| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2007 |
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| Session | November |
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| Topic | Parametric equations |
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1 A curve is defined parametrically by
$$x = a t ^ { 2 } , \quad y = a t$$
where \(a\) is a positive constant. The part of the curve joining the point where \(t = 0\) to the point where \(t = \sqrt { } 2\) is rotated through one complete revolution about the \(x\)-axis. Show that the area of the surface obtained is \(\frac { 13 } { 3 } \pi a ^ { 2 }\).