1MA0 Higher June 2017 Paper 2 Q13
13 The equation \[x^3 + x = 21\] has a solution between 2 and 3
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)
| Working | Answer | Mark | Notes |
|---|---|---|---|
| \(x = 2\) gives 10 \(x = 3\) gives 30 \(x = 2.1\) gives 11.(361) \(x = 2.2\) gives 12.(848) \(x = 2.3\) gives 14.(467) \(x = 2.4\) gives 16.(224) \(x = 2.5\) gives 18.(125) \(x = 2.6\) gives 20.(176) \(x = 2.7\) gives 22.(383) \(x = 2.8\) gives 24.(752) \(x = 2.9\) gives 27.(289) \(x = 2.61\) gives 20.3(89..) \(x = 2.62\) gives 20.6(04..) \(x = 2.63\) gives 20.8(21..) \(x = 2.64\) gives 21(.039..) \(x = 2.65\) gives 21.2(59..) | 2.6 | 4 | B2 for a trial \(2.6 \leqslant x \leqslant 2.7\) evaluated (B1 for a trial \(2 \leqslant x \leqslant 3\) evaluated) B1 for a different trial \(2.6 \lt x \leqslant 2.65\) evaluated B1 (dep on at least one previous B1) for 2.6 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. NB: no working scores no marks even if the answer is correct. |