A-LevelMathematicsDifferentiation9709/31 · May/June 2022 · Q89 Marks
The equation of a curve is x³ + y³ + 2xy + 8 = 0.
- (a)Express `dy/dx` in terms of x and y.[4]
- (b)The tangent to the curve at the point where x = 0 and the tangent at the point where y = 0 intersect at the acute angle α. Find the exact value of tan α.[5]
Mark scheme
Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.
- [B1] State or imply 3y² dy/dx as derivative of y³
- [B1] State or imply 2y + 2x dy/dx as derivative of 2xy
- [M1] Complete differentiation and equate attempted derivative to zero and solve for dy/dx
- [A1] Obtain answer (3x² + 2y) / (3y² + 2x)
- [M1] Find gradient at either (0, – 2) or (–2, 0)
- [A1 A1] Obtain answers 1/3 and 3
- [M1] Use tan(A±B) formula to find tanα
- [A1] Obtain answer tan α = 4/3
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