1MA0 Higher November 2014 Paper 2 Q10
10 The equation
\[x^3 - 2x = 125\]has a solution between 5 and 6
Use a trial and improvement method to find this solution.
Give your answer correct to 1 decimal place.
You must show all your working. (4)
| Answer | Mark | Notes |
|---|---|---|
| 5.1 | 4 | B2 for a trial \(5.1 \leqslant x \leqslant 5.2\) evaluated (B1 for a trial \(5 \leqslant x \leqslant 6\) evaluated) B1 for a different trial \(5.1 \lt x \leqslant 5.15\) evaluated B1 (dep on at least one previous B1) for 5.1 Accept trials correct to the nearest whole number (rounded or truncated) if the value of \(x\) is to 1 dp but correct to 1dp (rounded or truncated) if the value of \(x\) is to 2 dp. (Accept 124 for \(x = 5.12\)) NB : no working scores no marks even if the answer is correct. |
Working
| \(x\) | \(x^3 - 2x\) |
|---|---|
| 5 | 115 |
| 6 | 204 |
| 5.1 | 122.(451) |
| 5.2 | 130.(208) |
| 5.3 | 138.(277) |
| 5.4 | 146.(664) |
| 5.5 | 155.(375) |
| 5.6 | 164.(416) |
| 5.7 | 173.(793) |
| 5.8 | 183.(512) |
| 5.9 | 193.(579) |
| 5.11 | 123.2(12..) |
| 5.12 | 123.9(77..) |
| 5.13 | 124.7(45..) |
| 5.14 | 125.5(16..) |
| 5.15 | 126.2(90..) |