O-LevelAdditional MathematicsStraight line graphs4037/22 · May/June 2014 · Q108 Marks

Two variables x and y are connected by the relationship y = Abˣ, where A and b are constants. An experiment was carried out measuring values of y for certain values of x. The values of lny and x were plotted and a line of best fit was drawn. The graph is shown on the grid below. [Figure 10.1]

(i)Transform the relationship y = Abˣ into a straight line form.[2]
(ii)Use the graph to determine the value of A and the value of b, giving each to 1 significant figure.[4]
(iii)Find x when y = 220.[2]

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Mark scheme

Marking points from the official mark scheme (May/June 2014). The mark or mark type is shown in brackets.

[M1] Taking logs of both sides any base; must be an explicitly correct statement
[A1] log y = log A + x log b correct form; any base; no recovery from incorrect method steps
[B2] b: awrt 3 to one sf isw or awrt 4 to one sf isw or M1 for b = e^(their gradient) soi; their gradient must be correctly evaluated as rise/run
[B2] A: awrt 0.5 to one sf or B1 for A = e^-0.6 or SC1 for A = e^-0.3 = 0.7 (giving an awrt 0.7)
[M1] Evidence of graph used at ln y = 5.4 soi or 220 / (their4)ˣ = (their0.5) or 5.39... = their(1.4)x + their -0.6 or ln(220) = x ln(their 4)+ln(their0.5)
[A1] awrt 4.4 to two sf

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