| Date | May 2018 | Marks available | 2 | Reference code | 18M.1.sl.TZ1.15 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Find | Question number | 15 | Adapted from | N/A |
Question
Consider the functions \(f\left( x \right) = {x^4} - 2\) and \(g\left( x \right) = {x^3} - 4{x^2} + 2x + 6\)
The functions intersect at points P and Q. Part of the graph of \(y = f\left( x \right)\) and part of the graph of \(y = g\left( x \right)\) are shown on the diagram.
Find the range of f.
Write down the x-coordinate of P and the x-coordinate of Q.
Write down the values of x for which \(f\left( x \right) > g\left( x \right)\).
Markscheme
\(\left[ { - 2,\,\,\infty } \right[{\text{ or }}\left[ { - 2,\,\,\infty } \right)\) OR \(f\left( x \right) \geqslant - 2{\text{ or }}y \geqslant - 2\) OR \( - 2 \leqslant f\left( x \right) < \infty \) (A1)(A1) (C2)
Note: Award (A1) for −2 and (A1) for completely correct mathematical notation, including weak inequalities. Accept \(f \geqslant - 2\).
[2 marks]
–1 and 1.52 (1.51839…) (A1)(A1) (C2)
Note: Award (A1) for −1 and (A1) for 1.52 (1.51839).
[2 marks]
\(x < - 1,\,\,\,x > 1.52\) OR \(\left( { - \infty ,\,\, - 1} \right) \cup \left( {1.52,\,\,\infty } \right)\). (A1)(ft)(A1)(ft) (C2)
Note: Award (A1)(ft) for both critical values in inequality or range statements such as \(x < - 1,\,\,\left( { - \infty ,\,\, - 1} \right),\,\,x > 1.52\,{\text{ or }}\left( {1.52,\,\,\infty } \right)\).
Award the second (A1)(ft) for correct strict inequality statements used with their critical values. If an incorrect use of strict and weak inequalities has already been penalized in (a), condone weak inequalities for this second mark and award (A1)(ft).
[2 marks]
