O-LevelAdditional MathematicsDifferentiation and integration4037/11 · May/June 2023 · Q87 Marks
8 A curve has the equation y = (3x-4)¹ᐟ³ / (2x+1).
- (a)Show that dy/dx = (Ax + B) / ((2x+1)²(3x-4)²ᐟ³), where A and B are integers to be found.[5]
- (b)Find the coordinates of the stationary point on the curve.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.
- [5] B1 for (2x+1) × 1/3 × 3(3x-4)^(-2/3) oe
- B1 for -2(3x-4)^(1/3)(2x+1)^(-2)
- M1 for an attempt to differentiate a quotient.
- A1 for all terms other than 1/3 × 3(3x-4)^(-2/3) correct.
- Allow unsimplified.
- M1 dep for attempt to factorise, must be in the form (3x-4)^(-2/3) / (2x+1)² [(ax + 1) – b(3x - 4)]
- A1
- [2] B1 FT for their x-coordinate only.
- Do not allow FT if they score M0 in part (a)
- (2.25, 0.255)
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