1MA0 Higher June 2012 Paper 2 Q11
11 The equation
\[x^3 - 6x = 72\]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)
| Working | Answer | Mark | Notes |
|---|---|---|---|
| \(x = 4\) gives 40 \(x = 5\) gives 95 \(x = 4.1\) gives 44.(321) \(x = 4.2\) gives 48.(888) \(x = 4.3\) gives 53.(707) \(x = 4.4\) gives 58.(784) \(x = 4.5\) gives 64.(125) \(x = 4.6\) gives 69.(736) \(x = 4.7\) gives 75.(623) \(x = 4.8\) gives 81.(792) \(x = 4.9\) gives 88.(249) \(x = 4.61\) gives 70.3(12..) \(x = 4.62\) gives 70.8(91..) \(x = 4.63\) gives 71.4(72..) \(x = 4.64\) gives 72.0(57..) \(x = 4.65\) gives 72.6(44..) | 4.6 | 4 | B2 for a trial \(4.6 \leqslant x \leqslant 4.7\) evaluated (B1 for a trial \(4 \leqslant x \leqslant 5\) evaluated) B1 for a different trial \(4.6 \lt x \leqslant 4.65\) evaluated B1 (dep on at least one previous B1) for 4.6 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. (Accept 72 for \(x = 4.64\)) NB : no working scores no marks even if the answer is correct. |