O-LevelAdditional MathematicsDifferentiation and integration4037/22 · Oct/Nov 2024 · Q28 Marks

Variables x and y are related by the equation y = x√1+2x.

(a)Find dy/dx[3]
(b)It is given that when y = 12, x = 4. Find the approximate change in x when y increases from 12 by the small amount 0.06.[3]
(c)Find the x-coordinate of the stationary point on the curve y = x√1+2x.[2]

Mark scheme

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

[B2] d/dx √1+2x = (1/2)(1+2x)^(-1/2) × 2 oe [B1] for k(1+2x)^(-1/2) where k is a positive constant, k ≠ 1
[B1] x × their (1/2)(1+2x)^(-1/2) × 2 + [1](1+2x)^(1/2) oe, isw [FT] their d/dx √1+2x
[M1] Uses their 4(1+2(4))^(-1/2) + (1+2(4))^(1/2) in an attempt at a small changes relationship [FT] x = 4 substituted into their derivative
[M1] dep previous M1 0.06/δx = their 4(1+2(4))^(-1/2) + (1+2(4))^(1/2) oe
[A1] 0.0138 or 0.01384[6...] or 9/650 oe nfww [FT] their 13/3
[M1] x/√(1+2x) + √(1+2x) = 0 oe and solves as far as x = ... [FT] a derivative of the form (ax + b)/√(1+2x) oe
[A1] x = -1/3 oe

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Topic: Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.
Source: O-Level Additional Mathematics, Oct/Nov 2024 Paper 2 Variant 2, question 2.

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