| Date | May 2010 | Marks available | 8 | Reference code | 10M.1.hl.TZ1.5 |
| Level | HL only | Paper | 1 | Time zone | TZ1 |
| Command term | Find, Show, and Sketch | Question number | 5 | Adapted from | N/A |
Question
The graph of \(y = \frac{{a + x}}{{b + cx}}\) is drawn below.
(a) Find the value of a, the value of b and the value of c.
(b) Using the values of a, b and c found in part (a), sketch the graph of \(y = \left| {\frac{{b + cx}}{{a + x}}} \right|\) on the axes below, showing clearly all intercepts and asymptotes.
Markscheme
(a) an attempt to use either asymptotes or intercepts (M1)
\(a = - 2,{\text{ }}b = 1,{\text{ }}c = \frac{1}{2}\) A1A1A1
(b) 
A4
Note: Award A1 for both asymptotes,
A1 for both intercepts,
A1, A1 for the shape of each branch, ignoring shape at \((x = - 2)\).
[8 marks]
Examiners report
It was pleasing to see a lot of good work with part (a), though some candidates lost marks due to problems with the algebra which led to one or more incorrect values. Regarding part (b), most candidates did not succeed in finding the new intercepts and asymptotes and were unable to apply the absolute value function. A significant number of candidates misread part (b) and took it as the modulus of the graph in part (a).
