A-LevelMathematicsDifferentiation9709/32 · Feb/Mar 2025 · Q25 Marks
The equation of a curve is xy² +ln(x+2y) = 1. Find the gradient of the curve at the point where x = 0.
- (a)The equation of a curve is xy² +ln(x+2y) = 1. Find the gradient of the curve at the point where x = 0.[5]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2025). The mark or mark type is shown in brackets.
- [B1] State or imply (1+2(dy/dx))/(x+2y) as the derivative of ln(x+2y)
- [B1] State derivative of xy² is x2y(dy/dx) + y²
- [B1] Obtain y² + 2xy(dy/dx) + (1+2(dy/dx))/(x+2y) = 0 OE May be implied by correct final answer.
- [B1] Obtain y = -½e when x = 0 Allow ½×2.718 or 1.36 or better e.g. 1.359... May be implied by correct final answer.
- [B1] Obtain dy/dx = -⅛(e³+4) OE Accept AWRT –3.01. ISW.
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