O-LevelAdditional MathematicsDifferentiation and integration4037/21 · May/June 2021 · Q66 Marks
Variables x and y are such that y = e2 + x cos 2x, where x is in radians. Use differentiation to find the approximate change in y as x increases from 1 to 1+h, where h is small.
- Variables x and y are such that y = e2 + x cos 2x, where x is in radians. Use differentiation to find the approximate change in y as x increases from 1 to 1+h, where h is small.[6]
Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- [B1] d(e^(x/2))/dx = 1/2 e^(x/2)
- [B1] d(cos 2x)/dx = -2sin 2x soi
- [M1] x × their(-2sin2x) + cos2x
- [A1] dy/dx = 1/2 e^(x/2) - 2xsin2x + cos2x (FT their de^(x/2)/dx = ke^(x/2))
- [M1] δy ≈ their dy/dx |x=1 h
- [A1] -1.41[03...]h nfww
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