| Date | November 2011 | Marks available | 2 | Reference code | 11N.1.sl.TZ0.15 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 15 | Adapted from | N/A |
Question
The function \(g(x)\) is defined as \(g(x) = 16 + k({c^{ - x}})\) where \(c > 0\) .
The graph of the function \(g\) is drawn below on the domain \(x \geqslant 0\) .
The graph of \(g\) intersects the y-axis at (0, 80) .
Find the value of \(k\) .
The graph passes through the point (2, 48) .
Find the value of \(c\) .
The graph passes through the point (2, 48) .
Write down the equation of the horizontal asymptote to the graph of \(y = g(x)\) .
Markscheme
\(80 = 16 + k({c^0})\) (M1)
\(k = 64\) (A1) (C2)
[2 marks]
\(48 = 16 + 64({c^{ - 2}})\) (M1)
Note: Award (M1) for substitution of their \(k\) and (2, 48) into the equation for \(g(x)\).
\(c = \sqrt 2 \) (\(1.41\)) (\(1.41421 \ldots \)) (A1)(ft) (C2)
Notes: Award (M1)(A1)(ft) for \(c = \pm \sqrt 2 \) . Follow through from their answer to part (a).
[2 marks]
\(y = 16\) (A1)(A1) (C2)
Note: Award (A1) for \(y = \) a constant, (A1) for \(16\).
[2 marks]
Examiners report
This was perhaps the most difficult question on the paper. Being the last question some candidates may have felt that they were under pressure to complete and many scripts showed no attempt at an answer to this question. The response by the upper quartile of candidates was quite encouraging with many achieving at least 4 of the 6 marks available. For the rest, many fell at the first hurdle and were unable to obtain a value of \(k\). This, in turn, led to problems in finding \(c\). For a large number of candidates the only mark that they achieved was identifying that the asymptote was a linear equation in \(y\).
This was perhaps the most difficult question on the paper. Being the last question some candidates may have felt that they were under pressure to complete and many scripts showed no attempt at an answer to this question. The response by the upper quartile of candidates was quite encouraging with many achieving at least 4 of the 6 marks available. For the rest, many fell at the first hurdle and were unable to obtain a value of \(k\). This, in turn, led to problems in finding \(c\). For a large number of candidates the only mark that they achieved was identifying that the asymptote was a linear equation in \(y\).
This was perhaps the most difficult question on the paper. Being the last question some candidates may have felt that they were under pressure to complete and many scripts showed no attempt at an answer to this question. The response by the upper quartile of candidates was quite encouraging with many achieving at least 4 of the 6 marks available. For the rest, many fell at the first hurdle and were unable to obtain a value of \(k\). This, in turn, led to problems in finding \(c\). For a large number of candidates the only mark that they achieved was identifying that the asymptote was a linear equation in \(y\).
