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O-LevelAdditional MathematicsDifferentiation and integration4037/21 · May/June 2024 · Q74 Marks

It is given that y = mx² + x/2 + n, where m and n are non-zero constants. It is also given that 3(d²y/dx²) = (dy/dx)² - y for all values of x. Find the values of m and n.

It is given that y = mx² + x/2 + n, where m and n are non-zero constants. It is also given that 3(d²y/dx²) = (dy/dx)² - y for all values of x. Find the values of m and n.[4]

Mark scheme

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

[B1] dy/dx = 2mx + 1/2
[B1] d²y/dx² = 2m
[M1] for 3(2m) = (2mx + 1/2)² - (mx² + x/2 + n)
[A1] m = 1/4 and n = -5/4 and no other values

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About this question

Topic: Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 4 marks.
Source: O-Level Additional Mathematics, May/June 2024 Paper 2 Variant 1, question 7.

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