O-LevelAdditional MathematicsDifferentiation and integration4037/12 · May/June 2019 · Q117 Marks
The normal to the curve y = (x-2)(3x+1)^(1/2) at the point where x = 7/3, meets the y-axis at the point P. Find the exact coordinates of the point P.
- The normal to the curve y = (x-2)(3x+1)^(1/2) at the point where x = 7/3, meets the y-axis at the point P. Find the exact coordinates of the point P.[7]
Mark scheme
Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.
- [M1] dy/dx = (x-2) × 1/2 × 3(3x+1)^(-1/2) + (3x+1)^(1/2) For attempt at differentiating a product
- [B1] For × 3(3x+1)^(-1/2)
- [A1] For all other terms correct
- [B1] y = 4/3
- [M1] For attempt at normal equation using -1/their m and their y when x = 7/3
- [A1] Equation of normal: y - 4/3 = -4/13 (x - 7/3) For correct normal equation, may be implied by a correct final answer
- [A1] At y-axis, y = 73/39
- [A1] (0, 73/39) isw
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