O-LevelAdditional MathematicsDifferentiation and integration4037/12 · Oct/Nov 2019 · Q118 Marks

A curve is such that d²y/dx² = 2(3x-1)^(-3/2). Given that the curve has a gradient of 6 at the point (3, 11), find the equation of the curve.

A curve is such that d²y/dx² = 2(3x-1)^(-3/2). Given that the curve has a gradient of 6 at the point (3, 11), find the equation of the curve.[8]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

[1] M1 For dy/dx = 2(3x-1)^(-1/2) / (3 * -1/2) (+c) condone omission of + c
[1] A1 All correct, condone omission of c
[1] M1 Dep for attempt to find c
[1] A1 All correct, may be implied by c = 2
[1] M1 For attempt to integrate their dy/dx to obtain the form y = b(3x-1)^(1/2) (+mx+d)
[1] A1 All correct, condone omission of d
[1] M1 Dep for attempt to find d, a second arbitrary constant, having used an arbitrary constant for dy/dx
[1] A1 y = (2/3)(3x-1)^(3/2) + 2x - 3

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Topic: Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.
Source: O-Level Additional Mathematics, Oct/Nov 2019 Paper 1 Variant 2, question 11.

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