| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2008 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Fixed Point Iteration |
| Type | Find coordinate from gradient condition |
| Difficulty | Standard +0.3 This question involves standard differentiation using the chain rule, followed by routine iterative formula application with clearly specified steps. While it requires multiple techniques (differentiation, rearrangement, iteration), each step is straightforward and follows a predictable pattern typical of C3 coursework. The iteration converges easily and no novel problem-solving insight is needed. |
| Spec | 1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates1.09c Simple iterative methods: x_{n+1} = g(x_n), cobweb and staircase diagrams |
4 The gradient of the curve $y = \left( 2 x ^ { 2 } + 9 \right) ^ { \frac { 5 } { 2 } }$ at the point $P$ is 100 .\\
(i) Show that the $x$-coordinate of $P$ satisfies the equation $x = 10 \left( 2 x ^ { 2 } + 9 \right) ^ { - \frac { 3 } { 2 } }$.\\
(ii) Show by calculation that the $x$-coordinate of $P$ lies between 0.3 and 0.4 .\\
(iii) Use an iterative formula, based on the equation in part (i), to find the $x$-coordinate of $P$ correct to 4 decimal places. You should show the result of each iteration.
\hfill \mbox{\textit{OCR C3 2008 Q4 [9]}}