A-LevelMathematicsDifferentiation9709/32 · May/June 2018 · Q58 Marks
The equation of a curve is x²(x + 3y) – y³ = 3.
- (i)Show that dy/dx = (x² + 2xy) / (y² - x²)[4]
- (ii)Hence find the exact coordinates of the two points on the curve at which the gradient of the normal is 1.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.
- [B1] State or imply 3 y² dy/dx as derivative of y³
- [B1] State or imply 6xy + 3x² dy/dx as derivative of 3x²y
- [M1] Equate derivative of the LHS to zero and solve for dy/dx
- [A1] Obtain the given answer
- OR State or imply 2x(x+3y)+x²(1+3 dy/dx) as derivative of x²(x+3y)
- [M1*] Equate derivative to – 1 and solve for y
- [M1(dep*)] Use their y = – 2x or equivalent to obtain an equation in x or y
- [A1] Obtain answer (1, – 2)
- [B1] Obtain answer (√3, 0)
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