| Exam Board | OCR MEI |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2008 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Parametric differentiation |
| Type | Find gradient at given parameter |
| Difficulty | Moderate -0.8 This is a straightforward application of the parametric differentiation formula dy/dx = (dy/du)/(dx/du), followed by finding the parameter value at a given point and substituting. Both parts require only routine calculus techniques with no problem-solving insight needed, making it easier than average. |
| Spec | 1.03g Parametric equations: of curves and conversion to cartesian1.07s Parametric and implicit differentiation |
| Answer | Marks | Guidance |
|---|---|---|
| In the top row there are 9 ways of allocating a symbol to the left cell, then 8 for the next, 7 for the next and so on down to 1 for the right cell, giving \(9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 9!\) ways. | M1, E1 | So there must be \(9! \times\) the number of ways of completing the rest of the puzzle. |
In the top row there are 9 ways of allocating a symbol to the left cell, then 8 for the next, 7 for the next and so on down to 1 for the right cell, giving $9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 9!$ ways. | M1, E1 | So there must be $9! \times$ the number of ways of completing the rest of the puzzle.5 A curve has parametric equations $x = 1 + u ^ { 2 } , y = 2 u ^ { 3 }$.\\
(i) Find $\frac { \mathrm { d } y } { \mathrm {~d} x }$ in terms of $u$.\\
(ii) Hence find the gradient of the curve at the point with coordinates $( 5,16 )$.
\hfill \mbox{\textit{OCR MEI C4 2008 Q5 [5]}}