O-LevelAdditional MathematicsDifferentiation and integration4037/21 · May/June 2013 · Q36 Marks
Variables x and y are related by the equation y = 10 − 4sin² x, where 0 ≤ x ≤ π/2. Given that x is increasing at a rate of 0.2 radians per second, find the corresponding rate of change of y when y = 8.
- (a)Variables x and y are related by the equation y = 10 − 4sin² x, where 0 ≤ x ≤ π/2. Given that x is increasing at a rate of 0.2 radians per second, find the corresponding rate of change of y when y = 8.[6]
Mark scheme
Marking points from the official mark scheme (May/June 2013). The mark or mark type is shown in brackets.
- [1] dy/dx = ksinx cos x
- [1] k = -8
- [1] Attempt to find x when y = 8
- [1] x = π/4 (0.785)
- [1] Uses dy/dt = dy/dx * dx/dt
- [1] -0.8 (not rounded)
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