| Date | November 2014 | Marks available | 4 | Reference code | 14N.1.sl.TZ0.5 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 5 | Adapted from | N/A |
Question
Let \(f(x) = p + \frac{9}{{x - q}}\), for \(x \ne q\). The line \(x = 3\) is a vertical asymptote to the graph of \(f\).
Write down the value of \(q\).
The graph of \(f\) has a \(y\)-intercept at \((0,{\text{ }}4)\).
Find the value of \(p\).
The graph of \(f\) has a \(y\)-intercept at \((0,{\text{ }}4)\).
Write down the equation of the horizontal asymptote of the graph of \(f\).
Markscheme
\(q = 3\) A1 N1
[1 mark]
correct expression for \(f(0)\) (A1)
eg\(\;\;\;p + \frac{9}{{0 - 3}},{\text{ }}4 = p + \frac{9}{{ - q}}\)
recognizing that \(f(0) = 4\;\;\;\)(may be seen in equation) (M1)
correct working (A1)
eg\(\;\;\;4 = p - 3\)
\(p = 7\) A1 N3
[3 marks]
\(y = 7\;\;\;\)(must be an equation, do not accept \(p = 7\) A1 N1
[1 mark]
Total [6 marks]
Examiners report
Parts (a) and (b) were generally well done. Some candidates incorrectly answered \(q = - 3\), rather than \(q = 3\), in part (a), but then were able to earn follow-through marks in part (b).
Parts (a) and (b) were generally well done. Some candidates incorrectly answered \(q = - 3\), rather than \(q = 3\), in part (a), but then were able to earn follow-through marks in part (b).
Many candidates did not recognize the connection between parts (b) and (c) of this question, and many did a good deal of unnecessary work in part (c) before giving the correct answer. In part (c), many candidates did not write the equation of the asymptote, but just wrote the number.
