A-LevelMathematicsDifferentiation9709/32 · Feb/Mar 2020 · Q79 Marks
The equation of a curve is x³ + 3xy² – y³ = 5.
- (a)Show that dy/dx = (x² + y²) / (y² - 2xy)[4]
- (b)Find the coordinates of the points on the curve where the tangent is parallel to the y-axis.[5]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2020). The mark or mark type is shown in brackets.
- [B1] State or imply 3y² + 6xy dy/dx as derivative of 3xy²
- [B1] State or imply 3y² dy/dx as derivative of y³
- [M1] Equate attempted derivative of LHS to zero and solve for dy/dx (Need to see dy/dx factorised out prior to AG)
- [A1] Obtain the given answer correctly
- [*M1] Equate denominator to zero
- [A1] Obtain y = 2x, or equivalent
- [DM1] Obtain an equation in x or y
- [A1] Obtain the point (1, 2)
- [B1] State the point (√5,0) (Alternatively (1.71, 0).)
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