O-LevelAdditional MathematicsDifferentiation and integration4037/21 · May/June 2025 · Q54 Marks
Given that y = x² tan(x/2), use calculus to find the approximate change in y as x increases from π/3 to π/3 + h, where h is small.
- Given that y = x² tan(x/2), use calculus to find the approximate change in y as x increases from π/3 to π/3 + h, where h is small.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.
- [B2] B1 for d/dx (tan(x/2)) = 1/2 sec²(x/2) soi
- [M1] FT for a product rule of correct structure with their d/dx (tan(x/2))
- [M1] Correct small changes relationship δy/h = their dy/dx |_(x=π/3)
- [A1] Dependent on B2 1.94h
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