O-LevelAdditional MathematicsDifferentiation and integration4037/21 · May/June 2024 · Q65 Marks
Variables x and y are such that y = cosx sin²x. Use differentiation to find the approximate change in y as x increases from 3 to 3+h, where h is small.
- Variables x and y are such that y = cosx sin²x. Use differentiation to find the approximate change in y as x increases from 3 to 3+h, where h is small.[5]
Mark scheme
Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.
- [B1] d/dx (sin²x) = 2sinxcosx soi
- [M1] cosx × their(2sinxcosx) + (their – sinx) × sin²x
- [A1] cosx × their(2sinxcosx) + (–sinx) × sin²x isw
- [M1] δy/h = their(2sin3cos²3 – sin³3) or better (FT their derivative)
- [A1] 0.274h or 0.2738[08…]h where the coefficient of h is rot to 4 or more sf
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