O-LevelAdditional MathematicsDifferentiation and integration4037/12 · Oct/Nov 2019 · Q77 Marks

It is given that y = (1+e^(x²))(x+5).

(i)Find dy/dx.[3]
(ii)Find the approximate change in y as x increases from 0.5 to 0.5+p, where p is small.[2]
(iii)Given that y is increasing at a rate of 2 units per second when x = 0.5, find the corresponding rate of change in x.[2]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

[1] B1 For 2xe^(x²)
[1] M1 For attempt at differentiating a product or expanding brackets and differentiating a product
[1] A1 For all other terms, apart from 2xe^(x²), correct
[1] M1 For attempt to find their dy/dx when x = 0.5 and multiplication by p
[1] A1 Approximate change = 9.35p
[1] M1 For use of correct rates of change equation using their dy/dx when x = 0.5 and dy/dt = 2
[1] A1 dx/dt = 0.214 FT on 2/their 9.346 Must be correct to at least 3 sf

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Topic: Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 7 marks.
Source: O-Level Additional Mathematics, Oct/Nov 2019 Paper 1 Variant 2, question 7.

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