O-LevelAdditional MathematicsStraight line graphs4037/21 · May/June 2021 · Q58 Marks

The curves y = x² and y² = 27x intersect at O(0, 0) and at the point A. Find the equation of the perpendicular bisector of the line OA.

The curves y = x² and y² = 27x intersect at O(0, 0) and at the point A. Find the equation of the perpendicular bisector of the line OA.[8]

Mark scheme

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

[M1] 27x = (x²)² or y = (y/27)² oe
[A1] x⁴-27x = 0 or y⁴-729y = 0 oe nfww
[M1] x(x³ – 27) = 0 or y(y³ – 729) = 0 oe
[A1] A(3, 9) oe only nfww
[SC4] if M0 then, for first 4 marks, SC4 if (3, 9) only stated and verified in both equations, ignore (0, 0)
[SC2] for (3, 9) only stated with no working, ignore (0, 0)
[SC1] If first M1 then (3, 9) with no additional working award M1SC1
[B1] Mid-point = (1.5,4.5)
[B1] mOA = 9/3 oe
[M1] m⊥ = -3/9 oe
[A1] y - 4.5 = -3/9(x-1.5) oe isw (FT their mid-point and their -1/3)

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Topic: Straight line graphs, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.
Source: O-Level Additional Mathematics, May/June 2021 Paper 2 Variant 1, question 5.

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