A-LevelMathematicsDifferentiation9709/12 · Oct/Nov 2016 · Q79 Marks
The equation of a curve is y = 2 + 3/(2x – 1).
- (i)Obtain an expression for dy/dx.[2]
- (ii)Explain why the curve has no stationary points.[1]
- (iii)Show that the normal to the curve at P passes through the origin.[4]
- (iv)A point moves along the curve in such a way that its x-coordinate is decreasing at a constant rate of 0.06 units per second. Find the rate of change of the y-coordinate as the point passes through P.[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2016). The mark or mark type is shown in brackets.
- [B1] -3/(2x-1)²
- [B1] ×2
- [B1] e.g. Solve for dy/dx = 0 is impossible. Satisfactory explanation.
- [M1*] If x = 2, dy/dx = -6/9 and y = 3 Attempt at both needed.
- [M1*] Perpendicular has m = 9/6 Use of m1m2 = -1 numerically.
- [DM1] → y-3 = (3/2)(x-2) Line equation using (2, their 3) and their m.
- [A1] Shows when x=0 then y=0 AG
- [M1 A1] dy/dt = dy/dx * dx/dt → -2/3 * -0.06 = 0.04
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