O-LevelAdditional MathematicsDifferentiation and integration4037/11 · May/June 2017 · Q108 Marks

Given that y = e³ˣ / (4x² + 1), find dy/dx.

Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

[M1] differentiation of a quotient or equivalent product
[B1] correct differentiation of e³ˣ
[A1] dy/dx = (3e³ˣ(4x²+1)-8xe³ˣ)/(4x²+1)² or dy/dx = e³ˣ ( (3(4x²+1)-8x) / (4x²+1)² ) everything else correct including brackets where needed, allow unsimplified
[M1] one term differentiated correctly
[A1] dy/dx = -4sin(x+π/3) + 2√3cos(x+π/3) all correct
[A1] When x = π/2, dy/dx = -5
[M1] dy/dt = dy/dx * dx/dt correct use of rates of change
[A1] dx/dt = -2 FT answer to (i)

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.

Topic: Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.
Source: O-Level Additional Mathematics, May/June 2017 Paper 1 Variant 1, question 10.

Questions and mark schemes are from past examination papers and remain the copyright of the exam board. How Oracle Prep builds its content