres per hour requires time in hours if distance is to be in km.

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Write a formula by identifying fixed and changing quantities.

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For n identical tickets costing p pounds each with one q pounds booking fee, total cost is T equals n p plus q.

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Substitute into the original formula to check a rearrangement.

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If y equals 3 x plus 5 with x equals 4 gives y equals 17, the rearranged formula should recover x equals 4 from y equals 17.

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When the required variable appears in several terms, collect its terms on one side and factorise it out.

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Moving only one occurrence does not finish the rearrangement.

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Worked example: y equals a x plus b x gives y equals x multiplied by open bracket a plus b close bracket ,

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so x equals the fraction with numerator open bracket y close bracket and denominator open bracket a plus b close bracket ,

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end fraction ,

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provided a plus b is not equal to 0.

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Worked example: y equals the fraction with numerator open bracket 3 x plus 2 close bracket and denominator open bracket x minus 1 close bracket , end fraction .

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Multiply by x minus 1: yx minus y equals 3 x plus 2.

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Collect x terms: x multiplied by open bracket y minus 3 close bracket equals y plus 2,

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so x equals the fraction with numerator open bracket y plus 2 close bracket and denominator open bracket y minus 3 close bracket ,

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end fraction ,

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where y is not equal to 3 and the original x is not equal to 1.

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With squared variables,

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algebraic solutions may need plus or minus : y equals x squared plus 4 gives x equals plus or minus square root of open bracket y minus 4 close bracket ,

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for y is greater than or equal to 4.

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Context may select a positive solution.

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State restrictions introduced by division or roots.

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Dividing by a quantity that could be zero can lose valid cases or create undefined expressions.

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That completes Formulae and rearranging.

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Revisit the notes and test yourself on the revision website.