O-LevelAdditional MathematicsDifferentiation and integration4037/12 · May/June 2024 · Q88 Marks
A curve has equation y = (3x²-5)^(1/2) / (x+4).
- (a)Show that dy/dx can be written in the form (Ax² + Bx + C) / ((3x²-5)^(1/2) (x+4)²), where A, B and C are integers.[5]
- (b)Hence find the x-coordinates of the stationary points on the curve. Give your answers in their simplest exact form.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.
- [B1] 1/2 (6x)(3x²-5)^(-1/2) soi
- [M1] for attempt at differentiation of a quotient or valid product
- [A1] for all other terms correct
- [M1] (2x(x+4)-(3x²-5)) dep on previous M mark for simplification of their numerator Allow one sign slip but must be dealing with two quadratic terms.
- [A1] (-x² +8x+5) / ((3x²-5)^(1/2) (x+4)²)
- [M1] -x² +8x+5=0 oe, together with attempt to solve Allow for use of their quadratic numerator from part (a)
- [A1] 4+√21
- [A1] 4-√21
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