| Date | May 2012 | Marks available | 4 | Reference code | 12M.1.sl.TZ2.12 |
| Level | SL only | Paper | 1 | Time zone | TZ2 |
| Command term | Find | Question number | 12 | Adapted from | N/A |
Question
The diagram shows part of the graph of \(y = 2^{-x} + 3 \), and its horizontal asymptote. The graph passes through the points (0, a) and (b, 3.5).
Find the value of
(i) a ;
(ii) b .
Write down the equation of the horizontal asymptote to this graph.
Markscheme
(i) 20 + 3 (M1)
Note: Award (M1) for correct substitution.
= 4 (A1) (C2)
(ii) 3.5 = 2−b + 3 (M1)
Note: Award (M1) for correct substitution.
b = 1 (A1) (C2)
[4 marks]
y = 3 (A1)(A1) (C2)
Notes: y = constant (other than 3) award (A1)(A0).
[2 marks]
Examiners report
Most candidates answered parts (a) i and ii correctly, however a large number of candidates could not find the correct equation for part (b).
Most candidates answered parts (a) i and ii correctly, however a large number of candidates could not find the correct equation for part (b).
