O-LevelAdditional MathematicsStraight line graphs4037/22 · Oct/Nov 2021 · Q88 Marks

Variables x and y are such that when √y is plotted against log₂(x+1), where x > -1, a straight line is obtained which passes through (2,10.4) and (4,15.4).

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.

[M1] [Gradient =] (15.4-10.4)/(4-2) oe soi
[M1] FT their gradient 10.4 = their2.5 × 2 + c or 15.4 = their2.5 x 4 + c or (y-10.4)/(x-2) = (y-15.4)/(x-4) = their2.5
[A1] [Gradient = ] 2.5 soi and [intercept =] 5.4 soi
[A1] √y = 2.5log₂(x+1)+5.4 oe isw
[B1] 5929/25 or 237.16
[M1] FT their equation from (a) of correct form with m ≠ 1 or 0, and c ≠ 0 5 = their2.5log₂(x+1)+their5.4 and rearrange to make log₂(x+1) the subject Condone any base
[A1] Condone any base 4/25 = log₂(x+1) oe
[A1] x = -0.105 or -0.1049[74...] rot to 4 or more sf

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Topic: Straight line graphs, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.
Source: O-Level Additional Mathematics, Oct/Nov 2021 Paper 2 Variant 2, question 8.

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