O-LevelAdditional MathematicsDifferentiation and integration4037/22 · Oct/Nov 2021 · Q76 Marks
It is given that d²y/dx² = e^(2x) + 1/((x+1)²) for x > -1.
- (a)Find an expression for dy/dx given that dy/dx = 2 when x = 0.[3]
- (b)Find an expression for y given that y = 4 when x = 0.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.
- [B3] M2 for 1/2 e^(2x) - (x+1)⁻¹ + c oe or M1 for any two terms correct from 1/2 e^(2x), -(x+1)⁻¹, +c
- [M1] FT their c from (a), providing c ≠ 0 [y =] 1/4 e^(2x) - ln(x+1)
- [M1] +their c/2 x + d
- [A1] [y =] 1/4 e^(2x) - ln(x+1) + 5/2 x + 15/4 oe
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