1MA0 Higher June 2013 Paper 2 Q10
10 The equation \[x^3 + 2x = 110\] has a solution between 4 and 5
Use a trial and improvement method to find this solution.
Give your answer correct to one decimal place.
You must show ALL your working. (4)
| Answer | Mark | Notes |
|---|---|---|
| 4.7 | 4 | B2 for a trial \(4.6 \leqslant x \leqslant 4.7\) evaluated correctly (B1 for a trial evaluated correctly for \(4 \leqslant x \leqslant 5\)) B1 for a different trial evaluated correctly for \(4.65 \leqslant x \lt 4.7\) B1 (dep on at least one previous B1) for 4.7 [Note: Trials should be evaluated to at least accuracy shown in table, truncated or rounded] No working scores 0 marks |
Working
| \(x\) | \(x^3 + 2x\) |
|---|---|
| 4 | 72 |
| 4.1 | 77.(121) |
| 4.2 | 82.(488) |
| 4.3 | 88.(107) |
| 4.4 | 93.(984) |
| 4.5 | 100.(125) |
| 4.6 | 106.(536) |
| 4.7 | 113.(223) |
| 4.8 | 120.(192) |
| 4.9 | 127.(449) |
| 5 | 135 |
| 4.65 | 109.8(44625) |
| 4.66 | 110.5(14696) |
| 4.67 | 111.1(87563) |
| 4.68 | 111.8(63232) |
| 4.69 | 112.5(41709) |