O-LevelAdditional MathematicsDifferentiation and integration4037/12 · Oct/Nov 2024 · Q76 Marks

It is given that y = ln(3x²-1)/(x+2), for x > 1/√3. When x = 1, y is increasing at the rate of h units per second. Find, in terms of h, the corresponding rate of change in x, giving your answer in exact form.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.

[B1] for 6x / (3x²-1)
[M1] for correct attempt at differentiation of a quotient or a correct product
[A1] for all terms apart from 6x / (3x²-1) correct.
[M1] For use of x = 1 in their dy/dx, must see a substitution if in decimal form unless 0.923 obtained from a correct derivative
[M1] for dx/dt = h / (dy/dx with x=1) with x = 1
[A1] 9h / (9-ln2) or exact equivalent

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Topic: Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 6 marks.
Source: O-Level Additional Mathematics, Oct/Nov 2024 Paper 1 Variant 2, question 7.

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