| Date | May 2009 | Marks available | 5 | Reference code | 09M.2.sl.TZ2.6 |
| Level | SL only | Paper | 2 | Time zone | TZ2 |
| Command term | Find | Question number | 6 | Adapted from | N/A |
Question
Consider the curve \(y = \ln (3x - 1)\) . Let P be the point on the curve where \(x = 2\) .
Write down the gradient of the curve at P.
The normal to the curve at P cuts the x-axis at R. Find the coordinates of R.
Markscheme
gradient is \(0.6\) A2 N2
[2 marks]
at R, \(y = 0\) (seen anywhere) A1
at \(x = 2\) , \(y = \ln 5\) \(( = 1.609 \ldots )\) (A1)
gradient of normal \( = - 1.6666 \ldots \) (A1)
evidence of finding correct equation of normal A1
e.g. \(y = \ln 5 = - \frac{5}{3}(x - 2)\) , \(y = - 1.67x + c\)
\(x = 2.97\) (accept 2.96) A1
coordinates of R are (2.97,0) N3
[5 marks]
Examiners report
Although the command term "write down" was used in part (a), many candidates still opted for an analytic method for finding the derivative value. Although this value was often incorrect, many candidates knew how to find the equation of the normal and earned follow through marks in part (b).
Although the command term "write down" was used in part (a), many candidates still opted for an analytic method for finding the derivative value. Although this value was often incorrect, many candidates knew how to find the equation of the normal and earned follow through marks in part (b).
