A-LevelMathematicsIntegration9709/12 · Feb/Mar 2021 · Q67 Marks
A curve is such that dy 6 = and A (1, -3) lies on the curve. A point is moving along the curve dx (3x-2)3 and at A the y-coordinate of the point is increasing at 3 units per second.
- (a)Find the rate of increase at A of the x-coordinate of the point.[3]
- (b)Find the equation of the curve.[4]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2021). The mark or mark type is shown in brackets.
- [1] At x = 1, dy/dx = 6
- [2] dx/dt = (dx/dy) × (dy/dt) = 1/6 × 3 = 1/2 (Chain rule used correctly. Allow alternative and minimal notation.)
- [2] [y =] 6(3x-2)^(-2) / -2 * (1/3) [+c]
- [1] -3 = -1 + c (Substitute x = 1, y = -3. c must be present.)
- [1] y = -(3x-2)² -2 (OE. Allow f(x)=)
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