O-LevelAdditional MathematicsDifferentiation and integration4037/12 · May/June 2021 · Q46 Marks
A curve is such that d²y/dx² = (3x+2)^(-1/3). The curve has gradient 4 at the point (2, 6.2). Find the equation of the curve.
- (a)A curve is such that d²y/dx² = (3x+2)^(-1/3). The curve has gradient 4 at the point (2, 6.2). Find the equation of the curve.[6]
Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- [1] M1 For k₁(3x+2)^(2/3) where k₁ a constant.
- [1] M1 Dep for use of 4 and x = 2 in their dy/dx to obtain c
- [1] A1 May be implied by subsequent integration or by c = 2
- [1] M1 For k₂(3x+2)^(5/3) where k₂ is a constant.
- [1] M1 Dep on previous M1 for use of x = 2 and y = 6.2 in their y
- [1] A1 Must be an equation
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