O-LevelAdditional MathematicsDifferentiation and integration4037/12 · May/June 2025 · Q86 Marks
It is given that y = ln(3x² + 16) / (x+2).
- (a)Find dy/dx when x = 0. Give your answer in the form ln p, where p is a constant.[5]
- (b)Given that x increases from 0 to h, where h is small, write down the approximate change in y.[1]
Mark scheme
Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.
- [B1] 6x/(3x²+16)
- [M1] Differentiation of a quotient or equivalent product (dy/dx = [ (x+2)(6x/(3x²+16)) - ln(3x²+16)(1) ] / (x+2)²)
- [A1] All other terms apart from 6x/(3x²+16) correct
- [M1] dy/dx = -ln16 / 4 (dep for attempt to substitute in x = 0 and obtain a single log term)
- [A1] = ln(1/2) from correct work
- [B1] Change = hln(1/2) oe (FT on their single log answer to part (a))
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