| Date | May 2010 | Marks available | 3 | Reference code | 10M.1.sl.TZ1.15 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Sketch | Question number | 15 | Adapted from | N/A |
Question
The function \(f(x) = 5 - 3({2^{ - x}})\) is defined for \(x \geqslant 0\).
On the axes below sketch the graph of f (x) and show the behaviour of the curve as x increases.
Write down the coordinates of any intercepts with the axes.
Draw the line y = 5 on your sketch.
Write down the number of solutions to the equation f (x) = 5 .
Markscheme
(A1)(A1)(A1)
Notes: Award (A1) for labels and scale on y-axis.
Award (A1) for smooth increasing curve in the given domain.
Award (A1) for asymptote implied (\({\text{gradient}} \to {\text{0}}\)).
[3 marks]
(0, 2) accept x = 0, y = 2 (A1) (C4)
Note: If incorrect domain used and both (0, 2) and (\( - \)0.737, 0) seen award (A1)(ft).
[1 mark]
line passing through (0, 5), parallel to x axis and not intersecting their graph. (A1) (C1)
[1 mark]
zero (A1) (C1)
[1 mark]
Examiners report
Most candidates attempted this question and many gained 3 or 4 marks. All made an attempt at sketching the graph which demanded that students used their GDC. Many candidates failed to label their graphs and to give an indication of scale, and lost one mark in part (a). Some did not pay attention to the domain and sketched the graph in a different region. A significant number could also write down the coordinates of the y-intercept, although some wrote only y = 2 instead of giving the two coordinates. Almost all could draw the line y = 5 on the sketch but many could not find the answer for the number of solutions to the equation given in part c). Some candidates lost time in an attempt to draw this graph accurately on graph paper, which was not the intended task. Most candidates attempted this question, which clearly indicated that the time given for the paper was sufficient.
Most candidates attempted this question and many gained 3 or 4 marks. All made an attemptat sketching the graph which demanded that students used their GDC. Many candidates failed to label their graphs and to give an indication of scale, and lost one mark in part (a). Some did not pay attention to the domain and sketched the graph in a different region. A significant number could also write down the coordinates of the y-intercept, although some wrote onlyy = 2 instead of giving the two coordinates. Almost all could draw the line y = 5 on thesketch but many could not find the answer for the number of solutions to the equation given in part c). Some candidates lost time in an attempt to draw this graph accurately on graphpaper, which was not the intended task. Most candidates attempted this question, which clearly indicated that the time given for the paper was sufficient.
Most candidates attempted this question and many gained 3 or 4 marks. All made an attemptat sketching the graph which demanded that students used their GDC. Many candidates failed to label their graphs and to give an indication of scale, and lost one mark in part (a). Some did not pay attention to the domain and sketched the graph in a different region. A significant number could also write down the coordinates of the y-intercept, although some wrote onlyy = 2 instead of giving the two coordinates. Almost all could draw the line y = 5 on thesketch but many could not find the answer for the number of solutions to the equation given in part c). Some candidates lost time in an attempt to draw this graph accurately on graphpaper, which was not the intended task. Most candidates attempted this question, which clearly indicated that the time given for the paper was sufficient.
Most candidates attempted this question and many gained 3 or 4 marks. All made an attemptat sketching the graph which demanded that students used their GDC. Many candidates failed to label their graphs and to give an indication of scale, and lost one mark in part (a). Some did not pay attention to the domain and sketched the graph in a different region. A significant number could also write down the coordinates of the y-intercept, although some wrote onlyy = 2 instead of giving the two coordinates. Almost all could draw the line y = 5 on thesketch but many could not find the answer for the number of solutions to the equation given in part c). Some candidates lost time in an attempt to draw this graph accurately on graphpaper, which was not the intended task. Most candidates attempted this question, which clearly indicated that the time given for the paper was sufficient.
