The graph of $y = \ln (x)$ is transformed into the graph of $y = \ln \left( {2x + 1} \right)$ .

Describe two transformations that are required to do this.

Solve $\ln \left( {2x + 1} \right) > 3\cos (x)$, $x \in [0,10]$.

EITHER

translation of $- \frac{1}{2}$ parallel to the $x$-axis

stretch of a scale factor of $\frac{1}{2}$ parallel to the $x$-axis     A1A1

OR

stretch of a scale factor of $\frac{1}{2}$ parallel to the $x$-axis

translation of $- 1$ parallel to the $x$-axis     A1A1

Note: Accept clear alternative terminologies for either transformation.

[2 marks]

EITHER

$1.16 < x < 5.71 \cup 6.75 < x \leqslant 10$     A1A1A1A1

OR

]$1.16$, $5.71$[  $\cup$  ]$6.75$, $10$]     A1A1A1A1

Note: Award A1 for 1 intersection value, A1 for the other 2, A1A1 for the intervals.

[6 marks]

This question was well done by many candidates. It would appear, however, that few candidates were aware of the standard terminology – Stretch and Translation - used to describe the relevant graph transformations. Most made good use of a GDC to find the critical points and to help in deciding on the correct intervals. A significant minority failed to note $x = 10$ as an endpoint.

This question was well done by many candidates. It would appear, however, that few candidates were aware of the standard terminology – Stretch and Translation - used to describe the relevant graph transformations. Most made good use of a GDC to find the critical points and to help in deciding on the correct intervals. A significant minority failed to note $x = 10$ as an endpoint.