| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2015 |
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| Session | June |
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| Topic | Parametric equations |
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9 The curve \(C\) has parametric equations
$$x = 4 t + 2 t ^ { \frac { 3 } { 2 } } , \quad y = 4 t - 2 t ^ { \frac { 3 } { 2 } } , \quad \text { for } 0 \leqslant t \leqslant 4$$
Find the arc length of \(C\), giving your answer correct to 3 significant figures.
Find the mean value of \(y\) with respect to \(x\) over the interval \(0 \leqslant x \leqslant 32\).